A satellite of mass is in circular orbit above Earth’s surface

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A satellite of mass 500 kg500\,\text{kg} is in circular orbit 1000 km1000\,\text{km} above Earth’s surface. Take Earth’s mass ME=6.0×1024 kgM_{\rm E}=6.0\times10^{24}\,\text{kg}, Earth’s radius RE=6400 kmR_{\rm E}=6400\,\text{km}, and G=6.67×10−11 N m2 kg−2G=6.67\times10^{-11}\,\text{N\,m}^{2}\,\text{kg}^{-2}. (i) Calculate the orbital speed of the satellite. (ii) Determine the centripetal acceleration acting on the satellite. (iii) Find the value of gravitational acceleration at this altitude. (iv) Hence find the apparent weight of an astronaut of mass 75 kg75\,\text{kg} inside the satellite.

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