Escape Speed and Escape Energy
Ignoring drag and other bodies, setting K+U=0 at launch radius r gives v_e=sqrt(2GM/r); the required kinetic energy from rest is GMm/r and v_e=sqrt(2) v_c at the same radius.
Why this shows up in the exam
Planet escape-speed scaling · Minimum energy to infinity · Multi-source escape using total potential
Learn the idea
Escape is the zero-total-energy threshold, giving v_e=sqrt(2GM/r) from distance r. At the minimum escape speed an object reaches infinity with zero remaining speed; it need not keep accelerating outward.
🧠 Memory hook: Escape sets final speed at infinity to zero.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- v_e = sqrt(2GM/r) — escape speed from centre distance r
- K_escape = GMm/r — minimum launch kinetic energy from rest
- v_e = sqrt(2) v_c — relation to circular speed at the same radius
How to approach it
- 1Choose launch point and all gravitational sources
- 2Set final total energy to zero
- 3Solve for speed or energy and test units
Common slip-ups that cost marks
- •Using surface formula at altitude
- •Assuming escape speed depends on projectile mass
- •Adding separate escape speeds instead of potentials
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A satellite moves in a circular orbit where GM = 4 x 10^14 m^3/s^2 and orbital radius is 2 x 10^6 m. Find its orbital speed.
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