Direct MOND/TEVES test with LISA Pathfinder Christian Trenkel and Steve Kemble Astrium Ltd, Stevenage, UK Joao Magueijo and Neil Bevis Imperial College, London, UK Fabrizio io demarchi and Giuseppe Congedo University of Trento, Trento, Italy
Overview General Motivation LISA Pathfinder as Gravitational Instrument Direct MOND/TEVES tests with LISA Pathfinder Motivation and Background Gravitational Saddle Points in the Sun-Earth-Moon System LISA Pathfinder Trajectories MOND / TEVES Anomalous Gradients Estimates LISA Pathfinder Gradient Sensitivity Summary and Conclusions 2/33
Motivation LISA Pathfinder is actually becoming reality as we speak planned launch date late 2011 LISA Pathfinder nominally intended as mere technology demonstrator for LISA but can we also do some science with it? LISA Pathfinder total mission cost O(3x10 8 ) there is a moral obligation to exploit it to the maximum Timescale until another LISA Pathfinder comes along O(10-20years) so there is also a strong practical incentive to exploit it 3/33
Motivation The scientific community is therefore strongly encouraged to propose science to be done with LISA Pathfinder contact Science Team with any ideas! One constraint: LISA Pathfinder is being built at the moment, and it has to demonstrate t the technology for LISA Any proposal has to be based on LISA Pathfinder as is, and is also not allowed to interfere with the nominal mission 4/33
LISA Pathfinder as Gravitational Instrument LISA Pathfinder will offer the following (see ESA-SCI(2007)1): Differential Force Measurement Sensitivity: 1.3x10-14 N / Hz around 1mHz Drag-Free Platform Stability: Platform Free-Fall Quality of 10-13 ms -2 / Hz around 1mHz 10-9 ms -2 at DC Gravity Gradiometer Sensitivity: 1.5x10-14 s -2 / Hz around 1mHz Spacecraft Master Clock: (stability TBC) Our proposal exploits this! 5/33
MOND/TEVES Tests with LISA Pathfinder Background (brief): Newtonian dynamics are modified within composite system when system COM acceleration falls below 10-10 ms -2 (Milgrom 1983) Phenomonological formula with no underlying theory Extremely successful in describing galactic rotation curves without Dark Matter Relativistic theory (TEVES) developed with non-relativistic MOND limit (Bekenstein 2004) Prospects for tests within Solar system poor: solar acceleration at 1AU still 6x10-3 ms -2 But: Saddle Points may offer opportunities (Bekenstein and Magueijo 2006) Remains controversial (Saturn rings, Bullett cluster) 6/33
MOND/TEVES Tests with LISA Pathfinder TEVES predicts anomalous gravity gradients near the Saddle Points (Bekenstein and Magueijo 2006) Size and location of bubble in which gradients become significant (unperturbed, considering Sun and Earth only): Need to get within a few 100km of the SP 1532km 766km 259000km 7/33
MOND/TEVES Tests with LISA Pathfinder In order to propose a direct test of MOND / TEVES we need to: Understand d dynamic location of MOND bubbles bbl around SPs in the Sun-Earth-Moon System Establish that LISA Pathfinder can be made to fly through those special regions Estimate the anomalous MOND / TEVES gradients that LISA Pathfinder will experience Confirm that LISA Pathfinder s gradiometer sensitivity is adequate to detect them! 8/33
Gravitational SPs in the Sun Earth Moon System Defined by zero total gravitational field Not to be confused with Lagrangian points L1, L2, etc SPs are not a stable location for spacecraft In the Sun-Earth-Moon system, there are two SPs: Earth Sun Moon 9/33
Gravitational SPs in the Sun Earth Moon System The Sun-Earth SP is perturbed by the motion of the Moon*: 12000km Need to consider Moon position when targeting Sun-Earth SP *also, in much smaller measure, by Jupiter etc 10/33
Gravitational SPs in the Sun Earth Moon System The Earth-Moon SP is hugely perturbed by the Sun (in fact we should call it the Sun-Moon SP ) Sun orbits the Earth- Moon system 11/33
Gravitational SPs in the Sun Earth Moon System Should we target the Sun-Earth or the Earth-Moon SP? Newtonian gradients around Earth-Moon SP around 3 times larger than around Sun-Earth SP if region with certain maximum gravitational ti field is to be targeted, t the Sun-Earth SP offers a larger target to aim for Much less position variability of Sun-Earth SP, from the point of view of mission planning easier to assess feasibility Here we will focus on targeting the Sun-Earth SP 12/33
