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Calculating Speed of Asteroid at its Perihelion

  1. May 27, 2015 #1
    This is not part of my coursework; I am preparing for an exam and this is a question from a past paper to which answers are not given.

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

    An asteroid orbiting the sun has its perihelion at 1AU and its aphelion at 3AU. Calculate the speed of the asteroid at its Perihelion.

    2. Relevant equations
    Kepler s
    Universal Gravitation
    UCM ?
    3. The attempt at a solution

    I am a bit stuck on this. First I calculated its semi-major axis as I assume it will be needed,

    [itex]
    a=\frac{r_a + r_b}{2}=\frac{(1.49 \times 10^{11})+(3 \times 1.49 \times10^{11}}{2} = 2.98 \times 10^{11} m
    [/itex]

    Could I use the uniform circular motion equation [itex]F_c= \frac{mv^2}{r}[/itex] in this situation? I ask as its an a moderately eccentric ellipse.

    I was thinking of equating that to the force of gravity to get [itex]v[/itex], but if I could use it in this situation, what would I use as [itex]r[/itex], the semi-major axis, or 1AU?

    If I cannot use that UCM equation then I am more stuck than I realised, so would appreciate any help.

    Thanks,
     
    Last edited: May 27, 2015
  2. jcsd
  3. May 27, 2015 #2

    TSny

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    Homework Helper
    Gold Member

    Since the motion is not UCM, then you would need to justify using the UCM equation with the semi-major axis. I'm pretty sure it won't lead to the right result.

    Can you think of a couple of quantities that are conserved in the orbital motion?

    What units are you using for distance? The 1015 factors look strange to me.
     
  4. May 27, 2015 #3
    Sorry, I remembered incorrectly, it is 1011 in metres.

    Angular momentum? But I cannot see how I can work with that, not knowing the asteroids shape etc.
     
  5. May 27, 2015 #4

    TSny

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    Orbital angular momentum is conserved. Treat the asteroid as a point particle.

    You will need a second conserved quantity.
     
  6. May 27, 2015 #5
    Ok thanks. Have not done many problems in angular momentum, could I use the Earth?

    EDIT: Typo in op, the aphelion is 3AU, not 2.
     
  7. May 27, 2015 #6

    TSny

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  8. May 27, 2015 #7

    gneill

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    Staff: Mentor

    Hi FaraDazed. If I might offer a hint: what do you know about the relationship between the semi-major axis of an orbit and its specific mechanical energy?
     
  9. May 27, 2015 #8
    Thanks for the link. I didn't think I could, I just couldn't think what else, as it's not like it has any moons (the only question i did before with regarding the Earth Moon system.
     
  10. May 27, 2015 #9
    Nothing until now, did not know there was a link. But after doing a quick google search I found this http://en.wikipedia.org/wiki/Vis-viva_equation , thanks!
     
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