# science

posted by .

how is this equation derived from the momentum principle?

In the near-Earth orbit the rate of change of momentum is (v/R)p = (v/R)mv

• science -

and how does it go from there to this
In the near-Earth orbit the rate of change of momentum is (v/R)p = (v/R)mv toward the center of the Earth, and this must equal the gravitational force GMm/R2, so
mv2/R = GMm/R2, and
mv2 = GMm/R.
Therefore in this orbit
K+U = (1/2)mv2 - GMm/R = -(1/2)GMm/R
This is a negative number reflecting the fact that this is a bound state. To minimize the work required to move the satellite far away, we want the final kinetic energy to be zero, and if it is far away the gravitational potential energy is also zero. Since the change in K+U is equal to the work we do, we have
0 - (-(1/2)GMm/R) = W, so
W = (1/2)GMm/R.

## Similar Questions

1. ### Science

We are studying energy my questions What happens to the momentum of a car when it comes to a stop?
2. ### Physics - drwls?

A 2000 kg truck traveling north at 38 km/hr turns east and accelerates to 55 km/hr. What is the change in the truck's kinetic energy?
3. ### Physics - Angular Momentum

When the angular momentum changes, the 'change' in the angular momentum vector (ie. dL) is ____. [a.] perpendicular to the torque vector. [b.] parallel to the angular momentum vector. [c.] parallel to the torque vector. .. im confused …
4. ### Science

Explain how a parachutist's loss of momentum on landing is consistent with the principle of conservation of momentum?

What is the ratio of the spin angular momentum of the Earth and its orbital angular momentum about the Sun. The mean radius of the earth is R_earth = 6400 km. The radius of the Earth's orbit is r_s = 1.5 * 10^8 km. For simplicity you …
6. ### physics

What is the ratio of the spin angular momentum of the earth and its orbital angular momentum about the sun. The mean radius of the earth is R=6400km. The radius of the earth's orbit is r=1.5*10^8km. You may assume the mass of the earth …