LISA Pathfinder Trajectories Nominal LPF orbit is Lissajous orbit around L1 Only very weak stability in fact over long time scales orbit propagation is chaotic (deterministic over the time scales of interest here) Even small dv manoeuvres (as possible with FEEP micropropulsion system) allow LPF to reach many different destinations Back-up LPF orbit is Highly Elliptic Orbit (HEO) around Earth Less room for manoeuvre, given limited it micropropulsion i system authority, and Earth-bound orbit Synchronising HEO with lunar motion may still offer some possibilities Here we will focus on the nominal LPF orbit as starting point 13/33
LISA Pathfinder Trajectories Assumptions and approximations entering orbit propagation Single dv manoeuvres up to 1m/s have been considered compatible with residual FEEP control authority following nominal mission (estimated between 6m/s and 15m/s) reasonable timescales for manoeuvres, including single thruster failure (10-30days) maximum individual FEEP thrust 90μN Orbit propagation time limited to 2 years (arbitrary cut-off, but guided by lifetime concerns, eg Inertial Sensor vacuum) Nominal Solar Radiation Pressure on LPF assumed in practice this will be determined in-flight, and trajectory planning adapted accordingly Propagator includes standard gravitational environment 14/33
LISA Pathfinder Trajectories Assumptions and approximations entering orbit propagation For the purposes of the work presented here, control parameters have been restricted to: Time of initial dv manoeuvre (determines departure point) Magnitude of dv manoeuvre For a more exhaustive search, the number of control parameters could be increased: Additional dv manoeuvres In practice, any real trajectory would include continuous navigation and (small) additional trajectory correction manoeuvres Note: aim is not to find the exact trajectory, but to demonstrate that solutions exist, and to assess their general properties! 15/33
Illustration of the chaotic nature of the problem: LISA Pathfinder Trajectories 1.5mio km Earth Sun Single dv manoeuvres between 0.5m/s and 1m/s applied at 0.25 day intervals 16/33
LISA Pathfinder Trajectories Example of fast transfer: Solution missing Sun-Earth SP by 30000km after 340days Earth Sun Sun-Earth SP 17/33
LISA Pathfinder Trajectories Example of small miss distance: Solution missing Sun-Earth SP by 5000km after 480days Earth Sun Sun-Earth SP 18/33
LISA Pathfinder Trajectories SP miss distances from a simple two parameter search dv between 0.5 and 1.0m/s time of manoeuvre (arbitrary reference point) 0.0 5.3 10.6 15.8 21 1.1 26..4 time (days) 7 31.7 36.9 42.2 8 33 39 47.5 0.00 0.06 0.11 0.17 0.22 0.28 0.3 0. 0.44 0.50 0 100000 90000 80000 70000 60000 50000 40000 30000 20000 10000 0 DeltaV (m/s) (km) Miss distance 90000-100000 80000-90000 70000-80000 60000-70000 50000-60000 40000-50000 30000-40000 20000-30000 10000-20000 0-10000 Best solutions found this way achieve miss distances of 2000 3000 km after transfer times between 450 and 500 days 19/33
Summary of Results LISA Pathfinder Trajectories Chaotic nature of the problem makes it difficult to find the best local minimum to search for but there are probably many The main challenge to targeting the SP is to remove the out-of ecliptic component of LISA Pathfinder motion In general, smallest miss distances are found for longer timescales eg 30000km are obtained after 340days, but 2000-3000km require 450-500day 500da transfers and more than one apogee One family of solutions however has been found that bucks this trend 20/33
Trajectories including Lunar fly-bys LISA Pathfinder Trajectories Lunar fly-bys can be specifically targeted to amplify the effect of any active dv manoeuvre This amplification effect applies to both the magnitude and the direction of the dv manoeuvre Out-of ecliptic motion can be killed much sooner 21/33
Trajectory with lowest miss distance found: LISA Pathfinder Trajectories Miss distance 600km Transfer time from nominal orbit departure 410days Lunar flyby (60000km) after 300days 22/33
LISA Pathfinder Trajectories Lunar fly-bys could have additional spin-offs: Fly-by could be used as direct absolute calibration for the gradiometer, by providing the external gravity gradient due to the Moon If we are VERY lucky, we could fly through both the Earth-Moon and the Sun-Earth SPs unfortunately highly unlikely! 23/33
