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Thread: Momentum in space

  1. #1 Momentum in space 
    sak
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    How can we calculate the momentum of a satellite in orbit? This question strike me when I was reading orbital velocity of planets.
    Special thanks for simple notes


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    Brassica oleracea Strange's Avatar
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    Mass time velocity, mv, gives you it's linear momentum. The cross product of this with the radius gives you the angular momentum.

    More here: Angular momentum - Wikipedia, the free encyclopedia


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    A lot depends upon how circular the orbit is. If it is circular, or at least nearly circular(depending on how accurate an answer you need). The answer above will suffice.

    However, As the orbit becomes more eccentric, certain adjustments have to be made. In the case of angular momentum, there are only two points of the orbit where the cross product of linear momentum and radius will give you the angular momentum. These are the periapsis and apoapis, which are the closest and furthest points of the orbit. The good news is that once you find the angular momentum for one of these points, you've found it for all points of the orbit as it is conserved.

    This of course assumes that you know or can find the orbital speed at periapsis and apoapis. These depend on the eccentricity of the orbit, the mean radius of the orbit and the mass of the body it is orbiting.

    Linear momentum varies over the orbit. It is highest at periapsis and lowest at apoapsis.

    It depends on the orbital speed which can be found by



    Where G is the gravitational constant
    M and m are the masses of the orbited body and the satellite
    r is the orbital radius
    a is the mean orbital radius.

    If you know the periapsis or apoapsis for the orbit and the mean orbital radius, you can plug this value in for r and then use this above to find the angular momentum.

    Exactly how you arrive at an answer for the momentum really depends on just what information about the satellite's orbit you start out with.
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  5. #4  
    sak
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    I’ve gone through wiki and posts given, however my doubt the strength of gravitational field remains unclear. The doubt is a body of certain mass traveling 10 KM from earth will have a momentum but it will be far less if it ravel through a farther orbit at 1000 KM. How can I solve this?
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    Moderator Moderator Janus's Avatar
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    Quote Originally Posted by sak View Post
    I’ve gone through wiki and posts given, however my doubt the strength of gravitational field remains unclear. The doubt is a body of certain mass traveling 10 KM from earth will have a momentum but it will be far less if it ravel through a farther orbit at 1000 KM. How can I solve this?

    The linear momentum decreases with the altitude of the orbit since the orbital speed decreases with the altitude. Angular momentum increases as the mean orbital radius increases, as the increase the radius has a larger effect than the decrease in speed.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
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  7. #6  
    sak
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    Quote Originally Posted by Janus View Post
    The linear momentum.......radius has a larger effect than the decrease in speed.
    Thanks, Can you please tell me abut effect of gravity also?
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  8. #7  
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    Quote Originally Posted by sak View Post
    Quote Originally Posted by Janus View Post
    The linear momentum.......radius has a larger effect than the decrease in speed.
    Thanks, Can you please tell me abut effect of gravity also?
    The effect is more applicable when we calculate through centripetal force. A force by gravity drawing or repelling a body towards a point as to a center, always along a right line.
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