Question

Your spaceship lands on an unknown planet. To determine the characteristics of this planet, you drop a 1.50 kg wrench from 7.00 m above the ground and measure that it hits the ground 0.811 slater. You also do enough surveying to determine that the circumference of the planet is 6.24×10⁴ km .

1.) What is the mass of the planet, in kilograms?

2.) Express the planet’s mass in terms of the earth’s mass.

Answer 1

Acceleration of the wrench:

s = ut +0.5a*t²

7 = 0 + 0.5*a*0.811²

7 = 0.5*0.657*a

a = 7/0.3288605

a = 21.2856 m/s²

given circumference = 6.24 x 10⁴ km = 6.24 x 10⁷ km = 2*pi*r

r = (6.24 x 10⁷)/(2*3.1415)

r = 9.931 x 10⁶ m

and we have

a = GM/r²

M = (a*r²)/G

M = [21.2856*(9.931 x 10⁶)²]/6.673 x 10^-11

M = 3.1461122 x 10²⁵ kg

M = 3.14 x 10²⁵ kg

part 2

mass of earth = 5.972 x 10²⁴ kg

planet’s mass in terms of the earth’s mass. = (Me*3.14 x 10²⁶)/5.972 x 10²⁴

planet’s mass in terms of the earth’s mass. = 5.2681*Me

planet’s mass in terms of the earth’s mass. = 5.27 times of earth's mass