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magicuniverse
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An asteroid is on a circular orbit around the sun with an orbital radius of 3AU. It splits into two fragments, which initially move aparty along the direction of the original orbit. One fragment has a speed of 0.65 of the original speed, the other has a speed of 1.35 times the original speed.
Original Orbital speed is 2pi/(root3) AU per year.
1) Calculate the angular momentum per unit mass l, of the original asteroid and of each of the two fragments in units of AU^2 per year.
In these units l can be related to the semi-major axis a i (in AU) and eccentricity e of the orbit by the formula l = 2pi[a(1-e^2)]^0.5
2) Calculate the eccentricities of the two new orbits.
3) Calculate the orbital periods of the original astroid and the two fragments (in years).
I am very stuck on this and any assistance would be really be appretiated.
Original Orbital speed is 2pi/(root3) AU per year.
1) Calculate the angular momentum per unit mass l, of the original asteroid and of each of the two fragments in units of AU^2 per year.
In these units l can be related to the semi-major axis a i (in AU) and eccentricity e of the orbit by the formula l = 2pi[a(1-e^2)]^0.5
2) Calculate the eccentricities of the two new orbits.
3) Calculate the orbital periods of the original astroid and the two fragments (in years).
I am very stuck on this and any assistance would be really be appretiated.