1. Not finding help here? Sign up for a free 30min 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!

Planets orbiting stars?

  1. Nov 8, 2012 #1
    1. The problem statement, all variables and given/known data
    A planet orbits a star of mass M = (3*10^30)kg in an elliptical orbit.
    The planet is r_1 = (0.8*10^11)m from the star at its closest approach (periastron),
    and r_2 = (1.6*10^11)m at its furthest (apastron).
    (G = (6.67*10^-11) Nm^2kg^-2)

    (a) Calculate the semi-major axis a, and hence the period T of the planet's orbit.

    (b) Use the polar equation of an ellipse to calculate the orbital eccentricity, e.

    (c) Use conservation of energy and the total orbital energy per unit mass of the planet (epsilon = -GM/2a),
    to calculate the orbital speeds at the periastron and apastron, v_1 and v_2.

    (d) Use your values of v_1 and v_2 to show that the orbital angular momentum per unit mass is the same at periastron and apastron.


    2. Relevant equations
    r = (l)/(1+ecos(θ))
    a = (l)/(1-e^2)
    h=sqrt(GMl)
    ε=-(GM)/2a
    v=rω
    1/2(dr/dt)^2 + (h^2)/(2r^2) - (GM)/r = -(GM)/(2a)


    3. The attempt at a solution
    So far I have:
    (a) a = (r_1 + r_2)/2 = (1.2*10^11)m and T = sqrt((4pi^2(a^3))/(GM)) = (18464102.11)s = (213.7)days

    (b) r = (L)/(1 + e*cos(theta)) and a = (L)/(1-e^2) => L = a(1-e^2) => r = (a(1-e^2))/(1+e*cos(theta))
    get a quadratic in e and solve to get e = 1/3

    (c) not getting anywhere. know that 1/2(dr/dt)^2 + (h^2)/(2r^2) - (GM)/r = -(GM)/(2a)

    (d) no idea
     
  2. jcsd
  3. Nov 8, 2012 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    (c) hint: total energy is the sum of kinetic and potential energy.
    (d) having got the speeds in (c) use the angular momentum formula.
     
  4. Nov 8, 2012 #3
    Haha thanks, I worked it out in the end - was being stupid.
    Ended up with v_1 around 58km/s and v_2 around 29km/s. Then for (d) showed that specific angular momentum was the same for both periastron and apastron using r_1v_1 =r_2v_2
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook