Astronomers discover a small moon orbiting a distant exoplanet. From repeated observations they determine that the moon completes one revolution every 18.0hours in a nearly circular orbit whose altitude is 4.50×106m above the exoplanet’s surface. The planet’s radius is 7.00×106m. The moon’s own mass is negligible compared with that of the planet.
(1) Using the observed orbital period, determine the mass of the exoplanet. Show all algebraic steps that lead from the measured quantities to the numerical value of the mass.
(2) Calculate the orbital speed of the moon. Express the result with appropriate units and significant figures.
(3) Determine the magnitude of the gravitational acceleration experienced by the moon in its orbit.
(4) Suppose another moon is discovered orbiting the same planet twice as far from the planet’s center as the first moon. Predict the orbital period of the second moon and briefly explain the reasoning underlying your prediction.