Week 7 Orbits and Extrasolar planets Flashcards
what are Kepler’s 3 planetary laws
1 Planets orbit stars in ellipses with the star at one focus
2 Planets sweep out equal area in equal time
3 The period P and semi major axis a of the orbit are related through P^2 = 4π^2a^3 / G(M1+M2)
what is the ellipse equation
( x/a )^2 + ( y/b )^2 = 1
a is the semi major axis
b is the semi minor axis
what two things do Kepler’s laws demonstrate
angular acceleration is 0
gravity is a radial force
what is the procedure for deriving Kepler’s 3rd law for a binary star system
find the position of CoM for the two stars
find the centripetal acceleration
equate the centripetal acceleration to the gravitational acceleration
rearrange to make the time period the subject
replace r with the semi major axis
how do we detect exoplanets
we wait for them to transit past a star where we can easily see it as a dark spot
what is the exoplanet doppler shift/velocity equation
v / c = f0 - f / f0 = λ - λ0 / λ0 f0 is the rest frequency f is the observed frequency λ0 is the rest wavelength λ is the observed wavelength
what is the observed velocity equation if the orbital plane is inclined to the plane of the star by an angle i
v(doppler) = v(orbit)sini
what are the two methods for detecting exoplanets
Radial velocity hunting technique
Transit method
how does the transit method work
determine how much less light is given off by the star due to the transiting planets blocking it
what is the general rule for the detection probability of an exo-planet (3 points)
more massive planets and planets with smaller semi-major axis and planets that orbit around lower mass stars are easier to detect
what is the energy received from a star by a planet equation
L received = L* / 4πd^2 πR^2(planet)
d is the distance between the star and planet
what is the energy absorbed by a planet from a star equation
( 1 - ω ) L* / 4πd^2 πR^2(planet)
d is the distance between the star and planet
ω is the albedo (fraction of energy reflected)
planets emit energy as a blackbody
what is the planet blackbody equation
L(emit) = 4πR^2(planet)σT^4
what is the planet temperature equation
T = [ (1-ω)L* / 16πσ ]^1/4 sqrt(1/d)
what 3 things is the temperature of a planet dependent upon
luminosity
albedo
distance
