Question

A satellite of mass M is orbiting the earth at a height h from its surface the total energy of the satellite in terms of G note the value of acceleration due to gravity at the Earth's surface is

Answer 1

The gravitational potential energy is amount of energy that an object posses due to its position(gravitational field).The general form of gravitational potential energy usually denoted by "U" is :

U= -G M m / r

where we have G as the gravitational constant,M is the mass of the attracting body and r is the radius(between the centers).

The total energy in the terms of g₀ will be:

⇒ -(m*g₀*R²) / 2(R+H)

where ,

R is the radius of earth and H is the height from the earth to the surface.

Answer 2

Gravitational potential energy is given by,
$P.E=-\frac{GMM_e}{R+h}$.......(1)

but we know , $g=\frac{GM_e}{R^2}$

so, GMe= gR² .........(2)

put equation (1) in equation (2),

$P.E=-\frac{gR^2M}{R+h}$

or, $P.E=-\frac{gMR}{1+\frac{h}{R}}$

we know, total energy is the half of potential energy .
e.g., T.E = P.E/2

T.E = $-\frac{gMR}{2\left(1+\frac{h}{R}\right)}$

hence, total energy of the satellite in terms of G note the value of acceleration due to gravity at the Earth's surface is $-\frac{gMR}{2\left(1+\frac{h}{R}\right)}$