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What is the orbital period of a spacecraft orbiting the moon at an altitude of 200
km so that a given 20 km x 20 km patch on the lunar surface seen through a
detector on the spacecraft is viewed for 10 sec per orbit
A] 118 minutes B] 224 minutes
C] 91 minutes D] 66 minutes
91 minutes.
thanx 4 ur attempt , i don't know the correct answer bt wud u mind explaining ur answer
let the radiu of moon = r.
let the 20kmx20km patch subtends angle Q on spacecraft.
then rQ = 20 and also (r+200)Q = d,
where d is the total orbital distance during which the 20kmx20km patch is visible.
then (r+200)x20/r = d.
Speed of spacecraft,s = d/10.
Time period of space craft = 2*pi *(r+200)/s
If u calculate this by substituting the value of r = 1.738x10^6 m, u will get T= 91 minutes.