- #1

TheMaster...

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## Homework Statement

If a projectile orbits around a planet and lands after x cycles of the equation:

radius[n+1] = radius[n] - (M* v^2 / radius[n]*G*P/radius[n]^2)

at a final radius of C. What is the necessary v?

The only variable that isn't known at the time of solving is v.

Basically I think I need to solve in terms of v but in order to do that I need to make the recursive formula into an explicit one but I can't figure out how.

## Homework Equations

radius[n+1] = radius[n] - (M* v^2 / radius[n]*G*P/radius[n]^2)

## The Attempt at a Solution

I tried writing down the sequence to find a simpler pattern with no luck. Especially since even that seems to change drastically if I change the constants such as x (the number of cycles). I tried solving it as if it were a normal equation but couldn't figure out how to get rid of the radius[n+1] term to do that and tried setting it to C (the target radius) to radius[n] (so I could ignore it) and to 0 (seemed a better way of ignoring) all with no success seemingly. Setting to radius[n] led to a cubic explicit equation but that doesn't make as much sense as the quadratic equation from setting it to C since we are dealing with motion that is similar to a conic section which is where I derived the original recursive equation from. So how do I start, or how do I make it explicit so I can solve the rest of it.

This isn't a Real homework problem so much as a problem that I desperately need a solution to and couldn't find the right section.

Pointers or solutions are soooo welcome. Thanx :)