The Pioneer Anomaly. Claus Lämmerzahl

Transcription

1 The Pioneer Anomaly or Do We Really Understand the Physics Within the Solar System? Claus Lämmerzahl Center for Applied Space Technology and Microgravity (ZARM) University Bremen thanks to J. Anderson, H. Dittus, E. Hackmann, V. Kagramanova, J. Kunz, T. Morley, O. Preuss, P. Richter, S. Solanki, S. Turyshev and the Pioneer Exploration Collaboration Utrecht, C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

2 Bremen campus Campus of University of Bremen C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

3 Bremen Drop Tower of ZARM Tower 146 m drop tube 110 m free fall time = 4.7 s deceleration 30 g C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

4 Bremen Drop Tower of ZARM C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

5 First BEC in microgravity / extended free fall C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

6 First BEC in microgravity / extended free fall BEC in free fall may become colder that today s 500 fk (Ketterle) today s free expansion / free fall time > 1 s aim 1 fk C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

7 First BEC in microgravity / extended free fall C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

8 Outline 1 The situation of standard physics The status Problems? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

9 Outline 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

10 Outline 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

11 Outline 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

12 Outline 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

13 Outline 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

14 Outline The situation of standard physics 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

15 Outline The situation of standard physics The status 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

16 The present situation The situation of standard physics The status All predictions of General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

17 The present situation The situation of standard physics The status All predictions of General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance Implication Gravity is a metrical theory C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

18 The present situation The situation of standard physics The status All predictions of General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance Implication Gravity is a metrical theory Predictions for metrical theories Solar system effects Perihelion shift Gravitational redshift Deflection of light Gravitational time delay Lense Thirring effect Schiff effect Strong gravitational fields Binary systems Black holes Gravitational waves C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

19 The present situation The situation of standard physics The status All predictions of General Relativity are experimentally well tested and confirmed Foundations The Einstein Equivalence Principle Universality of Free Fall Universality of Gravitational Redshift Local Lorentz Invariance Implication Gravity is a metrical theory Predictions for metrical theories Solar system effects Perihelion shift Gravitational redshift Deflection of light Gravitational time delay Lense Thirring effect Schiff effect Strong gravitational fields Binary systems Black holes Gravitational waves General Relativity C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

20 Outline The situation of standard physics Problems? 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

21 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

22 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

23 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

24 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

25 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after flybys C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

26 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after flybys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

27 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after flybys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy Quadrupole and octupole anomaly (Tegmark et al 2004, Schwarz et al 2005) Quadrupole and octupole of CMB are correlated with Solar system ecliptic C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

28 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after flybys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy Quadrupole and octupole anomaly (Tegmark et al 2004, Schwarz et al 2005) Quadrupole and octupole of CMB are correlated with Solar system ecliptic Is the gravitational physics in the Solar system really well understood? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

29 The situation of standard physics Problems? But: Dark clouds over General Relativity? Unexplained observations Dark Matter (Zwicky 1933) Needed to describe galactic rotation curves, lensing, structure formation Dark Energy (Turner 1999) Needed to describe the accelerated expansion of our universe Pioneer Anomaly (Anderson et al, PRL 1998, PRD 2002) Non Newtonian acceleration of Pioneer spacecraft toward the Sun Flyby anomaly (ESA and NASA communications) Satellite velocities are too large by a few mm/s after flybys Increase of Astronomical Unit (Krasinski & Brumberg 2005, Pitjeva in Standish 2005) Distance Earth Sun increases by 10 m/cy Quadrupole and octupole anomaly (Tegmark et al 2004, Schwarz et al 2005) Quadrupole and octupole of CMB are correlated with Solar system ecliptic Is the gravitational physics in the Solar system really well understood? Gravity at large distances? Weak gravity? Small accelerations? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

30 Outline Anomalies related to the Solar system 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

31 Outline Anomalies related to the Solar system Ranging and tracking 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

32 Ranging Anomalies related to the Solar system Ranging and tracking Time and distance Constancy of speed of light c distance time x = ct t = x c Distance of satellite electromagnetic (radio) signal from Earth to satellite measured distance: t 2 t 1 r = c 2 (t 2 t 0 ) needs only good clock on Earth t 0 Earth satellite C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

33 Anomalies related to the Solar system Ranging and tracking Doppler tracking: The principal method of observation Two way Doppler tracking Sender at rest, moving receiver received frequency ν = 1 ( 1 v ) ν 1 v2 /c 2 c sender receiver ν ν v C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

34 Anomalies related to the Solar system Ranging and tracking Doppler tracking: The principal method of observation Two way Doppler tracking Sender at rest, moving receiver received frequency ν = 1 ( 1 v ) ν 1 v2 /c 2 c frequency sent back ν = 1 ( 1 v ) ν 1 v2 /c 2 c sender receiver ν ν v ν ν C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

35 Anomalies related to the Solar system Ranging and tracking Doppler tracking: The principal method of observation Two way Doppler tracking Sender at rest, moving receiver received frequency ν = 1 ( 1 v ) ν 1 v2 /c 2 c frequency sent back ν = 1 ( 1 v ) ν 1 v2 /c 2 c sender receiver ν ν v ν ν can extract velocity ν ν ν = 2 v/c 1 + v/c 2v c C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

36 Outline Anomalies related to the Solar system The anomalies 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

37 Anomalies related to the Solar system The Pioneer anomaly The anomalies Observation Anomalous acceleration of Pioneer 10 and 11 spacecraft of a Pioneer = (8.74 ± 1.33) m/s 2 toward the Sun (Anderson et al, PRL 1998, PRD 2002) Acceleration is constant starting with last flyby Remark / Question Systematic effect? Influence from cosmic expansion? New physics? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

38 The flyby anomaly Anomalies related to the Solar system The anomalies Observation After satellite flybys at Earth the velocity is too large by a few mm/s (Antreasian & Guinn 1998, Anderson & Williams 2001, Morley 2005, CL et al 2007) GEGA1: Two way S band Doppler residuals & range residuals NEGA: Two way X band Doppler residuals & range residuals A stone thrown up with v comes back with v + v C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

39 The flyby anomaly Anomalies related to the Solar system The anomalies Observations Earth flybys Mission agency year pericentre v [km/s] e v [mm/s] Galileo NASA Dec km ± 0.08 Galileo NASA Dec km a NEAR NASA Jan km ± 0.13 Cassini NASA Aug km Stardust NASA Jan km???? b Rosetta ESA Mar km ± 0.05 Hayabusa Japan May km???? c MESSENGER d private Aug km a no reliable data: too low orbit with too large atmospheric drag b no reliable data: thruster activities c no data available d US spacecraft operated by a private company KinetX Anomaly seems to exist also for flybys at other planets. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

