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Motion of Orbiting Satellites

AP Physics 1· difficulty 4/5

Planet X has twice the mass and half the radius of Earth. What is the ratio of escape velocity from X to escape velocity from Earth, vX/vEv_X/v_E?

  • A

    2\sqrt{2}

  • B

    22

    check_circle
  • C

    44

  • D

    12\tfrac{1}{2}

Explanation

vesc=2GM/Rv_{esc} = \sqrt{2GM/R}. Ratio is (2M)/(R/2)/M/R=4=2\sqrt{(2M)/(R/2)} / \sqrt{M/R} = \sqrt{4} = 2.

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