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## Homework Statement

If a satellite in orbit changes it's orbiting radius to 4 times its initial one, how does it's velocity change?

I get different answers by using Newton's Law of gravitation and conservation of angular momentum.

## Homework Equations

[itex]F = \frac{G M m}{R^2}[/itex]

[itex]a_c = \frac{v^2}{R}[/itex]

[itex]L=\mathbf{r} \times \mathbf{p}[/itex] is conserved.

## The Attempt at a Solution

one way uses Newton's gravitation equation to get v=[itex]\sqrt{\frac{GM}{R}}[/itex] so that we see that quadrupling R halves the speed. However, using conservation of angular momentum [itex] m v_i R_i = m v_f R_f[/itex] we see that by setting the final radius to 4 times it's initial, the final speed decreases by a factor of 4. Why don't these results agree?