PHY073 · Astronomy & Space · Classes 11–12
Escape velocity
Objective: To find the escape velocity of different planets and see whether a launched object returns or escapes.
🧰 Apparatus
- (Simulation) planet and rocket
- Planet data: mass and radius
- Calculator
📐 Formulas and SI units
v_e = √(2GM / R)
h_max = R v² / (v_e² − v²) (for v < v_e)
💡 Theory
An object escapes a planet's gravity if its kinetic energy is at least enough to climb out of the gravitational 'well': ½mv² ≥ GMm/R, so v_e = √(2GM/R). It does not depend on the object's mass. Below v_e the object rises to a height and falls back.
🪜 Procedure
- Choose a planet and read its escape velocity.
- Launch at a speed below v_e and note the maximum height.
- Increase the speed past v_e and see the rocket escape.
- Compare the Moon (small v_e) and Jupiter (large v_e).
📋 Observations Simulated values
✅ Result and conclusion
Earth's escape velocity is 11.2 km/s; the Moon's is only 2.4 km/s, which is why it has no atmosphere.
🔬 In a real lab
Real rockets are not fired at escape speed from the ground; they burn engines for minutes and lose energy to air drag.
⚠️ Safety
A calculation and simulation activity.
❓ Quick check
1. Escape velocity depends on the object's…
2. Why has the Moon lost its atmosphere?
3. Doubling the planet's mass (same R) makes v_e…
🏋️ Practice
Easyv_e on Mars?
Answer: ≈ 5.0 km/s
Mediumv_e on Jupiter?
Answer: ≈ 60 km/s
ChallengeDoes a 1 kg ball need the same v_e as a 1000 kg rocket?
Answer: Yes