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: Kepler's Second Law

  1. Jan 10, 2010 #1
    1. The problem statement, all variables and given/known data

    I have to prove that A1=A2, or the fact that planets will sweep out equal areas in equal amounts of time. The planet I have to do this for is Pluto. Basically, I need help finding the area it "sweeps out" over any length of time of my choosing.

    2. Relevant equations

    major axis = 11.8 x 10^9 km
    eccentricity = .25
    minimum orbital velocity = 3.7 km/s

    3. The attempt at a solution

    So far, I've found the distance of the perihelion and the aphelion.

    To do this I did: eccentricity = distance b/w foci / major axis

    then i solved for the foci by doing: dis b/w foci = .25 * 11.8e9

    that gave me the distance between the foci, so I was able to find out that the perihelion is 4425000000 km away and the aphelion is 7375000000 km.

    Now do I just make a triangle for each with the legs being the distance away and the other being time traveled. It's hard to explain, but this picture shows it well:

    http://outreach.atnf.csiro.au/education/senior/cosmicengine/images/cosmoimg/kepler2ndlaw.gif [Broken]

    So basically, how do I prove that those two areas equal with the info I now have

    Any help would be appreciated.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jan 10, 2010 #2
    I believe this equation may help

    Area=1/2 x (Distance to sun) x (Current Velocity) x (Time)

    so would it be

    (.5)(perihelion dis)(???)(anything)


    (,5)(aphelion dis)(???)(anything)

    I put "???"'s in the velocity spot because I dont know how to find the velocity
  4. Jan 10, 2010 #3
    I just noticed that it gives me Pluto's minimum orbital velocity at 3.7 km/s. So would plugging that into the formula above, the area one, give me the area of the aphelion (since it would be going slowest then)? Also, how would I determine the velocity of the perihelion.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook