A spacecraft begins at a distance of 8.42km above an asteroid's surface with an outward velocity of 5040. (the asteroid's gravity is negliable; onboar rockets provide all acceleration here. That gravity does define the "down" in this problem) * assuming constant acceleration, what acceleration is needed for the maximum height of the spacecraft 12.20km?

56.25 N

Explanation:

Given,

Radius of the planet, r = 1000 km

Gravitational force, F = 100 N

Initial distance from the planet, d = 500 km

Final distance from the planet, D = 1000 km

Lets assume, mass of planet = M

mass of the object = m.

As per the gravitational law, the force due to gravity is given as

where, G = gravitational constant

R =  distance between the two objects.

Case 1: when the object is at a distance of 500 km from the planet,

Here, R = 1000 + 500 = 1500 km, so

Case 2: when the object is at a distance of 1000 km from the planet, so

now, R = 1000 + 1000 = 2000 km

Now the gravitational force, F' will be

Thus, the gravitational force will now be reduced to 56.25 N.