The paths of two sma satellites, x and Y, of equal mass of 8.00 kg each, are sho

Question

The paths of two sma satellites, x and Y, of equal mass of 8.00 kg each, are shown below. They 29 orbit around a massive star, as ustrated, with M kg. The orbits are in the plane of 4.20x10 the paper and are drawn to scale In the statements below KE s kinetic energy, PE is potential energy, and ILI is magnitude of the angular momentum. At m, the KE of Y is that of X The PE of Y at i is the PE of X at p At m, the PE of X is that of Y The IL of X at a is that at n The speed of Y at i is that at m 13 Tries 0/12 Send Feedback

Explanation / Answer

1.  At m the KE of Y is Greater than that of X. Reason - V = sqrt(GM [2/r-1/a]) where a is semi major axis and r is distance of satelitte from star. Therefore at m speed of satelitte in Y orbital is greater than speed of satelitte in X orbital ,thus KE of Y is Greater than that of X.

2. The PE of Y at i is Greatert Than the PE of X at p. Reason - P.E = (- GMm/r), In this case r for Y is bigger than r for X , and as P.E is negative , thus making P.E at i Greater than P.E at p.

3. At m, the PE of X is Equal to that of Y. Reason -P.E = (- GMm/r), In this case for both the satellite , we have same values of M, m and r .Therefore P.E is same.

4. The |L| of X at a is Equal to that at n. Reason - Conservation of Angular Momentum in orbit . (Keplers Law)

5. The speed of Y at i is Less Than that at m. Reason - As satellite moves away from star, it loses Speed and as it comes close it gains speed.

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