Problem Graphic


NASA is planning an unmanned mission to Mars. Mission planners need the precise position of the planet relative to Earth on the launch date in order to determine the proper velocity for the spacecraft. If the distance or angle is incorrect, the spacecraft could be lost.

What is known:

  • The radius of Earth's orbit re is 150 x 106 km.
  • The radius of Mars's orbit rm is 207 x 106 km.
  • The angle α between Earth and Mars relative to the Sun is 30°.
  • Assume both Earth's and Mars' orbits around the Sun is circular.

Problem Diagram

What is the position of Mars relative to Earth on the launch day?


  • Draw a diagram and label the key points and known position vectors.
  • Determine the relationship between the unknown position vector and those that are given.
  • Using geometry, solve for the length and angle of the unknown vector.
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