On an exoplanet named Kepler-X

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

On an exoplanet named Kepler-X, the measured acceleration due to gravity at the surface is 12 m/s212\,\text{m/s}^2. The planet’s radius is 7.0×106 m7.0\times10^6\,\text{m}. (a) Rearrange the standard relation for surface gravity to obtain an expression for the mass of a planet in terms of its surface gravity and radius. (b) Calculate the mass of Kepler-X using the given data. (c) A rover of mass 150 kg150\,\text{kg} lands on Kepler-X. Find its weight on this planet. (d) Compare this weight with its weight on Earth by calculating the ratio WKepler-XWEarth\dfrac{W_{\text{Kepler-X}}}{W_{\text{Earth}}}. Take gEarth=9.8 m/s2g_{\text{Earth}} = 9.8\,\text{m/s}^2.

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