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Speed at a certain distance from the sun

  1. Mar 21, 2015 #1
    Hello! These problems of mine are due in the morning. I'm not sure whether or not I will be able to figure them out in time, but I do need to understand the process in order to prepare for my finals. So any help would be much appreciated! Thank you.

    1. The problem statement, all variables and given/known data

    A comet is in an elliptical orbit around the Sun. Its closest approach to the Sun is a distance of 4.6 multiply.gif 10^10 m (inside the orbit of Mercury), at which point its speed is 9.1 multiply.gif 10^4 m/s. Its farthest distance from the Sun is far beyond the orbit of Pluto. What is its speed when it is 6 multiply.gif 10^12 m from the Sun? (This is the approximate distance of Pluto from the Sun.)
    speed

    2. Relevant equations

    KSun,f + Kcomet,f + Uf = KSun,i + Kcomet,i + Ui

    3. The attempt at a solution

    I set KSun to 0 for both sides since the sun isn't moving.

    Then I set up this equation:

    (1/2)Mv2comet final+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet final=(1/2)Mv2comet initial+(6.7X10-11)(1.989x1030mass of the sun)/(distance)comet initial

    And I isolated one of the velocities:

    (vfinal2/2)+((6.67x-11)((1.989x1030)/6x1012)=((1/2)(9.1x104)2)+((6.67x10-11)(1.989x1030)/4.6x1010)

    vfinal=sqrt(2*((1/2)(9.1x104)2)+((6.67x10-11)-((6.67x-11)((1.989x1030)(1.989x1030)/4.6x1010))

    And I got 75,656 m/s, which isn't the correct answer. :(
     
  2. jcsd
  3. Mar 21, 2015 #2

    ehild

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    Homework Helper
    Gold Member

    The equation is wrong. Check the sign of PE.
     
  4. Mar 22, 2015 #3

    tms

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    There's more wrong with the PE than just the sign.
     
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