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:

mv^{2}/r = GMm/r^{2} 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**

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