Properties of the Solar System

Properties of the Solar System Dynamics of asteroids Telescopic surveys, especially those searching for near-earth asteroids and comets (collectively called near-earth objects or NEOs) have discovered large numbers of minor bodies in the Solar System Today s astro-colloquium Mikael Granvik University of Hawaii Bayesian methods for asteroid orbit computation

Properties of the Solar System Dynamics of asteroids Image of an NEO moving through a field of the Sloan Digital Sky Survey (SDSS) passing through three filters star star Today s astro-colloquium Mikael Granvik University of Hawaii Bayesian methods for asteroid orbit computation To be able to follow up and perform physical studies on these discoveries an orbit must be first generated. Since an object discovered by an NEO survey initially only gets a handful of detections and traditional methods require a fair amount of data to produce accurate results (or any results!), the worldwide effort put into the NEO search programme has produced increased interest in the development of new orbit-computation methods capable of providing accurate results when given a minimum of information

Properties of the Solar System Dynamics of asteroids NEOSSat Today s astro-colloquium Mikael Granvik University of Hawaii MOST As an example, he will show how nonlinear methods are used in the context of the Canadian Space Agency's NEOSSat spacecraft mission and explain why they are critical when maximising the scientific return of the mission

Properties of the Solar System Dynamics of planets, moons and Sun planets have nearly circular orbits in nearly the same plane all orbit in the same sense (the same sense as the Sun s rotation) planets have nearly all the angular momentum

Properties of the Solar System Composition planets close to the Sun are small, metallic and rocky outer planets are large, gaseous and icy Solar System is almost entirely hydrogen and helium gas

Nebular formation hypothesis

Another formation hypothesis

In science and in life A sample of one

Searching for exoplanets A sample of many To fully understand the process of Solar System birth and evolution, we need to have other examples

Other planetary systems Searching for exoplanets To fully understand the process of Solar System birth and evolution, we need to have other examples How do you look for exoplanets?

Other planetary systems Searching for exoplanets Can we photograph a Jupiter or an Earth around another star?

Exoplanets are faint! Other planetary systems Planets are seen only by reflected light at optical wavelengths The Voyager 1 spacecraft looked back from only 20 AU above the plane of our own Solar System

Exoplanets are faint! Other planetary systems Planets are seen only by reflected light at optical wavelengths Even from such a close distance, planets are relatively faint and not so easy to see Earth

Exoplanets are faint! Other planetary systems Planets are seen only by reflected light at optical wavelengths By eye from Earth, we can t see giant planets further than about 10 AU from us

Exoplanets are faint! Other planetary systems At visible wavelengths: Sun is 10 8 times brighter than Jupiter and 10 9 times brighter than Earth

Exoplanets are faint! Other planetary systems At infrared wavelengths: Sun is 10 4 times brighter than Jupiter and 10 6 times brighter than Earth

Exoplanets are faint! Other planetary systems You need a BIG telescope to try to see exoplanets directly

Telescopes Not big enough

Telescopes fisheye lens view of the Gemini North 8-m Telescope This is more like it

Telescopes three of the dishes in the VLA (Very Large Array) in New Mexico Sensitivity to other wavelengths helps

Telescopes Hubble Space Telescope Not big enough

Light collectors Telescopes To an astronomer, the most important aspect of a telescope is not its magnifying power, but its light-collecting area Telescopes are meant to collect as much light as possible making faint sources brighter

Light buckets Telescopes To an astronomer, the most important aspect of a telescope is not its magnifying power, but its light-collecting area Telescopes are meant to collect as much light as possible making faint sources brighter Because of this, astronomers sometimes refer to telescopes as light buckets, which collect light in the same way a bucket collects rainwater

Telescopes Light buckets The larger the bucket, the more you collect Because of this, astronomers sometimes refer to telescopes as light buckets, which collect light in the same way a bucket collects rainwater

Large reflectors BIG light buckets Telescopes Gemini 8-metre mirror blank

Telescopes What s important 1. Light-collecting area A = π (D/2) 2 where D is the diameter (or aperture) of the primary mirror 5 cm 8 m

