Question

4- how far above the earth's surface, will the acceleration of gravity be half

Answer 1

Answer:

Gravity (Accel const) rises linearly from the center of a planet to its surface where all of its mass is acting on your mass.

After lift off from the surface, gravity then drops by the inverse square of the distance from the planet’s center.

The mass of the earth is about 6E24 kg and the earth radius (Re) is 6371 km which gives G= 9.8m/s/s as the acceleration constant at earth’s surface.

Above the earth by its radius again (2Re), gravity acceleration is a fourth of that at the surface g= Me*G/4 = (1/4) * 9.8m/s/s = 2.45m/s/s

Half the gravity (g= Me*R/2) happens at an altitude of sqrt(2) * Re above the surface: 1.414 * 6371km = 8919.4 km altitude above the surface.

Here is a graph of the gravity curve in metric units: at Re the gravity is G (just under 10m/s/s) and at an altitude of 2Re, the earth’s radius (6371 km) above its surface, the gravity is a fourth of its acceleration at the surface (Re) and at an altitude of 8919.4 km above the surface the gravity is half of the surface value.

Explanation: