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exo planets > 1 > Flashcards

1 Flashcards

1
Q

bulk modulus of material equation

A

K = −V ∂P/∂V = ρ ∂P/∂ρ

V , P, and ρ are volume, pressure, and density respectively

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2
Q

what does a large bulk modulus mean

A

resist compression better than materials with a lower bulk modulus

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3
Q

when does “something interesting” happen if you keep adding mass to a pile

A

the material will begin to “fail” ( if this applied pressure is too great P ≈B
when the self-gravity of the pile becomes “important,”

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4
Q

expression of hydrostatic equilibrium

A

∇P = ρg

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5
Q

pressure at the center of a spherical body of uniform density

A

P = Cρ^2R^2

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6
Q

how to determine at what size self gravity is important

A

look at ratio between energy of bonds between atoms (1 eV works) and gravitational energy per particle

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7
Q

equation of hydrostatic equilibrium

A

∇P = ρg

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8
Q

polytropic equation of state

A

P = Kρ^( (n+1)/n)

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9
Q

gamma-law equation of state

A

P = (γ −1)ρu_m = (γ −1)u_v
um is the total internal energy (per unit mass) arising from microscopic processes, uv is the same quantity perunit volume, and γ is a constant

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10
Q

pressure scale height of the gas

A

HP = R_∗T/g

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11
Q

virial theorem

A

2U = −Ω
U = internal energy
Ω = −qGM^2/R is the gravitational binding energy

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12
Q

Degeneracy pressure in planet interiors

A

leads to a different equation of state (and in turn a different mass(radius) relationship). materials resist compression – that is, they have pressure – not just because of thermal pressure, but because of quantum mechanics - degenreacy pressure

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13
Q

pressure density relation for a non relativistic degenertate gas

A

P ∝ ρ^5/3

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14
Q

mass radius relation for a non relativistic degenertate gas

A

R ∝ M^−1/3,

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15
Q

Reynolds number

A

helps predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent.
uL/v=rho u L/ mu
inertial/ viscous term

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16
Q

rossby number

A

inertial/coriolis term = u/2ΩL^2

low if rapidly rotating

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17
Q

ekman number

A

viscous/ coriolis term = u/2ΩL

low if rapidly rotating

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18
Q

Very steep dT/dz

profiles are

A

unstable to

convection

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19
Q

“momentum equation,” aka“Navier-Stokes equation”

A

∂u/∂t +u.∇ u=-1/ρ∇P+ g -2sΩ x u + v∇^2u

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20
Q

Continuity equation (mass conservation)

A

∂ρ/∂t + ∇.(ρu)=0
for incompressible fluid
∇.u=0

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21
Q

eddy diffusivity

A

“eddy diffusivity” ~ velocity * length

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22
Q

eddy diffusion time

A

“eddy diffusion time” (~ dynamical time) L^2/velocity

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23
Q

pressure at center of planet

A

P~GM^2/R^4~Gρ^2R^2

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24
Q

how to find height of tallest mountain

A

bulk moduls = ρgh - when the pressure at the base of the mountain crushes the material

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25
Q

why can mountains be bigger on smaller planets

A

g scales with r and h max is inversly proportinal to g

as long as h max is still much smaller than r all good

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26
Q

mass radius relation for uncompressed rock

A

m ~ R^3

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27
Q

gamma law equation of state

A

P=(γ-1)ρu_m=(γ-1)u_v

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28
Q

polytropic equation of state

A

P=kρ^((n+1)/n)

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29
Q

ideal gas equation of state

A

PV=nRT or P=ρR_*T

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30
Q

viral theorem

A

the ke of a gravitationaly bound system is minus a half fof the gpe

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31
Q

internal potential energy of a gas

A

3/2nRT=U

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32
Q

degeneracy pressure scaling law

A

P~ρ^5/3

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33
Q

flux of energy due to radiation

A

F=-4acT^3/(3σn)dt/dx =-4acT^3/(3κρ)dt/dx

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34
Q

whats not a fluid

A

Enough collisions to isotropize quantities and lead to continuous density, velocity, etc. “Smoothing out” over inherent granularity of matter
Typically means we are looking at scales&raquo_space; mfp

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35
Q

escape velocity

A

v=sqrt(2GM/r)

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36
Q

body force

A

acts via center of mass

37
Q

categories of planetary materials

A

rocks/metals ices gasses

38
Q

rossby term

A

u/2omegaL
small if rotation is small compared to dynamical time
coriolis forces have time to influence
ie small if influenced by rotation

39
Q

geostrophic balance

A

state, in which horizontal pressure gradients are balancing Coriolis forces
flow along isobars

40
Q

flow is clockwise around

A

areas of high pressure

41
Q

geostrophic balance is applicaple when

A

rossby and ekman number small

presssure balance coriolis in horizontal

42
Q

taylor proudman constraint

A

flow constant on lines parallel to rotation axis - for barytropic fluid- obsticales project into atmosphere

43
Q

equation linking the orbital period and masses of two orbiting bodies

A

a_s/a_p=M_p/M_s

44
Q

kepplers thrird law

A

P^2/a^3 = 4π^2/G(Ms +Mp)

45
Q

astrometry equation

A

β = a_s/d = a_p/d(Mp/M)

with beta being the observed angular change in arcseconds

46
Q

astrometry

A

detecting the star’s reflex motion by simply observing its apparent position on the sky, and seeing whether this changes periodically over time

47
Q

radial velocity method

A

measure reflex motion of star via doppler shift

48
Q

star’s reflex velocity equation

A

vs/vp = −Mp/(Mp +Ms)

49
Q

transit method equation

A

∆F/F ≈(Rp/Rs)^2

.