Telescopes What s important 1. Light-collecting area A = π (D/2) 2 where D is the diameter (or aperture) of the primary mirror 2. Angular resolution The smallest angle that can be distinguished or resolved θ = 1.22 λ / D where λ is the wavelength of light in the same units as the aperture D of the telescope and the angle θ is measured in radians

Why is there a limit? Light behaves like a wave, so when it passes through any opening, it diffracts around the edges of that opening Angular resolution

Diffraction Light behaves like a wave, so when it passes through any opening, it diffracts around the edges of that opening This means that even the sharpest image is blurred slightly when light passes through an opening Angular resolution

Diffraction spikes Angular resolution It s the support struts of the secondary mirror in a reflector that cause the spikes we see in photographs of stars

Angular resolution Diffraction Light behaves like a wave, so when it passes through any opening, it diffracts around the edges of that opening The pupil of the eye and the primary mirror of a telescope are examples of circular openings (apertures) A point source of light passing through a circular aperture is spread into bright central peak circled by concentric rings Airy disk highly magnified

Angular resolution Diffraction limit Light behaves like a wave, so when it passes through any opening, it diffracts around the edges of that opening The pupil of the eye and the primary mirror of a telescope are examples of circular openings (apertures) The Rayleigh diffraction limit of angular resolution through a circular aperture is: θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Largest apertures Largest optical telescopes in the world: Keck Observatories Gran Telescopio Canarias D ~ 10 m Large Binocular Telescope

Angular resolution Largest apertures Largest optical telescopes in the world: Keck Observatories (Hawaii) and Hobby Eberly Telescope (Texas) D ~ 10 m θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Largest apertures Largest optical telescopes in the world: Keck Observatories λ = 550 nm = 5.5 10-7 m middle of visible spectrum D = 10 m θ = 6.7 10-8 radians ~ 0.014 second of arc 4 millionths of a degree! D = 10 m θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Blurring by the Earth s atmosphere Turbulence in the Earth s atmosphere blurs the light arriving from space craters on Moon seen through a ground-based telescope Telescopes on Earth do not naturally achieve the diffraction limit due to atmospheric distortions: seeing and scintillation

Angular resolution Blurring by the Earth s atmosphere Turbulence in the Earth s atmosphere blurs the light arriving from space craters on Moon seen through a ground-based telescope star image distorted by atmospheric seeing Telescopes on Earth do not naturally achieve the diffraction limit due to atmospheric distortions: seeing and scintillation

Angular resolution Blurring by the Earth s atmosphere Turbulence in the Earth s atmosphere blurs the light arriving from space craters on Moon seen through a ground-based telescope star image seen as Airy disk at diffraction limit Telescopes on Earth do not naturally achieve the diffraction limit due to atmospheric distortions: seeing and scintillation

Angular resolution Adaptive optics We can correct for atmospheric distortions in real time by changing the shape of some of the telescope optics from microsecond to microsecond

Angular resolution Adaptive optics We can correct for atmospheric distortions in real time by changing the shape of some of the telescope optics from microsecond to microsecond a binary star before adaptive optics

Angular resolution Adaptive optics and human vision Ophthalmologists are now using adaptive optics developed for astronomy to obtain the best images of the retina of the living human eye

Angular resolution Adaptive optics and human vision Ophthalmologists are now using adaptive optics developed for astronomy to obtain the best images of the retina of the living human eye retinal cells before adaptive optics

Angular resolution Adaptive optics and human vision There is now research into using adaptive optics to enable super-vision so 20-20 may not be the limit

Other planetary systems Searching for exoplanets Can we photograph a Jupiter or an Earth around another star? planet Earth θ a θ = a d where θ in radians, a and d in same units star

Other planetary systems Searching for exoplanets Can we photograph a Jupiter or an Earth around another star? planet Earth θ a θ = a d where θ in radians, a and d in same units star Consider a star only 20 light years away d ~ 6 parsecs with a planet in an orbit with semi-major axis a = 5 AU

Other planetary systems Searching for exoplanets Can we photograph a Jupiter or an Earth around another star? planet Earth θ a θ = a d Yes, we can resolve an angular separation of about 1 arcsec where θ in radians, a and d in same units star Consider a star only 20 light years away d ~ 6 parsecs with a planet in an orbit with semi-major axis a = 5 AU d ~ 6 pc 206,265 AU/pc ~ 1.2 10 6 AU θ ~ 5 / 1.2 10 6 ~ 4 10-6 rad ~ 1 arcsec

