1. Not finding help here? Sign up for a free 30min 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!

Related Rates, elliptical motion

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    A satellite is in an orbit around earth. The distance from the center of the earth is described by

    r= 4995/(1+.12cos@) R earth= 3960 mi

    find the rate at which the altitude is changing at the instant where @=120 degrees. d@/dt= 2.7 degrees/min



    2. Notes
    altitude equals r - (R earth)

    "@" describes the angle the satellite forms with the Perigee of earth (the closest point)


    3. The attempt at a solution

    a = r - (R earth) = 4995/(1+cos@) - 3960

    da/dt= [-4995(-sin@)d@/dt]/(1+cos@)^2

    by plugging in the values I get: ~ 46,700 mi/min

    The answer from back of book is 27.7 mi/min


    I do find it a mystery that the R earth is not used, that may be a key to solving it. Help!
     
  2. jcsd
  3. Oct 4, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Tclack! :smile:

    (have a theta: θ :wink:)
    erm :redface:

    what happened to .12? :cry:
     
  4. Oct 5, 2009 #3
    r=\frac{4995}{1+\frac{3}{25}cos{\theta}}

    \frac{dr}{dt}=\frac{374625sin{\theta}}{(3cos{\theta}+25)^{2}}\cdot\frac{d{\theta}}{dt}

    I am using radians, so be careful with the 2.7. That is \frac{3\pi}{200} rad.

    So, we get:

    \frac{dr}{dt}=\frac{374625sin{\frac{2\pi}{3}}}{(3cos{\frac{2\pi}{3}}+25)^{2}}\cdot\frac{3\pi}{200}=\frac{44955\sqrt{3}{\pi}}{8836}\approx 27.6843 \;\ \frac{mi}{min}

    The reason the R is not used is because the given equation has it incorporated and already gives the distance from the CENTER of the Earth.
     
  5. Oct 5, 2009 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Tclack! :smile:
    (you needed to type [noparse][tex] before and [/tex] after [/noparse] :wink: …)


    Sorry, but this is too difficult to check unless you show more of the steps. :redface:

    (and you have at least one minus sign wrong)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Related Rates, elliptical motion
  1. Elliptical Motion (Replies: 4)

  2. Related Rates (Replies: 2)

Loading...