6.
7. Earth does not appear to be at any risk of a particular catastrophe. Semi-major axis is randomly moving between the minimum detectable changes, and there is a slow tradeoff in parameters from eccentricity to inclination.
2)
Suitably apocalyptic results are obtained when adding a planet with the parameters of :
NIBIRU m=1.40000000000000000E-02 r=3.d0 d=28.0
3.14159265358979323E+01 -2.71828182845904528E+00 -1.01001000100001000E-01
7.36084560000000000E-04 7.43519750000000000E-07 -2.00460016972063023E-11
0. 0. 0.
A number of them simply disappear from the simulation after a bit.
3)
a. The two properties of a protoplanetary disk that determine what planets will form are mass, and metallicity.
*b. The three types of planetary migration are named Type I, II, and III. Type I are from the planet causing overdensities in the disk inside and outside of its orbit. The density profile of the disk results in the planet transferring angular momentum to the overdensities, and moving inwards. In Type II migration, the planet is sufficiently massive to open up a gap in the disk. (something about viscous forces and drag). Type III is runaway... Seager(?) describes the timescales for Type I and II as being much the same.
c. Terrestrial planets can survive giant planet migration (including the formation of hot Jupiters) by outwards scattering, or (more likely) forming exterior to the giant planet and migrating inwards.
4)
a. An "inversion layer" is a layer of a planet's atmosphere where the temperature profile is inverted; instead of decreasing, the temperature increases with altitude. This is important becauseof how it affects wind patterns and heat flow, with atmospheres partially stratifying into layers based on temperature inversions.
b.
Peverest = exp(-8.8/8) ~= 0.33287108369807955
Alternatively:
ln(Peverest) = -alt/scale
scale*8.8/8 = alt
For an isothermal atmosphere, scale = T*k/(M*g)
k = 1.38065582e-23
M (molecular weight of the atmosphere) is assumed to be the same as for Earth. Approximating as 80% Nitrogen, 20% Oxygen, M = (0.8*28+0.2*32)/6.022e26 = 4.782464297575557e-26 kg
(exoplanet properties: a = 0.2 AU, m = 5 M_earth, r = 1.2 R_earth, P_0 = 1.0 atm)
Simplifying the Stephan-Boltzmann equation for blackbody equilibrium:
T^4 = c/a^2; T = (c/a^2)^0.25
Earth: a = 1 AU, T = 287 K, c = 300^4
This planet:
T = 287/sqrt(0.2) = 641.75150954243963 K
g = 9.81*5/1.2^2 = 34.0625 m/s/s
scale = 641.75150954243963*1.38064852e-23/(28.8/6.022e26*34.0625) = 5439.03400930283 m
Checking scale height with assumed Earth parameters: 287*1.38064852e-23/((28*0.8+32*0.2)/6.022e26*9.81) = 8445.867900509964 m, a bit more than 5% larger than the given 8 km.
5439.03400930283*8.8/8 = 5982.937410233113 m
At the actual level of precision, ~6.0 km altitude.
5)
a. The primary cause of gaps in the asteroid belt is resonances with Jupiter causing the asteroids to be perturbed into increasingly eccentric orbits. The ultimate result is a close encounter (or coll
ision!) with another planet dramatically altering the asteroid's orbit.
b. The most surprising features of early exoplanet discoveries were the planets existing at all where they were found. Neither pulsars, nor <10 day orbits around FGK stars were expected.
c. Exoplanet letter designations are assigned in order of discovery, with ties being broken by whichever is closest to its parent star.
d. Kepler has demonstrated that smaller planets are more common than larger ones, at least down to where it begins to suffer from poor completeness (in the sub-neptune/super-earth range).
e. The "habitable" zone is the range of distances from a star where we expect that at least some kinds of rocky planets could have liquid water on their surfaces.
6)
a. The maximum phase amplitude will be just before secondary eclipse. The angle will be:
90-arccos(695700e3/0.723332/1459597870700) = 0.36837 degrees.
Lighting is ambiguous, and assumed to be cos(theta/2)**2 since that gives a plausible shape to the light curve. This gives a phase of 0.99998966614598372. (about 1 - 10^-6)
b. With this inclined orbit, maximum illumination will have the planet 40 degrees from conjuction. This is conveniently also peristron. Using the above guess at illumination, the phase is 0.88302222155948906. Apparent brightness at the same phase angle is proportional to 1/r^2, so the relative distance is:
sqrt(0.88302222155948906/0.99998966614598372) = 0.93969747614672106
0.9397 is the periastron for an orbit with a semi-major axis of 1.
p = a*(1-e)
e = 1-(p/a)
e = 1-(0.93969747614672106/1) = 0.060302523853278944
e ~= 0.06
(Venus' eccentricity is approximated as 0)
7)
a. Mean anomaly is where the body would be along its orbit if it were in a 0 eccentricity orbit. True anomaly is where along the orbit the body actually is. Eccentric anomaly is an auxiliary angle to facilitate converting between the easily found mean anomaly and more difficult true anomaly.
b.
