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!

Homework Help: 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,

    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

    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.

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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    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


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

  8. May 27, 2015 #7


    User Avatar

    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!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted