1 - You are visiting planet Xena and you find that a 3.3 kg rock falls 14.2 meters in 1.811 seconds when dropped from rest. Calculate the strength of the gravitational field on the surface of Xena.

2 - If Xena has a radius of 1.288*106 meters, find the mass of Xena.

1 - The acceleration of the rock is solve using the formula:

y = vot + 0.5gt²

14.2 = 0 + 0.5 g (1.811) ²

g = 8.659

The weight of the rock is the strength of the gravitation field on the surface of Xena, so:

F = mg

F = 3.3 (8.659) = 28.576 N

2-

Using the gravitational force formula:

F = G m₁ m₂ / r²

28.576 = 6.67 x 10 ⁻¹¹ (3.3) m₂ / 14.2²

m₂ = 2.618 x 10¹³ kg