40 The flyby anomaly Anomalies related to the Solar system The anomalies v [mm/s] NEAR Galileo Rosetta Messenger Cassini v as function of e. Earth flybys in barycentric coordinates (Campbell 2006) e C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

41 The flyby anomaly Anomalies related to the Solar system The anomalies v [mm/s] NEAR Galileo Rosetta Messenger Cassini v as function of e. Earth flybys in barycentric coordinates (Campbell 2006) Remarks / Questions Violation of energy conservation? More systematic study needed: Dependence on height, velocity, inclination, excentricity,...? Effect on escape orbits only e C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

42 The flyby anomaly Anomalies related to the Solar system The anomalies First analysis Velocity increase is related to an anomalous acceleration of a flyby ms 2, a flyby a Newton 10 5 First error analysis Atmospheric drag Errors in Earth gravity model Ocean tides Earth solid tides Charging of spacecraft Magnetic moment of spacecraft Further non gravitational forces (trapped air, ion plasma drag,...) Nothing could explain the flyby anomaly C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

43 The flyby anomaly Anomalies related to the Solar system The anomalies Attempts at explanation by new physics (not published) Non conservative potential energy Non Newtonian gravity (e.g. Moffat, PPN, Yukawa,...) Torsion (eps2 model); fit the data, but not compatible with stability of planetary orbits Nothing could explain the flyby anomaly Tasks Better observation of future flybys Flybys at other planets (Mars,...) Theory (dynamics of extended objects: gravity induced rotations) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

44 Anomalies related to the Solar system Increase of Astronomical Unit The anomalies Observation Various groups reported Krasinsky & Brumberg 2005: 15 ± 4 m/cy Pitjeva in Standish 2005: 7 ± 1 m/cy Remarks / Question Ġ excluded by LLR Mass loss of Sun leads only to 1 m/cy Influence of cosmic expansion by many orders of magnitude too small Increase of Solar wind plasma on long timescales? Drift of clocks t t αt2 with α s 1?... C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

45 Anomalies related to the Solar system The anomalies Quadrupole / Octopole anomaly Observation Oliveira-Costa et al, PRD 2004, Schwarz et al, PRL 2005 Anomalous behavior of low l contributions of CMB: Quadrupole and octopole are aligned to > 99.87% C.L. Quadrupole and octopole aligned to ecliptic to > 99% C.L. No correlation with the galactic plane Remarks / Question Influence of Solar system on CMB observations? Systematics? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

46 Status of Anomalies Anomalies related to the Solar system The anomalies The status of these anomalies Anomaly Observational status Interpretation Dark Energy, Dark Matter well established under discussion Flyby anomaly, Pioneer Anomaly quite well established unclear quadrupole anom., increase of AU unclear unclear It is worth to discuss these anomalies Try to find conventional explanations Try to find relations between anomalies (anomalies very probably are no isolated phenomena). Do some effects have the same cause? Influence of cosmic expansion or dark matter? (a Pioneer ch a MOND ) Are there similar influences in other gravitating systems, e.g., binary systems, stars moving around the black hole in the center of our galaxy,...? Something wrong with weak gravity? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

47 Status of Anomalies Anomalies related to the Solar system The anomalies The status of these anomalies Anomaly Observational status Interpretation Dark Energy, Dark Matter well established under discussion Flyby anomaly, Pioneer Anomaly quite well established unclear quadrupole anom., increase of AU unclear unclear It is worth to discuss these anomalies Try to find conventional explanations Try to find relations between anomalies (anomalies very probably are no isolated phenomena). Do some effects have the same cause? Influence of cosmic expansion or dark matter? (a Pioneer ch a MOND ) Are there similar influences in other gravitating systems, e.g., binary systems, stars moving around the black hole in the center of our galaxy,...? Something wrong with weak gravity? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

48 Status of Anomalies Anomalies related to the Solar system The anomalies The status of these anomalies Anomaly Observational status Interpretation Dark Energy, Dark Matter well established under discussion Flyby anomaly, Pioneer Anomaly quite well established unclear quadrupole anom., increase of AU unclear unclear It is worth to discuss these anomalies Try to find conventional explanations Try to find relations between anomalies (anomalies very probably are no isolated phenomena). Do some effects have the same cause? Influence of cosmic expansion or dark matter? (a Pioneer ch a MOND ) Are there similar influences in other gravitating systems, e.g., binary systems, stars moving around the black hole in the center of our galaxy,...? Something wrong with weak gravity? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

49 Status of Anomalies Anomalies related to the Solar system The anomalies The status of these anomalies Anomaly Observational status Interpretation Dark Energy, Dark Matter well established under discussion Flyby anomaly, Pioneer Anomaly quite well established unclear quadrupole anom., increase of AU unclear unclear It is worth to discuss these anomalies Try to find conventional explanations Try to find relations between anomalies (anomalies very probably are no isolated phenomena). Do some effects have the same cause? Influence of cosmic expansion or dark matter? (a Pioneer ch a MOND ) Are there similar influences in other gravitating systems, e.g., binary systems, stars moving around the black hole in the center of our galaxy,...? Something wrong with weak gravity? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

50 Outline The Pioneer anomaly 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

51 Outline The Pioneer anomaly The mission 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

52 The Pioneer spacecraft The Pioneer anomaly The mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

53 The orbits The Pioneer anomaly The mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

54 The environment The Pioneer anomaly The mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

55 The result The Pioneer anomaly The mission Result from Doppler tracking of the Pioneers with v observed v modeled = a Pioneer t v observed from Doppler tracking v modeled from calculations due to gravitational forces (and others) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

56 The result The Pioneer anomaly The mission The acceleration seems to appear just with the last flyby, that is, after entering an escape orbit. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

57 The result The Pioneer anomaly The mission The acceleration seems to appear just with the last flyby, that is, after entering an escape orbit. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

58 The basic observation The Pioneer anomaly The mission The observation (Anderson et al 1998, 2002) Status Measured anomalous, uniformly blue shifted Doppler frequency drift dν dt = (5.99 ± 0.01) 10 9 Hz/s Can be interpreted as a constant acceleration a Pioneer = (8.74 ± 1.33) m/s 2 Acceleration constant and toward the Sun Temporal and spatial variations less than 3% No cause for the effect has been found All errors are much smaller than the effect a Pioneer /a Newton 10 5 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

59 Outline The Pioneer anomaly Modeling and errors 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

60 The Pioneer anomaly Orbit determination: Modeling Modeling and errors Model of gravitational forces Model of external non gravitational forces Model of internal non gravitational forces Model of observation stations Model of signal propagation Codes = Orbit and velocity determination Model of gravitational forces Relativistic equations of motion for celestial bodies including order v 4 /c 4 Relativistic gravitational accelerations (EIH model) include: Sun, Moon, 9 planets are point masses in isotropic, PPN, N body metric Newtonian gravity from large asteroids Terrestrial and lunar figure effects Earth tides Lunar physical librations C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

