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Ratio between change in Energy(Gravitational Potential)

  1. Oct 4, 2008 #1
    Ratio between change of Energy(Gravitational Potential)

    I would like some assistance in understanding the ratio of change in energy between two objects.

    In this case, if object A goes from rest to an altitude (h) above earth but does not begin an orbit versus object B goes from rest to the same altitude and then proceeds to orbit the earth.

    The variables are as follows:
    Re=radius of earth
    h=altitude
    G=universal gravitational constant
    M=mass of earth
    m=mass of object(A=B, also known as A and B are the same)

    I'll need to transcribe my findings, which until now when comparing to my professors simplication are slightly off, a little later.

    I was told my error might occur in the initial change of energies for the respective objects, and this may very well be true. However, I did come across great challenges at first when trying to find a GCF for the variable laden energies.

    What I've been using prior to simplication:
    Object A = change in Eg = Eg2 - Eg1
    Object B = change in total energy = Ek - Eg1

    Eg as known is a negative value while Ek is positive.

    Any help is appreciated and I understand little help may be offered since I've yet to put up the actual attempts, but when I have more time I'll transcribe my most recent effort into mspaint.
     
    Last edited: Oct 5, 2008
  2. jcsd
  3. Oct 5, 2008 #2
    A good turnout.
    Ok, here's my most recent work.

    [​IMG]


    Am I not correct in choosing the E2 and E1 for the object heading into orbit?
    I choose Total Orbital Energy (-Ek) since that is energy required to orbit for object B. Although, wouldn't it be possible to put change of energy for the object heading to altitude h as simply Ek instead of -Ek-(Eg)? I would really like some input on this.


    Also, it's been a long time since I did any Calculus and or math in general, which may explain why I have trouble with simplification.

    Some ratios, albeit told as wrong by my professor include:

    [​IMG]

    With the last in the line being the earliest example and least correct.

    As mentioned, the first two were said to be nearly correct, although it's been a few days since I spoke to her so I cannot say which is more correct.

    Again, help is appreciated. Thank you.
     
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