Question

You and your survey crew have landed on an unknown planet. Sensors show that the planet has a radius of 3400 km. You launch a probe straight up from the north pole of the planet. The launch speed of the probe is 2.4 km/s and climbs to an altitude of 1023 km. Find the mass of the planet. You may ignore air resistance and planetary rotation.

Answer 1

Initial speed of the probe, U = 2.4 km/s = 2400 m/s

vertical distance travelled, H = 1023 km = 1023000 m

use the expression to know the gravitational acceleration -

V^2 = U^2 + 2*g*H

=> 0 = 2400^2 + 2*g*1023000

=> g = -2400^2 / (2*1023000) = 2.815 m/s^2

Now, the gravitational accleration for a palnet is -

g = G*M/R^2

where M = mass of planet

R = radius of the planet = 3400 km = 3400000 m

put the values -

2.815 = (6.674 x 10^-11 x M) / 3400000^2

=> M = (2.815 x 3400000^2) / (6.674 x 10^-11) = 4.876 x 10^23 kg.