The minimum energy required to launch an m kg satellite from the earth’s surface in a circular orbit at an altitude of 2R, where R is the radius of earth, will be?
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Solution :
Since gravitation force provides the necessary centripetal force;
∴
The velocity required by an object at distance 2R from centre is found out by putting in 2R in place of r in the above formula.
Now the total energy of an object at a height is given by :
E= P.E + K.E
Now putting in values of v and r as 2R, we get final energy of an orbiting body as :
Initial energy of satellite at earth's surface is given by
[where v' is the speed provided so as to reach orbit]
Now equating due to conservation of energy
So the minimum kinetic energy required is :
And minimum total energy(with PE component)is: [as obtained for ]
Hope this answer helped you :)
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