Angular resolution Other planetary systems Largest optical telescopes in the world: Keck Observatories λ = 550 nm = 5.5 10-7 m middle of visible spectrum D = 10 m θ = 6.7 10-8 radians ~ 0.014 arcsec D = 10 m

Angular resolution Other planetary systems Largest optical telescopes in the world: Keck Observatories λ = 550 nm = 5.5 10-7 m middle of visible spectrum D = 10 m D = 10 m θ = 6.7 10-8 radians ~ 0.014 arcsec This is the angular separation of a planet and star for a planet s orbit of semi-major axis a ~ 0.1 AU seen at a distance of d = 20 light years So we should be able to take a picture of a planet around another star, right?

Exoplanets are faint! Other planetary systems Planets are seen only by reflected light at optical wavelengths At the distance of another star the faint light of a planet is lost in the glare of the star Even in the infrared, where a Sun-like star puts out less light and a planet glows by its own thermal (blackbody) emission, it s not possible to get an image of an Earth or even a Jupiter image of a binary star with a faint companion barely visible even in IR

Resolution depends on wavelength λ The wavelengths of radio waves are long So the dishes which reflect them must be very large to achieve any reasonable angular resolution Angular resolution θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Resolution depends on wavelength λ The wavelengths of radio waves are long So the dishes which reflect them must be very large to achieve any reasonable angular resolution Angular resolution D ~ 300 m θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Angular resolution Largest radio telescope in the world: Arecibo (Puerto Rico) λ = 21 cm wavelength of radio waves emitted by cold hydrogen molecules D = 300 m = 3 10 4 cm θ ~ 8.4 10-4 radians ~ 170 arcsec 1/20th of a degree D ~ 300 m θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Interferometry Two (or more) radio dishes observe the same object The wave patterns of their signals are made to interfere with each other

Angular resolution Interferometry Two (or more) radio dishes observe the same object The wave patterns of their signals are made to interfere with each other An image is reconstructed with the angular resolution one would get from a dish the size of the distance between them but the light-collecting area is still only the sum of the areas of the individual dishes

Angular resolution Interferometry Penticton BC Algonquin Park, Ontario In 1968, Canadian astronomers used two radio telescopes to resolve a quasar, as if with one telescope 3000 km across

Angular resolution Interferometry at radio wavelengths Very large radio array: VLA = Very Large Array (New Mexico) D = 21 km

Very large radio array: VLA = Very Large Array (New Mexico) λ = 21 cm wavelength of radio waves emitted by cold hydrogen molecules D = 21 km = 2.1 10 6 cm θ = 2.3 10-5 radians ~ 5 seconds of arc Angular resolution Interferometry at radio wavelengths D = 21 km θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Angular resolution Interferometry at infrared wavelengths? Simulated image of Jupiter in a solar system at a distance of 10 parsecs Using interferometry in the infrared from the ground

Getting above the atmosphere Angular resolution Largest optical telescope in space: Hubble Space Telescope To detect the wavelengths blocked by the Earth s atmosphere, we must put telescopes in space Chandra X-ray Observatory

Angular resolution You get good resolution but limited by D Largest optical telescope in space: Hubble Space Telescope λ = 550 nm = 5.5 10-7 m middle of visible spectrum D = 2.4 m θ = 2.8 10-7 radians ~ 0.058 arcsec D = 2.4 m largest optical telescope on Earth D = 10 m θ min = 1.22 λ D where θ min in radians, λ = wavelength and D = aperture diameter (λ and D in same units)

Interferometry from space? Angular resolution TPF = Terrestrial Planet Finder SIM = Space Interferometry Mission

Interferometry from space? Earth Angular resolution Simulated family portrait of inner Solar System Mars Venus Jupiter TPF = Terrestrial Planet Finder SIM = Space Interferometry Mission

Interferometry from space? Angular resolution Simulated family portrait of inner Solar System Earth Mars Venus Jupiter The images are reflected about the origin (an artifact of the interferometry technique) TPF = Terrestrial Planet Finder SIM = Space Interferometry Mission