A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$32$$ times larger. Due to this the farthest distance from the center of the earth that the satellite reaches is R. Value of R is :

Question

A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth’s radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become $$32$$  times larger. Due to this the farthest distance from the center of the earth that the satellite reaches is R. Value of R is :

Infinity Learn · Accepted Answer

$$Ei=-GMm2ReAfter$$ supplying kinetic energy,$$Ef=-GMm2Re+12$$ $$m32GMRe2Ef=-GMm2Re+12$$ $$m32GMRe=-GMm4ReLet$$ say a is semimajor axis of new orbit.$$Ef=-GMm2a$$   ⇒$$-GMm4Re=-GMm2a$$   ⇒$$2a=4Re$$ We know that major axis can be given as, $$2a=rmin+rmax$$ ⇒$$4Re=Re+rmax$$  ⇒$$rmax=3Re$$

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material