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Math Help - need help!!

  1. #1
    Junior Member sweet's Avatar
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    need help!!

    hi
    how can i proof :
    <br />
v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2}<br />
    where  v =(v_{Ap}^2 + v_{peri}^2)^{1/2}

    if the planet orbit on ellipse ???
    Last edited by CaptainBlack; May 23rd 2006 at 02:49 AM.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sweet
    hi
    how can i proof :
    <br />
v=(mu/a)^{1/2} (1+e cosE/1-e cosE)^{1/2}<br />
    where  v =(v_{Ap}^2 + v_{peri}^2)^{1/2}

    if the planet orbit on ellipse ???
    A bit more explanation of what the symbols stand for is needed, also
    we are guessing what you have been asked to prove, I assume it is:

    <br />
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}<br />

    but that leaves us guessing is mu supposed to be \mu?

    Is e the eccentricity? a the semi-major axis?

    Also what is E?

    We can guess but it is just making it more work for the helpers here.


    RonL
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  3. #3
    Junior Member sweet's Avatar
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    ok

    mu = <br />
\mu<br />

    e= the eccentricity
    a= the semi-major axis
    E=the eccentric anomaly

    we want to proof
    <br />
v=(\mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}<br />
    if the planet orbit on ellipse ???
    where
    <br />
v =(v_{Ap}^2 + v_{peri}^2)^{1/2}<br />


    Thanks for helping me!
    Last edited by CaptainBlack; May 23rd 2006 at 04:27 AM.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by sweet
    ok

    mu = <br />
\mu<br />

    e= the eccentricity
    a= the semi-major axis
    E=the eccentric anomaly

    we want to proof
    <br />
v=(\mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}<br />
    if the planet orbit on ellipse ???
    where
    <br />
v =(v_{Ap}^2 + v_{peri}^2)^{1/2}<br />


    Thanks for helping me!
    Since the eccentric anomaly is a variable depending on the point of the
    planet in its orbit and v as defined here is a constant, as are e mu and a
    this cannot be true for almost all values of eccentricity.

    Or have I misunderstood something?

    RonL
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  5. #5
    Junior Member sweet's Avatar
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    E divined like in the graph


    and v isn't constant it's a Velocity
    Attached Thumbnails Attached Thumbnails need help!!-55.jpg  
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by sweet
    E divined like in the graph


    and v isn't constant it's a Velocity
    What's this:

    <br />
v =(v_{Ap}^2 + v_{peri}^2)^{1/2}<br />
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  7. #7
    Junior Member sweet's Avatar
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    v_{AP} is Aphelion Velocity
    v_{peri} is pericentre Velocity

    and v is aggregate of v_{AP} ,v_{peri}

    so
    <br />
v^2=v_{peri}^2+v_{AP}^2<br />
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by sweet
    v_{AP} is Aphelion Velocity
    v_{peri} is pericentre Velocity

    and v is aggregate of v_{AP} ,v_{peri}

    so
    <br />
v^2=v_{peri}^2+v_{AP}^2<br />
    which would make it a constant velocity.

    RonL
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  9. #9
    Junior Member sweet's Avatar
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    Quote Originally Posted by CaptainBlack
    which would make it a constant velocity.

    RonL

    why u say it's constant

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  10. #10
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sweet
    v_{AP} is Aphelion Velocity
    v_{peri} is pericentre Velocity

    and v is aggregate of v_{AP} ,v_{peri}

    so
    <br />
v^2=v_{peri}^2+v_{AP}^2<br />
    I know what a "perihelion" velocity would be. What is a "pericenter" velocity?

    -Dan
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  11. #11
    Junior Member sweet's Avatar
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    Thumbs down

    Quote Originally Posted by topsquark
    I know what a "perihelion" velocity would be. What is a "pericenter" velocity?

    -Dan


    i'm sorry it's Perihelion velocity not pericenter velocity
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  12. #12
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sweet


    i'm sorry it's Perihelion velocity not pericenter velocity
    In that case I agree with CaptainBlack. The perihelion and aphelion speeds are constant (meaning they don't vary with how many orbits have occurred.) Thus v^2 as you have defined it will also be constant. Since the eccentric anomaly changes over the course of the orbit (if I'm reading your diagram correctly) there must be an error in your formula.

    -Dan
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  13. #13
    Junior Member sweet's Avatar
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    Quote Originally Posted by topsquark
    In that case I agree with CaptainBlack. The perihelion and aphelion speeds are constant (meaning they don't vary with how many orbits have occurred.) Thus v^2 as you have defined it will also be constant. Since the eccentric anomaly changes over the course of the orbit (if I'm reading your diagram correctly) there must be an error in your formula.

    -Dan
    ok i agree with u that v is aconstant ...but the problem is how can i proof the formula
    <br />
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}<br />

    it,s verey hard ....
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  14. #14
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by sweet
    ok i agree with u that v is aconstant ...but the problem is how can i proof the formula
    <br />
v=(mu/a)^{1/2} \left(\frac{1+e\ \cos(E)}{1-e\ \cos(E)}\right)^{1/2}<br />

    it,s verey hard ....
    v is constant but E is not. The only way that formula can work is if you are calculating v for a particular point on the orbit (that is to say for a particular value of E), which we are not given.

    -Dan
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  15. #15
    Grand Panjandrum
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    Quote Originally Posted by topsquark
    v is constant but E is not. The only way that formula can work is if you are calculating v for a particular point on the orbit (that is to say for a particular value of E), which we are not given.

    -Dan
    No No No. v is now the speed of the planet as a function of eccentric anomaly.

    RonL
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