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Motion of Orbiting Satellites

AP Physics 1· difficulty 4/5

A B M

Satellite A orbits a planet of mass MM at radius rr, while satellite B orbits the same planet at radius 4r4r. What is the ratio vA/vBv_A / v_B of their orbital speeds?

  • A

    2\sqrt{2}

  • B

    12\tfrac{1}{2}

  • C

    22

    check_circle
  • D

    44

Explanation

For a circular orbit v=GM/rv = \sqrt{GM/r}. So vA/vB=rB/rA=4=2v_A/v_B = \sqrt{r_B/r_A} = \sqrt{4} = 2.

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