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Thread: Calculating orbital velocity

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    Junior Member Sp3ctre's Avatar
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    Calculating orbital velocity

    In question 26c of the 2015 HSC, the answers expected you to calculate orbital velocity by using Centripetal Force = Gravitational Force and then manipulating the equation in terms of velocity. Can you not just use the formula Orbital V = sqrt(GM/r) that's taught in the course immediately instead of deriving this equation from Fc and Fg?

    https://gyazo.com/fe725781429d1fc417b88457b4844ad6
    Last edited by Sp3ctre; 26 Oct 2017 at 2:58 PM.
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    Senior Member jazz519's Avatar
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    Re: Calculating orbital velocity

    Nope any formulas not on the sheet they provide, must be derived or you will lose marks
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    Re: Calculating orbital velocity

    The formula for orbital velocity isn't provided in the formula sheet though, so you're supposed to derive the equation to show the markers where the formula came from. That's what I've always been taught to do, anyway. Not sure if you'll get marks deducted for not doing it or not though.

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    Re: Calculating orbital velocity

    Oh, guess you do lose marks then.

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    Re: Calculating orbital velocity

    Thanks for the replies
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    Awesome Member clementc's Avatar
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    Re: Calculating orbital velocity

    Yeah, you need to derive it from scratch. This applies for escape velocity as well. It should be pretty straightforward anyway; takes literally 3 lines.

    For orbital velocity (you must have the first line as well):
    Fc = Fg
    mv²/r = GmM/r²
    v = sqrt (GM/r)

    For escape velocity (include first line):
    KE ≥ GPE
    ½mv² ≥ GmM/r (comparing just the magnitudes)
    v ≥ sqrt (2GM/r)
    pikachu975 likes this.



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    Re: Calculating orbital velocity

    Quote Originally Posted by clementc View Post
    Yeah, you need to derive it from scratch. This applies for escape velocity as well. It should be pretty straightforward anyway; takes literally 3 lines.

    For orbital velocity (you must have the first line as well):
    Fc = Fg
    mv²/r = GmM/r²
    v = sqrt (GM/r)

    For escape velocity (include first line):
    KE ≥ GPE
    ½mv² ≥ GmM/r (comparing just the magnitudes)
    v ≥ sqrt (2GM/r)
    Just a note for escape velocity, the first line would be Epi + Eki = Epf + Ekf
    and both Epf and Ekf are 0 therefore Eki = -Epi
    GMm/r = 1/2 mv^2
    v = sqrt(2GM/r)
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    Re: Calculating orbital velocity

    Quote Originally Posted by pikachu975 View Post
    Just a note for escape velocity, the first line would be Epi + Eki = Epf + Ekf
    and both Epf and Ekf are 0 therefore Eki = -Epi
    GMm/r = 1/2 mv^2
    v = sqrt(2GM/r)
    Damn, you’ve been taught well!

    pikachu975 likes this.
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