anonymous
  • anonymous
A satellite orbits the Earth such that it remains above the same point on the equator at all times. Another satellite orbits the Earth at a distance (from the Earth’s center) that is 4 times as far as the previous satellite. How long does it take the second satellite to orbit the Earth?
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
this is a matter of identifying the relationship between period and the radius
anonymous
  • anonymous
\[\frac{ T ^{2} }{ R ^{3} }=constant\]
anonymous
  • anonymous
let us suppose the period for the first planet is T1 radius R1 and for the second T2 and R2

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anonymous
  • anonymous
\[\frac{ T _{1}^{2} }{ R _{1}^{3} }=\frac{ T _{2}^{2} }{ R _{2}^{3} }\]
anonymous
  • anonymous
express R2 in terms of R1
anonymous
  • anonymous
\[R _{2}=4R _{1} => R _{2}^{3}=64R _{1}^{3}\]
anonymous
  • anonymous
\[\frac{ T _{1}^{2} }{ R _{1}^{3} }=\frac{ T _{2} ^{2}}{ 64R _{1}^{3}}=>T _{2}^{2}=64T _{1}^{2}\]
anonymous
  • anonymous
\[T _{2}=8T_{1}\]

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