Question

The binding energy of a satellite of mass m in an orbit of radius r is

Answer 1

actually Binding energy is the total amount of energy required by a satellite to go from its orbit to infinity.

binding energy = - total energy of satellite in its orbit.

= = -T.E = -(K.E + P.E)

we know, P.E is given by, P.E = -GMm/r
and K.E is given by , K.E = 1/2mv²

but we know, centripetal force = gravitational force [ in circular orbit at equilibrium]

so, mv²/r = GMm/r²

so, mv² = GMm/r or, K.E = 1/2mv² = GMm/2r

so, T.E = K.E + P.E = GMm/2r - GMm/r
= -GMm/2r

hence, binding energy of satellite =-(- GMm/2r)

= GMm/2r, where M is mass of earth , m is mass of satellite and r is the radius of satellite.

Answer 2

Answer:

Explanation:Binding energy is equal to negative value of total mechanical energy of a satellite.

The energy required to remove the satellite from its orbit around the earth to infinity is called binding energy of the satellite. It is equal to negative of total mechanical energy of satellite in its orbit.

Thus, binding energy =−E=

2r

GMm

​

but, g=

R

2

GM

​

⇒GM=gR

2

∴BE=

2r

gmR

2

​