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Old Jan 30th 2014, 01:04 AM   #1
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The path of Earth about sun

H!,
Im confused about calculate this problem plz solve this for me with second law of newton.
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Old Jan 30th 2014, 06:10 AM   #2
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Newton's 2nd Law for a body with constant mass is the well-known formula:

Newton's law of gravity for the force acting on body m in orbit about M:

where r_hat is the radial unit vector pointing from mass M to m. Set these equal, and the motion of the orbiting body (small m) is:



For a circular orbit of radius R you can replace the acceleration vector using: and from that derive a formula for the period of the orbit versus orbital velocity and mass M. Not sure what else you're looking for.

Last edited by ChipB; Jan 30th 2014 at 06:22 AM.
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Old Jan 30th 2014, 09:46 AM   #3
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im locking for path equation of earth about sun.i know it is a Oval.but i want its equation.
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Old Jan 30th 2014, 11:48 AM   #4
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The general formula is:


where l = the angular momentum of the orbiting body, which equals:

and 'e' is the eccentricity of the orbit. For Earth these parameters are:

l = 2.66 x 10^40 Kg m^2/s
m = masss of earth = 5.97 x 10^24 Kg
M = mass of sun = 1.99 x 10^30 Kg
e = 0.0167

Hope this helps.
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Old Jan 30th 2014, 01:05 PM   #5
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thanks but i want to know how this r is calculate?
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Old Jan 30th 2014, 02:19 PM   #6
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Please clarify your question - are you asking how Kepler's laws of planetary motion can be derived from Newtonian mechanics? If so, the following provides a good derivation. However I don't know your background in mathematics and whether it might be a bit advanced for you. Let me know if this helps:

http://en.wikipedia.org/wiki/Kepler%...anetary_motion
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Old Jan 31st 2014, 02:34 AM   #7
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tnx but i dont realize from this. <<are you asking how Kepler's laws of planetary motion can be derived from Newtonian mechanics?>> yes exact. i want to know this.my background in mathmatics is good.
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Old Jan 31st 2014, 03:24 AM   #8
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Read the section called "Inverse Square Law" on the wikipedia page I cited earlier - it shows how Kepler's Laws are consistent with Newton's law of gravity.
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Old Jan 31st 2014, 08:03 AM   #9
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sorry but i did'nt see that.
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