Summary and Conclusions LISA Pathfinder Trajectories It is possible to fly LISA Pathfinder through the region around the Sun-Earth SP following the nominal mission, based on the residual propulsion system (FEEP) control authority The most promising trajectories ie combining low miss distances and acceptable transfer times include a lunar flyby Best result found using a single manoeuvre has 600km miss distance after 410days In practice, the real trajectory will be flown iteratively through continuous navigation and trajectory correction manoeuvres actual miss distances of fthe order of f1020k 10-20km can be achieved Only one SP region crossing event possible any experiment will be a one-off 24/33
MOND/TEVES Anomalous Gradients TEVES gradients have been calculated for the 3 body problem in 3D brief numerical method description: In the non-relativistic limit, TeVeS yields: a = - ( + ) ( is the Newtonian potential and is an additional scalar field) This new scalar field obeys the equation: [ [ (κ /aa 0 ) ] = 4π κ G ρ (note the presence of the non-linear function and the parameters κ and a 0 ) Equation for solved for a cube volume containing the saddle point but large enough that the situation is Newtonian ( = κ ) ) on the boundary Use relaxation algorithm to solve for 25/33
MOND/TEVES Anomalous Gradients Prediction of anomalous gravity gradients that LISA Pathfinder will see: Numerical method yields cube volume with gradients at its grid points (as a function of Sun, Earth and Moon position) Representative LPF trajectory is propagated through the volume and the anomalous gradients are extracted at each point: Sun Sun-Earth SP 45 45 Typical LPF Trajectory Earth 26/33
MOND/TEVES Anomalous Gradients Prediction of anomalous gravity gradients that LISA Pathfinder will see Only gradients in the sensitive direction of the LPF gradiometer are relevant In principle, there is a choice of orientation for LPF around the Earth - Sun axis (no significant difference in gradients): Test Mass Earth Sun Earth Test Mass Sun Test Mass or Test Mass Solar Array Finally, the spacecraft speed (typically y around 1.5km/s) is used to predict the temporal gradient variations 27/33
MOND/TEVES Anomalous Gradients Results Presented for new Moon case no significant difference found for other Moon positions (except SP shift as shown before) robust signal prediction Anomalous TEVES gradients as a function of miss distance: 0km 50km 100km 400km 28/33
MOND/TEVES Anomalous Gradients Results Of course LPF will see the (much larger) Newtonian background gradient as well. For the 50km miss distance, it will see: Newtonian only Newtonian + TEVES Note: TEVES signal roughly at 1/1000s = 1mHz 29/33
LISA Pathfinder Gradient Sensitivity Results How will LPF noise affect this signal? Time series with simulated LPF gradiometer noise (between 50μHz and 50mHz) added: d 10 point moving average LPF Noise + Newtonian LPF Noise + Newtonian + TEVES 30/33
LISA Pathfinder Gradient Sensitivity Results It is useful to compare the relative spectral densities: Power in Signal / Power in Noise 20 around 1mHz! Newtonian TEVES LPF Gradiometer Noise [TBC] LISA Pathfinder has more than adequate sensitivity! 31/33
Summary and Conclusions If LISA Pathfinder goes ahead as planned and achieves its nominal performance, the following conclusions can be drawn: LISA Pathfinder can be flown through the Sun-Earth Saddle Point following the nominal mission, and miss distances of 10-20km will be achievable for transfer times of order 400days The predicted MOND/TEVES signal is robust against lunar position, and in conjunction with the spacecraft speed falls precisely in the mhz region ideally suited to LISA Pathfinder The nominal LISA gradiometer sensitivity allows for a clear measurement of MOND/TEVES anomalous gradients not a marginal detection More detailed work required (Operations) 32/33
Summary and Conclusions Having demonstrated the basic feasibility of the proposal, a few questions remain (feedback welcome!): Is the scientific motivation for such a MOND/TEVES test strong enough? The mission would be extended by just over a year, for a one-off experiment lasting around 1000s, at a financial cost estimated at 10 7 This proposal suffers, to some extent, from the common Fundamental Physics in Space syndrome : a positive detection would represent a major breakthrough, a null result would be less interesting but (relatively) low cost! Are there other meaningful GR tests that would benefit from the special gravitational environment found around SPs? If so, this would increase the motivation to make the trip to the SP! 33/33