Consider the two satellites A and B an earth orbit. Satellite A has a mass m , an orbital radius of r and a totalorbital energy of E. Satellite B has a mass of 4m and an orbital radius r/2. What is the orbital energy of satelliteB?(1) E (2) 2E (3) 4E (4) 8E (5) 16E
Question
Consider the two satellites A and B an earth orbit. Satellite A has a mass m , an orbital radius of r and a totalorbital energy of E. Satellite B has a mass of 4m and an orbital radius r/2. What is the orbital energy of satelliteB?(1) E (2) 2E (3) 4E (4) 8E (5) 16E
Solution
The total orbital energy of a satellite is given by the equation E = -GMm/2r, where G is the gravitational constant, M is the mass of the Earth, m is the mass of the satellite, and r is the radius of the orbit.
For Satellite A, we have E = -GMm/2r.
For Satellite B, we need to substitute the given values into the equation. The mass of Satellite B is 4m and the radius is r/2. So, the equation becomes E_B = -GM(4m)/2(r/2).
Simplify this to get E_B = -4GMm/r.
Comparing this with the energy of Satellite A, we see that the energy of Satellite B is 4 times the energy of Satellite A. So, the answer is (3) 4E.
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