Non-Uniform Acceleration

Changes in gravitational acceleration

Some sounding rockets are very powerful, reaching altitudes of 1000 miles or more. The factor that keeps them as "sounding" rockets is that they never achieve orbital velocity (~17,400mph @ 100miles above sea level.) Below is a picture of a night launch of an Orion Rocket. These rockets achieve altitudes of 50-60 miles.

Figure 1 Orion Night Launch. The rocket is UAF’s own TR-1 (Test Rocket #1)

The gravitational force between two bodies is given as follows:

Where m1 is the mass of the rocket, and m2 is the mass of the Earth. R is the distance between the rocket and the center of the earth. G is the Newtonian Gravitational constant, equal to: 6.67 x 10-11 N•m2/kg2. Thus using this equation, scientists can determine the exact force of gravity acting on a rocket at all times. They then can solve the integral of this to get an average, and also a theoretical altitude.