Gravitation – Complete Intermediate Notes

Stage 1 • Page 7 • Energy of a Satellite & Binding Energy

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1. Kinetic Energy of a Satellite

For a satellite of mass m revolving in a circular orbit of radius r, its orbital velocity is:

v = √(GM / r)

Hence, kinetic energy:

K = ½ m v² = GMm / (2r)

• Kinetic energy depends on orbit radius
• Decreases as orbit radius increases

Exam Insight:
Many questions ask for ratio of kinetic energies at different orbits.

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2. Potential Energy of a Satellite

Gravitational potential energy of satellite at distance r from Earth’s centre:

U = − GMm / r

• Always negative
• More negative for lower orbits
• Approaches zero as r → ∞

Board Favourite:
Explain why satellite has negative potential energy.

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3. Total Mechanical Energy of a Satellite

Total energy is the sum of kinetic and potential energies:

E = K + U = − GMm / (2r)

• Total energy is always negative
• Satellite remains bound to Earth
• Energy increases (less negative) with height

Key Result:
Satellite is bound because its total energy is negative.

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4. Binding Energy of a Satellite

Binding energy is the minimum energy required to remove a satellite from its orbit to infinity.

Binding Energy = |E| = GMm / (2r)

• Equal to magnitude of total energy
• Higher for lower orbits
• Zero at infinity

IIT Advanced Insight:
Binding energy concept is often tested indirectly through energy change problems.

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5. Effect of Changing Orbit Radius

• As r increases → K decreases
• As r increases → |U| decreases
• As r increases → |E| decreases

If satellite is moved to a higher orbit, additional energy must be supplied.

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6. Common Mistakes to Avoid

• Assuming total energy is positive
• Forgetting negative sign in potential energy
• Using mgh for satellites
• Mixing surface and orbital formulas

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Stage 1 • Page 7 Completed Successfully ✅

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