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: Comet in Parabolic Orbit

  1. Apr 11, 2012 #1
    1. The problem statement, all variables and given/known data

    A comet of mass m moves in a parabolic orbit in the ecliptic plane (the plane of Earth’s
    orbit), so its perihelion distance ρ (its closest distance to the Sun) is less than Ro (the orbital distance of the Earth around the Sun) and occurs when θ = 0 for the comet. (The comet will cross the orbit of the Earth twice- once moving inward and once moving outward.) In terms of p and Ro, find an expression for θ at the two times when the comet crosses the orbit of the Earth. Assume: m << Msun.

    2. Relevant equations

    E = .5m(dr/dt)^2 + .5l^2/(μr^2) - GmM/r

    where l is the angular momentum and μ is the reduced mass.

    3. The attempt at a solution

    Alrighty, so far I know that m is nothing in comparison to Msun, so μ≈m. At perihelion ρ, θ is zero, and dr/dt=0, so the velocity there Vmax = ρ(dθ/dt), and l = mrvsin(π/2)= mρ^2(dθ/dt). Plus, this being a parabolic orbit, E = 0.

    I've been trying to put that all together given that l is conserved and E remains zero at all distances:

    E = 0 = .5m(dθ/dt)^2 - GmM/ρ = .5m(dr/dt)^2 +.5m[ρ(dθ/dt)/Ro]^2 - GmM/Ro

    but I end up with a bunch of dr/dt and dθ/dt variables that I can't figure out how to eliminate... I just don't see how I can isolate and solve for θ at Ro. It seems like my whole approach is probably wrong. :/

    Any help from you good folk would be MUCH appreciated.

    EDIT: Whoops this was actually super simple. I'd just forgotten that the semi latus rectum = 2p= Ro(1+εcosθ), and that epsilon for the parabola ia 1.
    Last edited: Apr 11, 2012
  2. jcsd
  3. Mar 27, 2014 #2
    Assuming that your edit is correct, what ends up being the solution? I am working on the same problem, and I am lost myself as well! Some guidance would be wonderful! Thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted