Two Questions on Satellites

In the post (titled ‘Questions on Satellites’) dated August 30, 2006, two questions were discussed. The following question similar to the first question appeared in KEAM 2007 (Engineering) question paper:

A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01 R. The period of second satellite is longer than the first one (approximately) by

(a) 1.5% (b) 0.5% (c) 3%

(d) 1% (e) 2%

In the question discussed in the earlier post, the orbital radius was 1.02 R instead of 1.01R and the answer was obtained as 3%.

You may work out the present question to obtain the answer as 1.5%. If you have any difficulty, see the earlier post dated August 30, 2006. You may easily do this by clicking on the label satellite below this post.

Now see the following MCQ:

If the orbital radius of an artificial satellite is to be increased by 5%, the orbital speed will have to be

(a) decreased by 5% (b) increased by 5% (c) decreased by 2.5%

(d) increased by 2.5% (e) decreased by10%

The orbital speed is obtained by equating the centripetal force to the gravitainal pull:

mv²/r = GMm/r² where ‘m’ is the mass of the satellite, ‘v’ is the orbital speed, ‘r’ is the orbital radius, G is the gravitational constant and M is the mass of the earth.

From this v = √(GM/r).

Since G and M are constants, dv/v = – ½ dr/r

Instead of the fractional changes dv/v and dr/r, we can use percentage changes and write this equation as

percentage change in v = – ½ ×percentage change in r

Since the change in ‘r’ is an increment of 5%, the change in ‘v’ will be an increment of – ½ ×5%, which means a decrement of 2.5% [Option (c)].

All the essential points to be remembered in gravitation can be found at AP Physics Resources: Gravitation –Equations to be Remembered