radiation from solar system objects

8/3/2019 Radiation From Solar System Objects

1/22

Radiation from Solar System

Objects


2/22

Types of observation

Photometry: estimating sizes of unresolvedobjects and scattering properties of theirsurface material

Thermal radiometry: sounding the near-surface temperature distribution

Spectrophotometry: identifying minerals orchemical compounds via theirabsorption/emission features

Radar: estimating surface roughness andcomposition; constructing 3D size/shapemodels of visually unresolved objects


3/22

Observing Geometry

External planet: outsidethe Earths orbit

- example:Mars Internal planet: inside the

Earths orbit

- example:Venus

Elongation: angle S-E-P

Phase angle: angle S-P-E

Earth

Planet

Sun


4/22

Phases Opposition: E = (external planets)

Conjunction: E = 0 (all planets)

Quadrature (external planets): E = /2 and

Max. elongation (internal planets): = /2 and

max arctan 1 r2 1

Emax

arcsin r

Phases of Venus:


5/22

Elongations & Phase Angles

Planet |E|max (deg) max (deg)

Mercury

Venus

Mars

Jupiter

SaturnUranus

Neptune

23

46

180

180

180180

180

180

180

41

11

63

2


6/22

Bond Albedo

Albedo= whiteness

R: specularly reflectedflux

S: scattered flux in all

directions I: solar energy flux

AB R S

Isun cosi

AB= fraction not absorbed; 1-AB=absorbed fraction


7/22

Phase Function

Ratio between the fluxscattered at phase angle and the backscattered fluxwith =0

Phase integral:

f() F() /F(0)

q 2 f()sind0


8/22

Geometric Albedo

Backscattered flux: Fb

Incident solar flux: Fsun

- AB is omnidirectional, Ap is unidirectional

- AB is frequency averaged, Ap refers to aphotometric passband

- AB is theoretical, Ap is observational

Ap Fb /Fsun

AB Ap q


9/22

The Lambert Disk

Non-absorbing isotropicscatterer with f() = cos

Same surface brightnessfrom all directions (


10/22

Geometric Albedos, Phase Integrals

Object Ap q

Mercury

Venus

Earth

Moon

Mars

JupiterSaturn

Uranus

Neptune

0.136

0.65

0.367

0.152

0.15

0.520.47

0.51

0.41

0.46

1.0

1.07

0.45

1.07

1.41.3

1.4

1.4


11/22

Observed Magnitudes

If S is the solar flux at the Earth in a certainpassband, the flux leaving an object towardthe Earth is:

If R is the radius of the object, the fluxobserved at the Earth is:

In magnitude units:

where and

F SrAU2 Ap f()

Fobs RAU2 Ap f() SrAU

2AU

2

m mo 5lg rAU 5lgAU m()m() 2.5lg f() mo msun 2.5lg RAU

2 Ap


12/22

Colours

The magnitudes mare usually measured withdifferent 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()

BV (BV)sun 2.5lg Ap(B) /Ap(V) B V


13/22

Phase Curves

At small , a linearformula is often used asphase curve:

Opposition effect: spikein brightness at very small for atmospherelessobjects

PhotometryR2Ap : Size-albedo ambiguity

m()


14/22

Opposition Effect in Saturns A Ring

Cassini image

Cause of thebrightness spike at

opposition:

- Lack of shadowing

- Coherent backscatter


15/22

Light scattering from grains (1)

Examples: the zodiacal light,dust tails in comets, etc.

Observed brightness: collectiveamount of scattered sunlightfrom all grains along the line ofsight

The grain size distributionis

important for interpreting theobservations:

- for grains of radius a, thesurface/volume ratio is a-1


16/22

Light scattering from grains (2)

Large grains or bouldersscatter light like planets

without atmospheres:backscattering

Very small grains (~)

are much more forwardscattering

Jupiters rings seen

against the Sun


17/22

Temperature & radiometry (1)

Incident energy flux (insolation)depends on the distance to theSun and the solar elevation angle

Insolation = Scattering + Thermal

radiation + Heat conduction

The scattering efficiency ismeasured by AB

Thermal emissivityIR:

- Is IR = 1-AB? No, IR0.9 isassumed in general


18/22

Planetary spectra

Common planetaryminerals have spectralfeatures in the IR:

- e.g. stretching of bondswithin molecules

- local variation ofemissivity

Important for chemicalanalysis and thermalmodelling

Infrared spectrum of Mercury

Jupiters spectrum


19/22

Temperature & radiometry (2)

Emitted flux of thermal radiation from theStefan-Boltzmann radiation law:

Assume isothermal, spherical object!

Absorbed insolation per unit time:

Emitted radiation per unit time:

Equilibrium temperature for thermal balance:

FT4

Ein R2 (1 AB )SrAU

2

Eout 4R2

T4

Teq S(1 AB )

4IRrAU2

1/ 4


20/22

Bond albedos & Eq. temperatures

Object AB Teq (K)

Mercury

Venus

EarthMoon

Mars

JupiterSaturn

Uranus

Neptune

0.063

0.65

0.390.068

0.16

0.730.61

0.71

0.57

450

260

250280

220

9073

48

42


21/22

Radar observations (1)

Send a radio pulse toward the object; receiveand 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,)


22/22

Radar observations (2)

Echo frequency range:

Noise level for integrationtime t:

Received signal:

Signal/Noise ratio:

Toutatis, small near-Earthasteroid

Kleopatra, large main-beltasteroid

D /P

N t D /P 1/ 2

So4D2A2tt

SNRo4D3 / 2A2tP

1/ 2t1/2

radiation from solar system objects

Documents