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Radius of an Ellipse

  1. Dec 22, 2003 #1
    "Radius" of an Ellipse

    a couple things i'm trying to fit together.

    First: a planet orbits a sun (positioned at one focus) at an certain speed. At any given time of year it will be at that same spot year after year... i have little clue how to make that work or solve for it.

    Second: i need to take that point and deterimine what it's distance is from the sun.

    Note: i am a highschool graduate, but did only average in mathematics and conics was most certainly not a strong point, however i have a bascic understanding.

    Purpose: i need to determine the distance a planet is from it's sun for a 1 year cycle to determine the amount of energy it will recieves on any given day.

    thx
     
  2. jcsd
  3. Dec 22, 2003 #2
    Re: "Radius" of an Ellipse

    That only works if your definition of 'year' is the time it takes for the planet to go around the sun once. But that's circular reasoning and not very interesting...


    You might want to study Kepler's laws
     
  4. Dec 22, 2003 #3

    HallsofIvy

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    Make what work? Solve for what? What exactly are you trying to do? Do you know the equation for the ellipse? Do you have it in terms of time?

    If you have the equation for the ellipse in a coordinate system with the sun at the origin it's easy.

    If you know the maximum and minimum distances from the sun to the planet, then you can set it up the equation of the ellipse:
    x2/a2+ y2/b2= 1.

    You're not completely out of the woods after you have done that. You still need to associate each point with time. You say "at a constant speed". You do understand that planets do not maintain a constant speed as they orbit the sun? (They move faster as the get closer to the sun, slower as they move away.)
     
    Last edited: Dec 23, 2003
  5. Dec 22, 2003 #4
    well, i suppose speed is less relavent... hmm. uh well, ok i'll try to explain.

    i want to be able to model any planet orbitting any star at any distance. so i need to be able to have a general equation and have numbers plug into that and then get a nice answer.

    first thing i need to figure out is how do i determine the distance the planet is from a star if i know it's major and minor axis.

    i sorta re-thought the orbital speed and that's less important, because if i use a cartesian plane then it will move around the star focus at X-degrees per day kinda thing i guess.. and that would stay constant.. so orbital speed is not important really.

    i know the quation of an ellipse is (a^2/x^2)+(b^2/y^2)=1 but i don't really understand how to use that or re-arrange it to determine any sort of distance equation (or find a point at a certain time of year or in my case a certain angle in relation to the sun focus).

    so i guess what i'm saying is that if the planet is at 180 degrees, then it's on the left side of the major axis (of a horizontal ellipse), and is lined up with both foci. i don't know how to figure out how close the star is though (if the star is the left focus). nor do i know how to determine the distance at any other point in the orbit (or degree compared to the left focus, where the right side of the x-axis would be 0 degrees and the left side would be 180)...

    i hope i didn't confuse anyone more.. i just don't have an equation, so there are no specific numbers. if you must, you can use an ellipse with a minpr axis of 3 and a mojor of 4, the star is the left focus of a horizontal ellipse. it would be much appreciated if you could give me any sort of general equation(s) to find the distance the planet is from the sun at anypoint of the ellipse and also determine that point based on any sort or method of a "time of year" scale
     
  6. Dec 24, 2003 #5

    HallsofIvy

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    Generally, "orbital mechanics" is done in polar coordinates with the origin at the sun. In polar coordinates the equation of an ellipse (in fact, any conic section) is

    r2= a2(1- e2)/(1- e2cos2θ)

    where (a,0) is the point where the orbit crosses the positive x axis (θ= 0) and e is the eccentricity of the orbit.
     
  7. Dec 25, 2003 #6
    ok thx, i'll look up stuff on orbital mechanics... i'll ask if i have more questions. thnks for the help
     
  8. Dec 25, 2003 #7

    Hurkyl

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    That's incorrect too...
     
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