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Motion of Orbiting Satellites

AP Physics 1· difficulty 4/5

A satellite has period T=24T = 24 h around Earth at radius RgR_g. A second satellite has period T=3T = 3 h. What is its orbital radius?

  • A

    Rg/4R_g/4

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  • B

    Rg/3R_g/3

  • C

    Rg/8R_g/8

  • D

    Rg/2R_g/2

Explanation

T2∝r3T^2 \propto r^3. r2/Rg=(3/24)2/3=(1/8)2/3=1/4r_2/R_g = (3/24)^{2/3} = (1/8)^{2/3} = 1/4.

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