1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Recursive Projectile To Explicit Formula

  1. Nov 25, 2009 #1
    1. The problem statement, all variables and given/known data

    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.

    2. Relevant equations

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

    3. 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 :)
  2. jcsd
  3. Nov 25, 2009 #2


    User Avatar
    Science Advisor

    I am a bit confused by the fractions on the right side. Is that
    [tex]r_n- \frac{Mv^2}{r_n}\frac{GP}{r_n^2}[/tex]?

    Why not just
    [tex]r_n- \frac{MGP v^2}{r_n^3}[/tex]?

  4. Nov 25, 2009 #3
    I'm sorry there should actually be a - inbetween the radius and G not a *. Thanks for taking the time to reply though.

    [tex]r_n_+_1 = r_n- \frac{Mv^2}{r_n}-\frac{GP}{r_n^2}[/tex]

    (I stole your LaTex by the way:biggrin:)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Recursive Projectile To Explicit Formula
  1. Explicit formula (Replies: 6)