Question

While visiting Planet Physics, you toss a rock straight up at 10 m/s and catch it 2.3 s later. While you visit the surface, your cruise ship orbits at an altitude equal to the planet's radius every 210 min .

a)What is the mass of Planet Physics?

b)What is the radius of Planet Physics?

Answer 1

Step 1 find Planet physics gravity

using kinematic equation

vf = vi - g*t

g = (vi - vf)/t

vi = V, vf = -V

g = 2V/t = 2*10/2.3 = 8.695 m/sec^2

Step 2: Use kepler's law

T^2 = 4*pi^2*r^3/GM

altitude = r = R + R = 2R

T^2 = 32*pi^2*R^3/GM

M = 32*pi^2*R^3/(G*T^2)

T = 210 min = 1260 sec

Now use newton's law of gravitation

m*g = GMm/R^2

M = g*R^2/G

Use both equations

g*R^2/G = 32*pi^2*R^3/(G*T^2)

R = g*T^2/(32*pi^2)

R = 8.695*12600^2/(32*pi^2) = 4.37*10^6 m

Step 3:

M = g*R^2/G

M = 8.695*(4.37*10^6)^2/(6.674*10^-11)

M = 2.488*10^24 Kg