# Total energy of a satellite?

What is the total energy of a 2.0*10^3 kg satellite in a circular orbit around the earth at an altitude of 5.0*10^2 Km ? (Ans. 5.8 * 10^10 J)

Relevance

r = re+h = 6878100 m

Specific potential energy SPE = -GM/r = -57971654.3464038 J/kg

Specific kinetic energy SKE = GM/2r = 28985827.1732019 J/kg

Total specific energy = SPE + SKE = -28985827.1732019 J/kg

Total energy = m(SPE + SKE) = -57971654346.4038 J

Notice the minus sign. Potential energy is zero at infinite distance and negative at finite distance. In a circular orbit, PE = -2*KE so total energy = -KE.

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• All satellites without exception have finished mechanical capability E = KE + PE = -KE = a million/2 PE. that's consequence of so-stated as virial, which ensures that any physique orbiting in inverse sq. a million/R² rigidity field has ability capability unfavorable two times kinetic capability: PE = -2KE so which you ought to calculate purely the two ability capability or kinetic capability, in spite of is greater uncomplicated for you. for the reason that they gave you orbital velocity v=5km/s, kinetic capability is trivial: KE = a million/2 mv² = +18.seventy 5 GJ answer: finished capability mechanical capability is -18.seventy 5 GJ

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