Two spherically symmetric planets with no atmosphere have the same average density, but planet B has twice the radius of planet A. A small satellite of mass mA has period TA when it orbits planet A in a circular orbit that is just above the surface of the planet. A small satellite of mass mB has period TB when it orbits planet B in a circular orbit that is just above the surface of the planet. How does TB compare to TA?
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Two spherically symmetric planets with no atmosphere have
the same average density, but planet B has twice the radius of planet A.
A small satellite of mass mA has period TA when it orbits planet A in a
circular orbit that is just above the surface of the planet. A small satellite
of mass mB has period TB when it orbits planet B in a circular orbit that
is just above the surface of the planet. How does TB compare to TA?

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- Scientists have discovered a distant planet with a mass of 8.2x1023 kg. The planet has a small moon that orbits with a period of 6 hours and 36 minutes. Use only this information (and the value of G) to calculate the radius of the moon's orbit (in units of 106 m).A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.The mean diameters of planets A and B are 9.3 × 103 km and 1.8 × 104 km, respectively. The ratio of the mass of planet A to that of planet B is 0.88. (a) What is the ratio of the mean density of A to that of B? (b) What is the ratio of the gravitational acceleration on A to that on B? (c) What is the ratio of escape speed on A to that on B?