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
- 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.