Escape Velocity & Energy of Orbits — A/L Physics

What must I remember about Escape Velocity & Energy of Orbits?

• Escape Velocity (v_e): Minimum initial speed required for a projectile launched from a planetary surface to completely escape the planet's gravitational field (reach r = ∞ with zero KE): Total Energy = (1/2)m v_e² - (G M m) / R = 0 => v_e = √(2 G M / R) = √(2 g0 R).
• Comparison: Escape Velocity vs Orbital Velocity: Escape velocity is √2 times the close-orbit velocity: v_e = √2 * v_orbit; for Earth: v_orbit ≈ 7.9 km/s, v_e ≈ 11.2 km/s.
• Total Mechanical Energy of an Orbiting Satellite: Kinetic Energy KE = (1/2)m v_o² = (G M m) / (2r); Potential Energy PE = - (G M m) / r; Total Mechanical Energy E = KE + PE = - (G M m) / (2r).
• Energy Relations for Bound Circular Orbit: KE = - E; PE = 2 E (Virial Theorem for inverse-square gravity); Total energy E is NEGATIVE, confirming a gravitationally bound system.

Test yourself (1 minute)

1. Planetary Atmospheres

   Why Moon has no atmosphere: Moon's escape velocity (v_e ≈ 2.4 km/s) is comparable to thermal rms speed c_rms of gas molecules, allowing gases to leak into space; Earth's v_e (11.2 km/s) comfortably retains O2, N2, and CO2.

2. Black Hole Event Horizon

   When escape velocity reaches speed of light c: Radius R_s = 2GM / c² (Schwarzschild Radius).

Practise Escape Velocity & Energy of Orbits questions today

Must know

• Escape velocity is independent of projectile mass and launch angle (as long as it clears terrain and atmosphere); depends solely on planetary mass M and radius R.

Source: NIE G.C.E. (A/L) Physics Resource Book - Unit 5: Gravitational Fields

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Next in the syllabus

Where does Escape Velocity & Energy of Orbits fit in the syllabus?

Unit 5.5 · Year 1 · Term 3