Results 1 to 3 of 3

Math Help - need help with equilibrium question!

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    39

    need help with equilibrium question!

    A satellite probe is put into an orbit around a distant planet such that at apoapsis its orbital radius is 4989 km and at periapsis its orbital radius is 2959 km. If it has a speed of 1.36 km/s at apoapsis what is its speed at periapsis?

    [Specify units of 'km/s' or 'm/s' in your answer (without quotes).]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2008
    From
    West Malaysia
    Posts
    1,261
    Quote Originally Posted by jddery View Post
    A satellite probe is put into an orbit around a distant planet such that at apoapsis its orbital radius is 4989 km and at periapsis its orbital radius is 2959 km. If it has a speed of 1.36 km/s at apoapsis what is its speed at periapsis?

    [Specify units of 'km/s' or 'm/s' in your answer (without quotes).]
    HI

    In an orbital system , the gravitational force=centripetal force from the energy principles again .

    \frac{GMm}{r^2}=\frac{mv^2}{r} ,

    where G is the gravitational constant , M is the mass of planet , m : mass of satelite , r : orbitral radius

    v^2=\frac{GM}{r}

    Since GM are both constants , v^2\propto \frac{1}{r}

    v\propto \frac{1}{\sqrt{r}}

    At apoapsis , r=4989 , v=1.36

    At periapsis , r=2959 , v=??

    Now substitute appropriately ,

    1.36 \propto \frac{1}{\sqrt{4989}} ----- 1

    v\propto \frac{1}{\sqrt{2959}} ---- 2

    Divide them to get v which is approximately 1.77 km/s
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,108
    Thanks
    970
    Quote Originally Posted by jddery View Post
    A satellite probe is put into an orbit around a distant planet such that at apoapsis its orbital radius is 4989 km and at periapsis its orbital radius is 2959 km. If it has a speed of 1.36 km/s at apoapsis what is its speed at periapsis?

    [Specify units of 'km/s' or 'm/s' in your answer (without quotes).]
    ar periapsis and apoapsis, the velocity and position vectors are perpendicular. use conservation of angular momentum ...

    mv_ar_a = mv_br_b

    v_a = \frac{v_b r_b}{r_a}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question about unstable equilibrium
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: May 24th 2011, 11:06 AM
  2. Replies: 6
    Last Post: November 28th 2010, 04:56 AM
  3. Replies: 1
    Last Post: December 1st 2009, 05:41 AM
  4. Replies: 0
    Last Post: November 27th 2009, 04:40 PM
  5. Equilibrium Point Question
    Posted in the Math Software Forum
    Replies: 0
    Last Post: December 9th 2007, 03:24 PM

Search Tags


/mathhelpforum @mathhelpforum