Question

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 17000 km and its rotation period to be 22.8 hours. You have previously determined that the planet orbits 240000000 km from its star with a period of 500 Earth days. Once on the surface you find that the free-fall acceleration is 11.8 m/s22. What is the mass of the planet?

What is the mass of the star?

Answer 1

mass of the planet

from g=GM/R^2

where G is newtonian grav cst, M the mass of the planet, R the radius and g thelocal accel due to grav

solving for M:

M=gR^2/G=11.8*(8.5*10^6)^2/(6.67x10^(-11))

M=1.27*10^25 kg

b.)

mass of the star

from Kepler's 3rd law (or the procedure that derives the law)

equate grav force to centripetal force

GMm/r^2=mv^2/r

M=mass of star

m=mass planet

r=size of orbit

v=orbital speed

this becomes M=v^2r/G

v=circumference of orbit/time = 2 pi r/time

v = 2 *3.14 * 2.4*10^11/500days * 86,400sec/day

v = 34906.85 vm/s

M = (34906.85)^2*2.24*10^11/(6.67*10^-11)

M = 4.09*10^30 kg