61 The Pioneer anomaly Orbit determination: Modeling Modeling and errors Model of external non gravitational forces Solar radiation and Solar wind pressure Drag from interplanetary dust Model of internal non gravitational forces Thermal radiation Attitude control propulsive maneuvers and propellant (gas) leakage from propulsion system Torques produced from above forces Modeling of signal propagation Relativistic model for light propagation including order v 2 /c 2 Dispersion C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

62 The Pioneer anomaly Orbit determination: Modeling Modeling and errors Model of observation stations Orbit determination includes Codes Precession, nutation, sidereal rotation, polar motion, tidal effects, and tectonic plates drift Informations on tidal deceleration, non uniformity of rotation, Love numbers, and Chandler wobble from LLR, SLR, and VLBI (from ICRF) DSN antennae contributions to the spacecraft radio tracking data Use of four independent codes JPL Orbit Determination Program (various generations from ) The Aerospace Corporation code POEAS (during period ) Goddard Space Flight Center conducted a study in 2003 (data from NSSDC) Code of University of Oslo Next discussion: Errors C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

63 The Pioneer anomaly Orbit determination: Modeling Modeling and errors Model of observation stations Orbit determination includes Codes Precession, nutation, sidereal rotation, polar motion, tidal effects, and tectonic plates drift Informations on tidal deceleration, non uniformity of rotation, Love numbers, and Chandler wobble from LLR, SLR, and VLBI (from ICRF) DSN antennae contributions to the spacecraft radio tracking data Use of four independent codes JPL Orbit Determination Program (various generations from ) The Aerospace Corporation code POEAS (during period ) Goddard Space Flight Center conducted a study in 2003 (data from NSSDC) Code of University of Oslo Next discussion: Errors possible conventional explanations C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

64 On board error The Pioneer anomaly Modeling and errors Heat Heat is an important source of error, but It is not strong enough (from geometry) to explain the anomaly Exponential decay of heat (and related errors) not seen C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

65 Drag through dust? The Pioneer anomaly Modeling and errors Interplanetary medium Interplanetary dust Hot wind plasma (mainly protons and electrons) distributed within the Kuiper belt (from 30 AU to 100 AU) Modelled density ρ IPD g/cm 3 (Man and Kimura 2000) Interstellar dust Fractions of total dust (characterized by greater impact velocity) Measured by Ulysses ρ ISD g/cm 3 Effect on Pioneers (Nieto et al, MPJ 2005) Drag on spacecraft a s = K s ρv 2 s A s /m s Only dust of a density of ρ (ρ IPD + ρ ISD ) can lead to a Pioneer acceleration Dust cannot be the origin of the Pioneer acceleration C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

66 The Pioneer anomaly Errors by external effects Modeling and errors Further external effects Gravity from the Galaxy Gravity from dark matter distributed in the halo around the Solar system Errors in the planetary ephemerides, Earth orientation parameters, precession, and nutation Rejected as explanation C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

67 Signal errors The Pioneer anomaly Modeling and errors The transponders The transponders cannot show any drift because they transform the incoming frequency through multiplication with a simple ratio 240/221. ν sent = 240 ν received 221 This is implemented into the hardware and can not drift. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

68 Signal errors The Pioneer anomaly Modeling and errors The transponders The transponders cannot show any drift because they transform the incoming frequency through multiplication with a simple ratio 240/221. ν sent = 240 ν received 221 This is implemented into the hardware and can not drift. Influence of medium on signals Influence gives redshifted modification. Anomalous acceleration corresponds to blueshift. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

69 The Pioneer anomaly Error budget: external effects Modeling and errors Sources of external systematic error Error budget constituents Bias Uncertainty m/s m/s 2 Solar radiation pressure ± From the mass uncertainty ± 0.01 Solar wind contribution ± < 10 5 Effects of the solar corona ± 0.02 Electro-magnetic Lorentz forces ± < 10 4 Influence of the Kuiper belt s gravity ± 0.03 Influence of the Earth orientation ± DSN Antannae: mechanical/phase stability ± < Phase stability and clocks ± < DSN station location ± < 10 5 Effects of troposphere and ionosphere ± < C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

70 The Pioneer anomaly Error budget: simulation Modeling and errors Computational systematics Error budget constituents Bias Uncertainty m/s m/s 2 Numerical stability of least-squares estimation ± 0.02 Accuracy of consistency/model tests ± 0.13 Mismodeling of maneuvers ± 0.01 Mismodeling of the solar corona ± 0.02 Annual/diurnal terms ± 0.32 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

71 The Pioneer anomaly Error budget: on board effects Modeling and errors Sources of internal systematic error Error budget constituents Bias Uncertainty m/s m/s 2 Radio beam reaction force ± 0.11 Thermal/propulsion effects from RTGs: RTG heat reflected off the craft 0.55 ± 0.55 Differential emissivity of the RTGs ± 0.85 Non-isotropic radiative cooling of s/c ± 0.16 Expelled He produced within the RTGs ± 0.16 Propulsive mass expulsion: gas leakage ± 0.56 Variation between s/c determinations ± 0.17 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

72 Conclusion The Pioneer anomaly Modeling and errors Observation All data analyses show that there is an anomalous acceleration a Pioneer = (8.74 ± 1.33) m/s 2 of the Pioneer 10 and 11 spacecrafts. General theoretical description C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

73 Conclusion The Pioneer anomaly Modeling and errors Observation All data analyses show that there is an anomalous acceleration a Pioneer = (8.74 ± 1.33) m/s 2 of the Pioneer 10 and 11 spacecrafts. No cause for the effect has been found All errors are much smaller than the effect General theoretical description C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

74 Conclusion The Pioneer anomaly Modeling and errors Observation All data analyses show that there is an anomalous acceleration a Pioneer = (8.74 ± 1.33) m/s 2 of the Pioneer 10 and 11 spacecrafts. No cause for the effect has been found All errors are much smaller than the effect Question What is the origin of the acceleration? General theoretical description C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

75 Outline Attempts at explanation 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

76 Attempts at explanation Helicity rotation coupling Anderson & Mashhoon, PLA 2003 ω and k are frequency and wave vector measured by inertial observer frequency measured by moving v and rotating Ω observer helicity operator for the photon Ĥ = ± 1 ω k ω = 1 ) ( ( (ω Ĥ Ω v k 1 = ω v Ω ) ) k 1 v 2 1 v 2 ω Simulates v v = v c ω Ω Effect on Pioneer too small C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

77 Attempts at explanation Masses in the Kuiper belt Nieto, PRD 2005 Newton potential µ(x ) U(r) = G x x d3 V 10 8 m/s 2 AU dashed line 3D ring with 1/r density for 1 m C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

