Orbital & Escape Velocities

v_orb = √(GM/r), v_e = √(2GM/R).

Concept

Orbital & Escape Velocities is a foundational idea in this chapter. The defining relationship is:

$v_e = \sqrt{2}\,v_{\rm orb}$

Escape from surface: ~11.2 km/s for Earth.

Worked Application

Apply the formula to a typical problem from your textbook. Identify the knowns, plug into the equation, and check that the units work out. Always sanity-check the magnitude before accepting an answer.

Common Confusions

• Confusing the variables in the formula — re-read the symbol definitions in the chapter.
• Forgetting unit conversions (cm vs m, g vs kg).
• Ignoring sign conventions where direction matters.

Key Takeaways

• Master the formula $v_e = \sqrt{2}\,v_{\rm orb}$ and one canonical example.
• See the chapter index for full derivations, traps and exam-grade problems.