Gravitational force question

Question

A 60.0 kg mass is located 1500 km above the surface of the Earth. The acceleration due to gravity on the Earth’s surface is g= 9.80m/s² and the radius of Earth is 6.37 x 10⁶ m.

(a) What is the mass of the 60.0 kg object at an altitude of 1500 km?

(b) What is the acceleration due to gravity at an altitude of 1500 km?

(c) What is the magnitude of the centripetal acceleration of a satellite orbiting at an altitude of 1500 km?

(d) At what distance above the Earth’s surface would the acceleration due to gravity be 1/5 of its value on the surface of the Earth?

Answer 1

a) mass doesn't change ever (unless the object is leaking somehow), it's an inherent property of matter

b) a = GM_Earth/((1500000+r)²) because its the force of gravity equation but without the objects mass becasue F=ma so F/m = a.

c) a_c = v²/(r+1500000) and I would prove that but I'd need to draw so that should just be memorized.so set that equal to the equation from b and solve that for v ... this works because in a circular orbit acceleration is centripetal, you're going around in a circle imagine swinging a ball around on a rope only now that rope is gravity.

d) a @ surface = 9.8 so you want to find where a = 9.8/5 = 1.96 so set 1.96 = GM_Earth/(r+h)² and solve for h