A moon rotates about its axis. In the future, scientists may wish to put a satellite into an orbit around the moon such that the satellite remains stationary above one point on moon surface, the period of rotation of moon about its axis is 27.4 days,what is the radius of required orbit? Mass of the moon =7.35x10²²kg
Correct answer: C. 8.86 x 10^7 m
- A. 3.59 x 10^7 m
- B. 4.23 x 10^7 m
- C. 8.86 x 10^7 m
- D. 6.96 x 10^6 m
Explanation
In this case, once the satellite has been launched, the gravitational force between the satellite and the moon would be providing the centripetal force hence the centripetal force, mrw2 is equal to the gravitational force, GMm/r2 where r is the radius of the orbit, w being the angular velocity that can be simplified to 2π/T(time period) and M being the mass of the moon. Equating the two expressions would give us r= (GMT2/4π2)1/3 Plugging in all the values, performing mathematical operations and then finally taking cube root of the expression gives you the answer i.e 8.8x10⁷m
This question appeared on the UHS MDCAT 2017 paper, which you can sit online with every answer explained.
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