50
Q

transit method

A

look for dipped luminosity

51
Q

what are the axis for a cratering diagram

A

no of craters per unit area and crater size

52
Q

saturation equilibrium

A

max number of craters per unit area - new impact kills old impact crater

53
Q

effect of atmosphere on cratering

A

small impactors are screened off by atmosphere

54
Q

planet resurfacing effect on cratering

A

younger surface will have fewer craters

55
Q

what will slow a metorite

A

traveling through a collum of atmosphere roughly its own mass

56
Q

conductive transport equation

A

F=-kdT/dr

57
Q

possible heating sources for planets

A 
Gravitational (accretion) energy
Differentiation (grav PE)
Latent heat/condensation effects
Radioactivity
\+ (of course) stellar insolation
58
Q

Bond albedo

A

the fraction of power in the total electromagnetic radiation incident on an astronomical body that is scattered back out into space

59
Q

planet cooling mechanisms

A

radiation conduction convetion and erruprion

60
Q

diffusion equation

A

dT/dt=k/ρc ∇^2T

61
Q

thermal diffusion time

A

t ∼ L^2/κ ,

62
Q

equation for how flux and luminosity are related

A

F=L/4pid^2

63
Q

energy absorbed by planet from star

A

E_in = (1 −a)πR^2F(d)

64
Q

energy radiatied out by planet

A

E_out = 4πR^2pεσT^4

65
Q

planet’s “radiative equilibriun temperature”

A

Te =((F(1 −a))/4εσ)^1/4

66
Q

what happens to the radiative equilibrium surface as the atmo gets thicker

A

moves higher up

67
Q

3 sources / types of atmos

A

primary - acreted from nebula
secondary - outgassing
tertiary- deliverd via impactors

68
Q

how to determine type of atmo

A

composition - primary will be similar composition to central star

69
Q

could earths atmosphere be primitive

A

no - consider neon in atmosphere - neon us heavy and primitive what we have is what had but extrapolataing back get only 0.9% of current atmo

70
Q

4 ways the atmosphere is lost

A

thermal - jeans escape , dissociation via uv photons, impacts, loss to interior

71
Q

exobase

A

mean free path > scale height - region in atmosphere where easy for molecules to escape

72
Q

mean free path equation

A

1/n x cross sectional area

73
Q

ice albedo feedback

A

positive feedback climate process where a change in the area of ice caps, glaciers, and sea ice alters the albedo and surface temperature of a planet

74
Q

optically thick limit

A

I_v(D)=S_v

75
Q

optically thin limit

A

I_v(D)=I_v(0)+[S_v-I_v(0)]T_v(D)

76
Q

energy density of the radiation

A

U = aT^4 (with a = 4σ/c)

77
Q

optical depth equation

A

dτ_v=s(α)ds=nσds=ds/mfp

78
Q

optical deptha and pressure equation

A

P/g=τ/κ

79
Q

lapse rate

A

rate of change in temperature observed while moving upward through the atmosphere. The lapse rate is considered positive when the temperature decreases with elevation

80
Q

derivation of dry adiabatic lapse rate

A

this state has dθ/dz=0
use chain rule dT/dz=dT/dP dP/dz +dθ/dz dT/dθ
and ideal gas equation

81
Q

typical structure of atmospheres

A

near surface dT/dz close to adiabatic laps rate then sabtle stratifications

82
Q

dry adiabatic lapse rate final solution

A

dT/dz=-g/c_p

83
Q

Boussinesq approximation

A

we assume that density fluctuations are negligible except where ρ is multiplied by g density fluctuations are linked only to temperature fluctuation

84
Q

size of the perturbations relative to the mean in the Boussinesq approximation

A

ρ′/ρ = −αT ′

85
Q

The non-intuitive result is that a horizontal density/temperature gradient

A

leads to vertical shear, that is to

variations with height of the horizontal wind

86
Q

Rayleigh number in convection

A

Ra = gαΓL^4/νκ ∼ buoyancy driving/dissipation
with Γ = dT /dz = ∆T /L
this must hit a crit number b4 convection happnes

87
Q

he temperature gradient approaches

A

the adiabatic value for efficient convection

88
Q

velocity of heat flux

A

v ≈(F/ρ)^1/3

89
Q

magnetic diffusivity

A

η = c^2/4πσ

exo planets (1 decks)

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