Radiation from Solar System Objects

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Radiation from Solar System Objects
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Types of observation

• Photometry estimating sizes of unresolved
  objects and scattering properties of their
  surface material
• Thermal radiometry sounding the near-surface
  temperature distribution
• Spectrophotometry identifying minerals or
  chemical compounds via their absorption/emission
  features
• Radar estimating surface roughness and
  composition constructing 3D size/shape models of
  visually unresolved objects

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Observing Geometry

• External planet outside the Earths orbit
• - example Mars
• Internal planet inside the Earths orbit
• - example Venus
• Elongation angle S-E-P
• Phase angle angle S-P-E

Sun
Earth
Planet
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Phases

• Opposition E ? (external planets)
• Conjunction E 0 (all planets)
• Quadrature (external planets) E ? ?/2 and
• Max. elongation (internal planets) ? ?/2 and

Phases of Venus
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Elongations Phase Angles
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Bond Albedo

• Albedo whiteness
• R specularly reflected flux
• S scattered flux in all directions
• I? solar energy flux

AB fraction not absorbed 1-ABabsorbed fraction
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Phase Function

• Ratio between the flux scattered at phase angle ?
  and the backscattered flux with ?0
• Phase integral

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Geometric Albedo

• Backscattered flux Fb
• Incident solar flux Fsun
• - AB is omnidirectional, Ap is unidirectional
• - AB is frequency averaged, Ap refers to a
  photometric passband
• - AB is theoretical, Ap is observational

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The Lambert Disk

• Non-absorbing isotropic scatterer with f(?)
  cos?
• Same surface brightness from all directions
  (?lt?/2)
• q 1
• Ap AB 1
• Ap is the amount of backscattered sunlight
  relative to a Lambert disk with the same area

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Geometric Albedos, Phase Integrals
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Observed Magnitudes

• If S is the solar flux at the Earth in a certain
  passband, the flux leaving an object toward the
  Earth is
• If R is the radius of the object, the flux
  observed at the Earth is
• In magnitude units
• where and

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Colours

• The magnitudes m are usually measured with
  different broadband filters (U, B, V, R, etc.)
• The differences, e.g. BV, are called colour
  indices
• From the magnitude formula for a Solar System
  object, we get
• Thus the measured colour index depends on
• the solar colour (BV)?
• the albedo ratio Ap(B)/Ap(V)
  (true colour)
• the phase reddening ?B(?)?V(?)

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Phase Curves
Photometry ? R2Ap Size-albedo ambiguity

• At small ?, a linear formula is often used as
  phase curve
• Opposition effect spike in brightness at very
  small ? for atmosphereless objects

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Opposition Effect in Saturns A Ring

• Cause of the brightness spike at opposition
• - Lack of shadowing
• - Coherent backscatter

Cassini image
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Light scattering from grains (1)

• Examples the zodiacal light, dust tails in
  comets, etc.
• Observed brightness collective amount of
  scattered sunlight from all grains along the line
  of sight
• The grain size distribution is important for
  interpreting the observations
• - for grains of radius a, the surface/volume
  ratio is ? a-1

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Light scattering from grains (2)

• Large grains or boulders scatter light like
  planets without atmospheres backscattering
• Very small grains (?) are much more forward
  scattering

Jupiters rings seen against the Sun
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Temperature radiometry (1)

• Incident energy flux (insolation) depends on the
  distance to the Sun and the solar elevation angle
• Insolation Scattering Thermal radiation
  Heat conduction
• The scattering efficiency is measured by AB
• Thermal emissivity ?IR
• - Is ?IR 1-AB? No, ?IR?0.9 is assumed in
  general

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Planetary spectra

• Common planetary minerals have spectral features
  in the IR
• - e.g. stretching of bonds within molecules
• - local variation of emissivity
• Important for chemical analysis and thermal
  modelling

Infrared spectrum of Mercury
Jupiters spectrum
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Temperature radiometry (2)

• Emitted flux of thermal radiation from the
  Stefan-Boltzmann radiation law
• Assume isothermal, spherical object!
• Absorbed insolation per unit time
• Emitted radiation per unit time
• Equilibrium temperature for thermal balance

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Bond albedos Eq. temperatures
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Radar observations (1)

• Send a radio pulse toward the object receive and
  analyze the echo
• Two main variables Delay and Doppler shift
• Received intensity I(?t,??)
• Find a model of the objects size, shape and spin
  that represents I(?t,??)

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Radar observations (2)

• Echo frequency range
• Noise level for integration time ?t
• Received signal
• Signal/Noise ratio

Toutatis, small near-Earth asteroid
Kleopatra, large main-belt asteroid