Question

In a galaxy far far away, an imperial probe is characterizing distant planets. The first planet has the probe orbiting with a period of 2.65days while orbiting the planet with an orbital radius of 1.05×10^8m. (a) What is the mass of this planet? The next planet takes the probe 5.92 days to orbit at an orbital radius of 2.25×10^8m. (b) What is the mass of this planet?

Answer 1

here,

a)

Time period , T = 2 * pi * sqrt(r^3/(G*m))

2.65 days = 2 * pi * sqrt(r^3/(G*m))

2.65 * 24 * 60 * 60 = 2 * pi * sqrt(r^3/(G*m))

2.65 * 24 * 60 * 60 = 2 * pi * sqrt((1.05 * 10^8)^3/(6.67 * 10^-11 * m))

solving for m

m = 1.3 * 10^25 kg

b)

Time period , T = 2 * pi * sqrt(r^3/(G*m))

5.92 days = 2 * pi * sqrt(r^3/(G*m))

5.92 * 24 * 60 * 60 = 2 * pi * sqrt(r^3/(G*m))

5.92 * 24 * 60 * 60 = 2 * pi * sqrt((2.25 * 10^8)^3/(6.67 * 10^-11 * m))

solving for m

m = 2.6 * 10^25 kg