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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 1024 kg]
Solution
Given:
h = 1800km = 1.8 × 106m
G = 6.67 × 10-11Nm2/kg2
R = 6400km = 6.4 × 106m
m = 800kg
M = 6 × 1024kg
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 × 107 / 16.4
T.E = -1.952 × 1010 J
Now,
B.E = -T.E
B.E = 1.952 × 1010 J
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