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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)

    then

    (,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.
     
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