78 Attempts at explanation Observation station errors Drift of clocks Quadratic drift of clocks on Earth may simulate the effect (Anderson et al, PRD 2002, Ranada, FP 2005) t t a Pt 2, a P s 1 Consistency with other satellites? Consistency with observation of pulsars and binary systems (define also clocks)? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

79 Attempts at explanation Attempted explanations Attempted explanations within standard physics An intriguing observation: a Pioneer c H a MOND Influence of cosmology? Influence of dark matter? Explanations using non standard physics Running coupling constant (Jaekel and Reynaud, CQG 2004) Antisymmetric Gravity (Moffat 2004) Braneworld scenarios (Bertolami, CQG 2003) Projective geometry (Schmutzer, GRG 2000)... C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

80 Outline Cosmology and local physics 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

81 Outline Cosmology and local physics Physics in the expanding universe 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

82 The Questions Cosmology and local physics Physics in the expanding universe Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics CL, Preuss & Dittus 2007 Sun C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

83 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe Conserved quantities Light Hubble red shift ν u (t)r(t) = const. ν u (t) = R(t 0) R(t) ν u(t 0 ) (1 H(t t 0 )) ν u (t 0 ) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

84 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe Conserved quantities Light Hubble red shift Massive particles R 2 (t) dr(s) ds ν u (t)r(t) = const. ν u (t) = R(t 0) R(t) ν u(t 0 ) (1 H(t t 0 )) ν u (t 0 ) 1 = const. R(t) V (t) = const. 1 V 2 (t) For small velocities R(t)V (t) = const. slowing down of velocity V (t 2 ) = R(t 1) R(t 2 ) V (t 1) = (1 H(t 2 t 1 ))V (t 1 ) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

85 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe D = const. r = const. particle light ray Kinematics: Distance and velocity Distance D measured by time of flight of light rays D = R(r 2 r 1 ) Change of measured distance (r 1 = const.) r 0 t = const. d dt D = Ṙ(r 2 r 1 ) + Rṙ 2 = HD + V 2 Trajectory at constant distance to observer has local velocity 0 = Ḋ = HD + V 2 V 2 = HD. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

86 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe Distance and velocity of moving objects: Application to moving spacecrafts Observer and observed spacecraft Pioneer spacecrafts move on geodesics: slowing down of the spacecraft Cosmic red shift of frequency Velocity of points of constant distance with respect to the cosmic substrate final Doppler effect ν 2 (t 2 ) = ( 1 H(t 2 t 1 ) V tot 2 ) ν0 (t 1 ). Here V tot 2 is the total velocity of the spacecraft with respect to cosmic substrate V tot 2 = H(t 2 t 1 ) V (t 1 )H(t 2 t 1 ) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

87 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe Result ν 2 (t 2 ) = (1 + V (t 1 )H(t 2 t 1 )) ν 0 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

88 Cosmology and local physics Physics in the expanding universe Cosmology: Doppler ranging in the expanding universe Result ν 2 (t 2 ) = (1 + V (t 1 )H(t 2 t 1 )) ν 0 Discussion Cosmological red shift and Doppler effect from the velocity with respect to coordinates given by constant distances cancel Object at constant distance cannot make a Doppler effect Only the satellite s slowing down is left over Results in chirp of Doppler signal related to an acceleration a = HV = V c ch Acceleration is V/c smaller than observed Pioneer acceleration a Pioneer ch. Therefore, Doppler tracking in an expanding universe cannot account for the observed Pioneer Anomaly (agrees with Carrera & Giulini 2007) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

89 The Questions Cosmology and local physics Physics in the expanding universe Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics Planet C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

90 Cosmology and local physics Physics in the expanding universe Cosmology and Solar system physics Small isolated mass in expanding universe Ansatz Weak field ansatz Linearized Einstein equations for h µν Solution h 00 = 2GM R g µν = b µν + h µν, h µν b µν. b ρσ D ρ D σ hµν + 2b ρσ R κ µρν h κσ = 16πGT µν, ( cos 6 Ṙ r) = 2GM ( 1 3H 2 (Rr) 2 ±... ) r Rr Lowest order: standard Newtonian potential with measured distance R(t)r Additional acceleration toward the gravitating body, second order in H Potential practically does not participate in the cosmic expansion C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

91 The Questions Cosmology and local physics Physics in the expanding universe Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics Escape C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

92 Cosmology and local physics Physics in the expanding universe Cosmology: Modification of planetary orbits General question Behavior of bound systems in expanding universe Electromagnetically bound systems (Audretsch & Schäfer 1975, Bonnor 2000) Gravitationally bound systems Adiabatic invariants Action S = mc U(x) (t)ẋ2 c 2 R 2 c 2 dt ( mc 2 + mu(r) + m 2 R2 (t) ( ṙ 2 + r 2 ϕ 2)) dt For weak time dependence of R(t): two adiabatic invariants I ϕ = L, I r = L + GmM m R 2 E. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

93 Cosmology and local physics Physics in the expanding universe Cosmology: Modification of planetary orbits Adiabatic invariants Result: E = m3 G 2 M 2 2(I r + I ϕ ), p = I2 ϕ m 2 MR, ( ) 2 Iϕ e2 = 1 I r + I ϕ E, e, and R(t)p are nearly constant, Rp and e of the planetary orbits practically do not participate in cosmic expansion Stability of adiabatic invariants estimated by exp( τ/t), τ = characteristic time of change of external parameter (here: τ = 1/H), T = characteristic time of the periodic motion (here: T = period of planets) exp( τ/t) e 1010 : any change of the adiabatic invariants is truly negligible Analysis applies to periodic orbits = bound orbits Secular increase of AU cannot be explained by that C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

94 The Questions Cosmology and local physics Physics in the expanding universe Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics Lambda C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

95 Cosmology and local physics Physics in the expanding universe Cosmology: Modified PPN formalism Escape orbits PPN inspired space time metric g 00 = 1 + 2α U U2 2β c2 c 4, g ij = (1 + 2γ Uc 2 ) R 2 (t)δ ij. Equation of motion in terms of measured distances and times: ( d 2 X i dt 2 = U X i α + γ 1 ( ) 2 dx c 2 + ( 2α 2 γα 2β ) ) U dt c 2 ( ) (α + γ) 1 U dx j c 2 X j dt + Ṙ R dx i dt Cosmological expansion results in a decelerating drag term which is a factor v/c too small to account for the Pioneer effect Bound orbits behave differently than escape orbits C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

96 The Questions Cosmology and local physics Physics in the expanding universe Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

97 Outline Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

98 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Schwarzschild (anti-)de Sitter space time Post Newtonian approximation: Kagramanova, Kunz & CL, PLB 2006 Kerr, Hauck and Mashhoon, CQG 2003 Sereno & Jetzer, PRD 2006 Analytic treatment: Hackmann & CL, PRL 2008 The metric The metric ds 2 = αdt 2 α 1 dr 2 r 2 ( dθ 2 + sin 2 θdφ 2), with α = 1 2M r 1 3 Λr2 and Λ is the cosmological constant and M the mass of the source. Λ < 0 attraction, Λ > 0 repulsion C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

99 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Schwarzschild (anti-)de Sitter first order effects Results Observed effect Estimate on Λ gravitational redshift Λ m 2 perihelion shift Λ m 2 light deflection no effect gravitational time delay Λ m 2 geodetic precession Λ m 2 Pioneer anomaly Λ = m 2 Table: Estimates on Λ from Solar system observations. Cosmological constant has no influence on Solar system effects If some other Λ is assumed to account for the Pioneer anomaly, then it conflicts with Perihelion shift A constant Λ cannot be responsible for Pioneer anomaly May not describe critical orbits (near separatrix) needs exact calculations C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

100 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Geodesic eqn in Schwarzschild (anti-)de Sitter space time Geodesic equation 0 = d2 x µ ds 2 + { ρσ µ } dxρ dx σ ds ds, g(u,u) = ǫ conservation of energy E and angular momentum L effective equations ( ) 2 dr = r4 dϕ L 2 ( dr ds ( dr dt ( ( E 2 1 r S ) 2 = E 2 ( 1 r S ) 2 = 1 ( E 2 1 r S r 1 3 Λr2 Enhancement of influence of Λ near critical orbits... r 1 )) )(ǫ 3 Λr2 + L2 r 2 r 1 ) ) (ǫ 3 Λr2 + L2 r 2 = E 2 V eff (r) ) 2 ( ( E 2 1 r S r 1 )) )(ǫ 3 Λr2 + L2 r 2 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

101 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild angular momentum L 2 2m 2 r 2 r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

102 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild de Sitter angular momentum L 2 2m 2 r 2 r effective potential Newton potential m r cosmological constant > 0 relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

103 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild angular momentum L 2 2m 2 r 2 bound orbit r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

104 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild de Sitter angular momentum L 2 2m 2 r 2 escape orbit r effective potential Newton potential m r cosmological constant > 0 relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

105 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild angular momentum L 2 2m 2 r 2 r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

106 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild anti-de Sitter angular momentum L 2 2m 2 r 2 cosmological constant < 0 r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

107 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild angular momentum L 2 2m 2 r 2 escape orbit r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

108 Cosmology and local physics Geodesic equation: effective potential Physics in the Schwarzschild (anti-)de Sitter space time V eff Schwarzschild anti-de Sitter angular momentum L 2 2m 2 r 2 bound orbit cosmological constant < 0 r effective potential Newton potential m r relativistic gravity L2 m r 3 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

109 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Geodesic eqn in Schwarzschild (anti-)de Sitter space time Effective equation of motion (u = r S /r) ( u du ) 2 = u 5 u 4 + ǫλu 3 + (λ(µ ǫ) + 13 ) dϕ ρ u 2 + ǫ 3 λρ =: P 5(u) with ( rs ) 2 λ =, µ = E 2, ρ = ΛrS 2 L Polynomial of 5th order beyond elliptic integral: hyperelliptic integral P 5 possesses at most 4 real positive zeros ǫ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Λ has no influence on light propagation) Λ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Hagihara, JJAG 1931) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

110 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Geodesic eqn in Schwarzschild (anti-)de Sitter space time Effective equation of motion (u = r S /r) ( u du ) 2 = u 5 u 4 + ǫλu 3 + (λ(µ ǫ) + 13 ) dϕ ρ u 2 + ǫ 3 λρ =: P 5(u) with ( rs ) 2 λ =, µ = E 2, ρ = ΛrS 2 L Polynomial of 5th order beyond elliptic integral: hyperelliptic integral P 5 possesses at most 4 real positive zeros ǫ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Λ has no influence on light propagation) Λ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Hagihara, JJAG 1931) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

111 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Geodesic eqn in Schwarzschild (anti-)de Sitter space time Effective equation of motion (u = r S /r) ( u du ) 2 = u 5 u 4 + ǫλu 3 + (λ(µ ǫ) + 13 ) dϕ ρ u 2 + ǫ 3 λρ =: P 5(u) with ( rs ) 2 λ =, µ = E 2, ρ = ΛrS 2 L Polynomial of 5th order beyond elliptic integral: hyperelliptic integral P 5 possesses at most 4 real positive zeros ǫ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Λ has no influence on light propagation) Λ = 0 P 5 (u) = u 2 P 3 (u) elliptic function (Hagihara, JJAG 1931) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

112 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Orbits in Schwarzschild (anti-)de Sitter space time P 5 P 5 P 5 u u u (a) No real positive zero P 5 (b) One real positive zero P 5 (c) Two real positive zeros u u (d) Three real positive zeros (e) Four real positive zeros Five possibilities of having real positive zeros of P 5 (u) Zeros correspond to the zeros of V eff = E Bound non terminating, quasi periodic orbits exist (planetary orbits) only for three or more positive zeros C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

113 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Orbits in Schwarzschild (anti-)de Sitter space time (f) Λ = 10 5 km 2 (g) Λ = km 2 (h) Λ = km 2 (i) Λ = 0 (j) Λ = km 2 (k) Λ = km 2 (l) Λ = 10 5 km 2 violet = 4, blue = 3, green = 2, gray = 1, black = 0 zeros of P 5. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

114 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Orbits in Schwarzschild (anti-)de Sitter space time (m) Λ = km 2 (n) Λ = 0 (o) Λ = km 2 color # zeros > 0 types of orbits black 0 particle from infinity to singularity gray 1 bound terminating orbits green 2 bound terminating and escape orbits blue 3 bound terminating and quasi periodic bound orbits violet 4 bound terminating, escape and quasi periodic bound orbits C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

115 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Separation of variables ϕ ϕ 0 = u u du u 0 P5 (u ) Looked for: u = u(ϕ) inversion problem Not well defined in complex plane Uniqueness of integration: u is function with 4 periods z 0 Iz C 1 x C 2 C 2 e 3 e 2 e 1 Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

116 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

117 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

118 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

119 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

120 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

121 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Iz Iz Rz Rz Iz Iz Iz Rz Rz Rz Iz Iz Iz Rz Rz Rz C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

122 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Copy 1 of C Iz b 1 b 2 Copy 2 of C Iz e 1 e 2 e 3 e 4 e 5 e 6 a 1 a 2 Rz e 1 e 2 e 3 e 4 e 5 e 6 b 1 b 2 Rz b 1 a 1 a 2 b 2 P 5 X = pretzel C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

123 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Holomorphic and associated meromorphic differentials dz 1 := dx P5 (x), dz 2 := xdx P5 (x) dr 1 := 3x3 2x 2 + λx 4 dx, dr 2 := x2 dx P 5 (x) 4 P 5 (x) Period matrices (2ω,2ω ) and (2η,2η ) 2ω ij := dz i, 2ω ij := dz i a j b j 2η ij := dr i, 2η ij := dr i a j b j Normalized differentials and their period matrix d z d v = (2ω) 1 d z, (2ω,2ω ) (1 2,τ) with τ = ω 1 ω C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

124 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Preliminaries definitions Theta function ϑ : C 2 (for construction of functions with 4 periods) ϑ( z;τ) := t (τ m+2 z) m Z 2 e iπ m Periodicity: ϑ( z n; τ) = ϑ( z; τ) Quasi periodicity: ϑ( z + τ n; τ) = e iπ nt (τ n+2 z) ϑ( z; τ) Theta function with characteristics g, h 1 2 Z2 ϑ[ g, h]( z;τ) := e iπ gt (τ g+2 z+2 h) ϑ( z + τ g + h;τ) Sigma function σ( z) = Ce 1 2 zt ηω 1 z ϑ Generalized Weierstrass functions [( 1/2 1/2 ), ( 0 1/2) ] ((2ω) 1 z;τ) ij ( z) = log σ( z) = iσ( z) j σ( z) σ( z) i j σ( z) z i z j σ 2 ( z) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

125 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Only formalism where 1/ P 5 appears: Jacobi s inversion problem Determine u for given ϕ from ϕ = A u0 ( u) (Abel map), i.e. ϕ 1 = ϕ 2 = u1 u 0 u1 u 0 du u2 P5 (u) + du P5 (u) u 0 udu P5 (u) + u2 u 0 udu P5 (u) Solution of inversion problem Solution u of inversion problem given by u 1 + u 2 = 4 22 ( ϕ) u 1 u 2 = 4 12 ( ϕ) Our problem: two positions u, two angles ϕ requires reduction C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

126 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Only formalism where 1/ P 5 appears: Jacobi s inversion problem Determine u for given ϕ from ϕ = A u0 ( u) (Abel map), i.e. ϕ 1 = ϕ 2 = u1 u 0 u1 u 0 du u2 P5 (u) + du P5 (u) u 0 udu P5 (u) + u2 u 0 udu P5 (u) Solution of inversion problem Solution u of inversion problem given by u 1 + u 2 = 4 22 ( ϕ) u 1 u 2 = 4 12 ( ϕ) Our problem: two positions u, two angles ϕ requires reduction C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

127 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Rewrite inversion problem as (based on Enolskii, Pronine & Richter, JNS 2005) φ = A ( u) with φ = ϕ u 0 d z Extraction of one component of u (namely u 2 in Jacobi inv. prob.) through a limit with u 1 u 2 u 1 = lim = σ( φ ) 1 2 σ( φ ) 1 σ( φ ) 2 σ( φ ) u 2 u 1 + u 2 ( 2 σ) 2 ( φ ) σ( φ ) 2 2 σ( φ ) φ = lim u 2 ( ) φ = A u1 ( u ), u = One u but still two ϕ: Lemma (Mumford 1983 Riemann vanishing theorem): (2ω) 1 A ( u ) Theta divisor Θ K = { z ϑ( z + K ) = 0} with the vector of Riemann constants K ) = τ + ( ) 0 1/2 ( 1/2 1/2 σ( φ ) = 0, gives a relation between φ,1 and φ,2. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

128 Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Analytic solution of geodesic eqn in S(a)dS space time Define ( ) x ϕ Θ := ϕ ϕ 0 and choose x so that (2ω) 1 ϕ Θ Θ K. with ϕ 0 = ϕ 0 + dz 2 u 0 Complete analytic solution of equation of motion in Schwarzschild de Sitter space time u(ϕ) = u 1 = 1σ( ϕ Θ ) 2 σ( ϕ Θ ) r(ϕ) = r S u(ϕ) = r 2 σ( ϕ Θ ) S 1 σ( ϕ Θ ) where (2ω) 1 ϕ Θ Θ K New result, Hackmann & CL, PRL 2008 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

129 Orbits Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time V eff r (p) Λ = 0, r 0 = 5.010km (q) Λ = 0, r 0 = km (r) effective potential (s) Λ = 10 5 km 2, r 0 = 5.013km (t) Λ = 10 5 km 2, r 0 = km (u) Λ = 10 5 km 2, r 0 = km C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

130 Orbits Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time V eff r (v) Λ = 0, r 0 = 3.625km (w) effective potential (x) Λ = 10 5 km 2, r 0 = 3.625km (y) Λ = 10 5 km 2, r 0 = km C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

131 Orbits Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time (z) Λ = 0, r 0 = 6.776km () Λ = 0, r 0 = 4.642km () Λ = 10 5 km 2, r 0 = km () Λ = 10 5 km 2, r 0 = 4.639km C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

132 Application to Pioneer Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Influence of Λ on Pioneer satellites (orbital parameters from Nieto & Anderson 2005) Pioneer 10: µ = , λ = Pioneer 11: µ = , λ = For given angle ϕ: r Λ (ϕ) r Λ=0 (ϕ) 10 3 m For given distance r = 65 AU: rϕ Λ (r) rϕ Λ=0 (r) 10 5 m Form of the Pioneer orbits practically does not change. Cosmological constant cannot be origin of Pioneer anomaly. In principle we need also ϕ = ϕ(t) and Doppler tracking. C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

133 Cosmology and local physics Post Schwarzschild of perihelion shift Physics in the Schwarzschild (anti-)de Sitter space time Perihelion shift in Schwarzschild de Sitter (for bound orbit, Kraniotis & Whitehouse 2003) xdx δϕ perihelion = 2π ω 22 = 2π P5 (x) Approximation to first order in Λ x p5 (x) = 1 P3 (x) 2 x 2 + λ 3 m2 x 2 P 3 (x) P 3 (x) Λ + O(Λ2 ) with P 3 (x) = x 3 x 2 + λx + λ(µ 1) Schwarzschild polynomial This has to be integrated: gymnastics in elliptic integration C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

134 Cosmology and local physics Post Schwarzschild of perihelion shift Physics in the Schwarzschild (anti-)de Sitter space time structure of result xdx = P5 (x) a 2 x P3 (x) 2 3 m2 a 2 1 = ω 1 + Λ m2 96 ( 3 +λ +O(Λ 2 ) j=1 a 2 η 1 + ω 1 z j ( (ρ j )) 2 ( 2η1 1 6 ω 1 16( (u 0 )) x 2 + λ x 2 P 3 (x) P 3 (x) Λ + O(Λ2 ) ( ) λ 1 + ( ) 4zj ) ) (u 0 ) ( (u 0 )) 5 (ζ(u 0) η 1 u 0 ) Needs introduction of r min and r max or a and e for interpretation Needs relativistic approximation for interpretation C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

135 Further applications Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Formalism can be further applied to Geodesic equation in Plebanski Demianski space times Geodesic equation in Schwarzschild space times in 5, 6, 7, 9, and 11 dimensions Geodesic equation in Schwarzschild de Sitter space-times in 5, 6, 7, 9, 11 dimensions Geodesic equation in Reissner-Nordström space-times in 5 and 7 dimensions Geodesic equation in Reissner-Nordström de Sitter space-times in 5 and 7 dimensions crystal with anharmonic potential of 6th order (Hackmann, Kagramanova, Kunz & C.L. in preparation) No scheme known for polynomials of order 7 or higher C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

136 The Questions Cosmology and local physics Physics in the Schwarzschild (anti-)de Sitter space time Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

137 Outline Cosmology and local physics Gravity on large scales 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

138 Gravity on large scales Cosmology and local physics Gravity on large scales Models Yukawa (rotation curves of galaxies, Sanders, AA 1986) U(r) = U Newton (r) (1 + αe r/λ) Running coupling constant model (Jaekel & Reynaud, CQG 2004) U(r) = U Newton (r) + ar Parameter a fixed by Pioneer effect Pioneer effect should be v 2 Compatible with all other Solar system effects (Standish 2008) Higher dim. braneworld models (Dvali, Gabadadze & Porrati, PLA 2002) U(r) = U Newton (r) ± 2 U Newton (r 0 ) r, r 0 5 Gpc r 0 Perihelion shift: 5 µas/y Secular increase of AU: increase of 5 m/cy C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

139 Cosmology and local physics Gravity on large scales Yukawa modification: A viable model? The ansatz The ansatz V (r) = G m r (1 + αe r/λ) Ansatz can explain many galactic rotation curves (Sanders, AA 1984) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

140 Cosmology and local physics Gravity on large scales Yukawa modification: A viable model? Acceleration Taylor V (r) = (1 + α) G M r acceleration a(r) = V αg M λ M r M r + αg 2λ λ αg 2 6λ λ ±... 2 r 2 + αgm 2λ 2 αgm r 3λ 2 r = (1 + α) GM λ ±... Identification G 0 := (1 + α) G = observed gravitational constant for r 0 acceleration a(r) = G 0 M r 2 + α 1 + α G M 0 2λ 2 α 1 + α G M r 0 3λ 2 λ ±... C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

141 Cosmology and local physics Gravity on large scales Yukawa modification: A viable model? Compatibility Identification a Pioneer = α 1 + α G M 2λ 2 a Pioneer 0 2λ 2 α = G 0 M 2λ 2 a Pioneer λ GM /(2a Pioneer ) λ m log λ > 16 with log α 0 is compatible with existing data C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

142 Cosmology and local physics Gravity on large scales Yukawa modification: A viable model? Compatibility M acceleration a(r) = G 0 r + a 2 Pioneer 2 3 a Pioneer r λ ±... Next order term smaller by 2 r 3 λ 0.06 might account for the small decrease of the observed acceleration Result: rather strong α 1 Yukawa coupling with very long range; yields an acceleration plateau in some range between 1 and 100 AU. V and a for parameters compatible with Pioner acceleration. red = standard Newtonian case. black = parameters (λ, α + 1) = (10 15, ), (10 16, ), (10 17, ), (10 18, ), (10 19, ), (10 20, ) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

143 Cosmology and local physics Gravity on large scales Yukawa modification: A viable model? Compatibility with rotation curve fit Pioneer: log λ > 16, α Galactic rotation curve: log λ > 16, α Local strength: Modification by Yukawa in Yukawa C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

144 The Questions Cosmology and local physics Gravity on large scales Questions Does the coupling of the expansion to light lead to an effect? Does the cosmological expansion influence the physics in the Solar system? Does the gravitational field of the Sun feel the expansion? Do planetary orbits (bound orbits) feel the expansion? Do escape orbits behave differently than bound orbits? Does a cosmological constant influence the physics in the Solar system? Additional Yukawa coupling? MOdified Newtonian Dynamics C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

145 Outline Cosmology and local physics MOND 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

146 Cosmology and local physics MOND MOdified Newtonian Dynamics MOND ansatz Modification of Newton s second law = modification of relation between applied force and resulting acceleration (Milgrom ApJ 1983,...) mẍ = F mẍµ( ẍ /a 0 ) = F with function µ(x) = { 1 for ẍ a 0 x for ẍ a 0 For Newtonian gravity Newtonian force F = m U large accelerations / large forces ẍ = U small accelerations / small forces ẍ ẍ = a 0 U ẍ = a 0 U MOND = modified inertia C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

147 Cosmology and local physics Implications of MOND MOND Galactic rotation curves circular orbit, small distance, large accelerations: a centrifugal = v2 r = GM r 2 v = GMr 1/2 circular orbit, large distance, small accelerations: a centrifugal = v2 r = a0 GM a 0 U = v 4 = GMa 0 r reproduces many galactic rotation curves for a m/s 2 may also reproduce dynamics of galactic clusters Pioneer anomaly In strong Newtonian regime a 0 U parametrization µ(x) = 1 ξx 1 additional acceleration a = GM r 2 + ξa 0 MOND reproduces Pioneer anomaly C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

148 Testing MOND Cosmology and local physics MOND Torsion balance (Gundlach et al, PRL 2007) transscribes acceleration into torque (for hollow cylinder with radius R): τ = I R aµ(a/a 0) takes r θ = a as acceleration no deviation from Newton s second law down to a m/s 2 Earlier experiment by Abramovici and Vager, PRD 1986 (to a 10 9 m/s 2 ) These are no tests of MOND: is it not allowed to separate components Free fall experiment (Ignatiev, PRL 2007) Free fall with respect to galaxy: MOND situation possible on Earth once a year for 0.1 s within 1 l volume General question Gravity is what we explore by the free motion of particles and light rays General test of Newton s second law... 0 = f(x,ẋ,ẍ,... x,...,x (n) ) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

149 Outline Summary and outlook 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

150 Outline Summary and outlook Summary 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

151 Summary Summary and outlook Summary Summary: Observation The Pioneer acceleration, a constant acceleration a Pioneer = (8.74 ± 1.33) m/s 2 of the spacecrafts toward the sun seems to be a real physical effect No conventional explanation has been found Largest scaled experiment mankind ever carried out Potential indication for new physics? C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

152 Summary and outlook Summary and outlook Summary Summary: theory Pioneer scenario treated with Effects on radio signal Effects on gravitational field of Sun Effects on particle trajectory Despite a Pioneer ch a MOND, Pioneer anomaly cannot be explained by Cosmic expansion Cosmological constant Outlook: Future work More on conventional physics... New physics Dilaton scenarios Dark energy / Quintessence Dark matter Higher dimensional braneworld models Baseline: PA probably related to some other unexplained effect C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

153 Outline Summary and outlook Further studies 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

154 Summary and outlook Summary and outlook Further studies Outlook: Future work on data analysis Data recovering almost completed: Doppler and telemetry data New analysis of complete data set previously used data set time span AU distance Pioneer Pioneer data set to be analyzed time span AU distance Pioneer Pioneer With different codes Independent modeling Direction of acceleration (toward Sun, Earth, along spin axis, along velocity) C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

155 Summary and outlook Summary and outlook Further studies Available data Parameters Subsystem Telemetry words TEMPERATURES RTG fin root temps Thermal C 201, C 202, C 203, C 204 RTG hot junction temps Thermal C 220, C 219, C 218, C 217 TWT temperatures Communications C 205, C 206, C 207, C 228, C 223, C 221 Receiver temperatures Communications C 222, C 227 Platform temperatures Thermal C 301, C 302, C 304, C 318, C 319, C 320 PSA temperatures Thermal C 225, C 226 Thruster cluster temps Propulsion C 309, C 326, C 310, C 311, C 312, C 328, C 325 SRA/SSA temperatures ACS C 303, C 317 Battery temperature Power C 115 Propellant temperature Propulsion C 327 N2 tank temperature Propulsion C 130 Science instr temps Science E 101, E 102, E 109, E 110, E 117, E 118, E 125, E 128, E 201, E 209, E 213, E 221 VOLTAGES Calibration voltages Data handling C 101, C 102, C 103 RTG voltages Power C 110, C 125, C 131, C 113 Battery/Bus voltages Power C 106, C 107, C 117, C 118, C 119 TWT voltages Communications C 224, C 230 Science instr voltages Science E 119, E 129, E 210, E 211, E 217, E 220 CURRENTS RTG currents Power C 127, C 105, C 114, C 123 Battery/Bus currents Power C 109, C 126, C 129 Shunt current Power C 122, C 209 TWT currents Communications C 208, C 211, C 215, C 216 Science instr currents Science E 111, E 112, E 113 PRESSURE Propellant pressure Propulsion C 210 OTHER ANALOG TWT power readings Communications C 231, C 214 Receiver readings Communications C 111, C 212, C 232, C 121, C 229, C 213 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

156 Summary and outlook Summary and outlook Further studies Available data Parameters Subsystem Telemetry words OTHER ANALOG TWT power readings Communications C 231, C 214 Receiver readings Communications C 111, C 212, C 232, C 121, C 229, C 213 BINARY/BIT FIELDS Conscan Communications C 313, C 314, C 315, C 316 Stored commands Electrical C 305, C 306, C 307 Thruster pulse counts Propulsion C 329, C 321, C 322, C 330 Status bits Data handling C 104 Power C 128 Electrical C 120, C 132, C 324, C 332 Communications C 308 Power switches Electrical C 108, C 124 Roll attitude Data handling C 112, C 116 Precession ACS C 403, C 411, C 412, C 415, C 416, C 422, C 423, C 424, C 425, C 428, C 429, C 430 Spin/roll Data handling C 405, C 406, C 407, C 408, C 417 Delta V ACS C 413, C 414, C 426 ACS status Propulsion C 409 ACS C 410, C 427, C 431, C 432 Star sensor ACS C 404, C 419, C 420, C 421 SCIENCE INSTRUMENTS Status/housekeeping Science E 108, E 124, E 130, E 202, E 224, E 131, E 132, E 208 JPL/HVM readings Science E 103, E 104, E 105, E 106, E 107, E 203, E 204, E 205 UC/CPI readings Science E 114, E 115, E 116, E 206, E 212, E 214, E 215, E 216 GE/AMD readings Science E 122, E 123, E 222, E 223 GSFC/CRT readings Science E 126, E 127 LaRC/MD readings Science E 207 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

157 Summary and outlook Outlook: thermal model Further studies B. Rievers et al 2008 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

158 Summary and outlook Outlook: thermal model Further studies B. Rievers et al 2008 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

159 Summary and outlook Outlook: thermal model Further studies B. Rievers et al 2008 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

160 Summary and outlook Outlook: thermal model Further studies B. Rievers et al 2008 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

161 Outlook:thermal model Summary and outlook Further studies Computation of solid angle force F θϕ = force generated by heat radiating surfaces da B. Rievers et al 2008: This model gives 12.5% of the Pioneer anomaly More information about material properties and cross check with housekeeping data and orbital data C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

162 Outline Summary and outlook A new Pioneer Exploration mission 1 The situation of standard physics The status Problems? 2 Anomalies related to the Solar system Ranging and tracking The anomalies 3 The Pioneer anomaly The mission Modeling and errors 4 Attempts at explanation 5 Cosmology and local physics Physics in the expanding universe Physics in the Schwarzschild (anti-)de Sitter space time Gravity on large scales MOND 6 Summary and outlook Summary Further studies A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

163 Outlook: New mission Summary and outlook A new Pioneer Exploration mission C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

164 Outlook: New mission Summary and outlook A new Pioneer Exploration mission Active spacecraft, passive test mass Accurate tracking of test mass 2 step tracking Radio: Earth spacecraft Laser: spacecraft test mass Flexible formation: varying distance Test mass is at environmentally quiet distance from spacecraft 200 m Occasional manoeuvres to maintain formation New Pioneer Explorer should be equipped with stable clock For Pioneer anomaly: Pioneer ν = 1 90 AU ν c 2 a Pioneer dx = Jupiter C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

165 ESA Cosmic Vision Summary and outlook A new Pioneer Exploration mission ESA Cosmic Vision call 4 Pioneer proposals 4 of 13 Fundamental Physics proposals! Class M missions Deep Space Gravity Explorer (DSGE) Bremen ODYSSEY Paris Zacuto Lisboa Class L mission Search for Anomalous Gravitation using Atomic Sensors (SAGAS) Paris Pioneer coordination meeting Paris, April 20 Merger to two missions Class M Mission: ODYSSEY (more conventional, macroscopic test mass) Class L Mission: SAGAS (with atomic interferometry and clocks as gravity sensors) Problem RTGs C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123

166 The end Summary and outlook A new Pioneer Exploration mission Position of Pioneer 10 on distance from Sun AU position, SE lat SE lon (3.0, 77.4 ) speed relative to Sun km/s distance from Earth Gkm Round-trip light time 24h 32min The latest successful precession manoeuvre to point the s/c to Earth was accomplished on 11 Feb 2000 (distance from the Sun of 75 AU) Picture of Pioneer 10 in 80 AU as seen from Arecibo in 2000 C. Lämmerzahl (ZARM, Bremen) The Pioneer Anomaly Utrecht / 123