#### Question

Find the total energy and binding energy of an artificial satellite of mass 800 kg orbiting at a height of 1800 km above the surface of the earth.

[G = 6.67 x 10^{-11} S.I. units, Radius of earth : R = 6400 km, Mass of earth : M = 6 x 10^{24} kg]

#### Solution

Given:

h = 1800km = 1.8 × 10^{6}m

G = 6.67 × 10^{-11}Nm^{2}/kg^{2}

R = 6400km = 6.4 × 10^{6}m

m = 800kg

M = 6 × 10^{24}kg

To find:

T.E = ?

B.E = ?

Formulae:

- T.E = `-(GMm)/(2(R + h))`
- B.E = -T.E

Solution:

T.E = `-(GMm)/(2(R + h))`

T.E = `-(6.67xx10^-11 xx 6 xx 10^24 xx 800)/(2(6.4 + 1.8) xx 10^6)`

T.E = -32016 × 10^{7} / 16.4

T.E = -1.952 × 10^{10} J

Now,

B.E = -T.E

B.E = 1.952 × 10^{10} J

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Total Energy and Binding Energy of an Artificial Satellite of Mass 800 Kg Orbiting at a Height of 1800 Km Above the Surface of the Earth. Concept: Binding Energy and Escape Velocity of a Satellite.