Orbits of four different planets about the same star are shown. The masses of th

Question

Orbits of four different planets about the same star are shown. The masses of the planets, expressed in terms of the mass M of the smallest planet, can be found in the included table, while the relative sizes of the orbits can be determined from the diagram. Assume that the mass of the star is much larger than the mass of the planets. Rank the period of the four orbits, from longest to shortest.

Orbits of four different planets about the same star are shown. The masses of the planets, expressed in terms of the mass M of the smallest planet, can be found in the included table, while the relative sizes of the orbits can be determined from the diagram. Assume that the mass of the star is much larger than the mass of the planets. Rank the period of the four orbits, from longest to shortest. Longest Period Shortest Period

Explanation / Answer

T^2 is proportional to R^3

Where T = Time Period

R = Radius of orbit

In case of elliptical orbits, R = Semi Major Axis i.e. Length of orbit divided by 2.

Thus we get Ra = 4, Rb = 2, Rc = 3.5 and Rd = 3

Hence, Ta > Tc > Td > Tb

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