Escape Velocity: The velocity needed for an object to completely escape the gravity of a large body such as moon, planet, or star

If an object gains enough orbital energy, it may escape (change from a bound to unbound orbit).

18/02/09 Habbal Astro110-01 Lecture 12 21 Escape velocity

For object to escape gravity must have:

E k ≥ E p

½ m v2 ≥ m g h Or for Earth, h = R

vesc ≥ √2 g R ≥ √ 2 G M/R  independent of mass of object

18/02/09 Habbal Astro110-01 Lecture 12 22 Escape velocity: Exercise

Calculate escape velocity for Earth

vesc ≥ √ 2 G M/R G = 6.67 10-11 M = 5.97 1024 kg R = 6378 km

V esc = 11 km/s

18/02/09 Habbal Astro110-01 Lecture 12 23 Escape velocity: Illustrated

Escape velocity from Earth ≈ 11 km/s from sea level (about 40,000 km/hr)

Escape velocity from Earth

18/02/09 Habbal Astro110-01 Lecture 12 24  Escape and orbital velocities don’t depend on the mass of the cannonball.

18/02/09 Habbal Astro110-01 Lecture 12 25 How does gravity cause tides?

• The Moon’s gravity pulls harder on near side of Earth than on far side. • The difference in the Moon’s gravitational pull stretches Earth.

18/02/09 Habbal Astro110-01 Lecture 12 26 Tides and Phases

Size of tides depends on the phase of the Moon.

18/02/09 Habbal Astro110-01 Lecture 12 27 Tidal Friction

• Tidal friction gradually slows Earth rotation (and makes Moon get farther from Earth). • Moon once orbited faster (or slower); tidal friction caused it to “lock” in synchronous rotation.

18/02/09 Habbal Astro110-01 Lecture 12 28 What have we learned? • What determines the strength of gravity? — Directly proportional to the product of the masses (M × m) — Inversely proportional to the square of the separation • How does Newton’s law of gravity allow us to extend Kepler’s laws? — Applies to other objects, not just planets — Includes unbound orbit shapes: parabola, hyperbola — Can be used to measure mass of orbiting systems 18/02/09 Habbal Astro110-01 Lecture 12 29 What have we learned? • How do gravity and energy together allow us to understand orbits? — A change in total energy is needed to change orbit. — Add enough energy (escape velocity) and the object leaves. • How does gravity cause tides? — The Moon’s gravity stretches Earth and its oceans.

18/02/09 Habbal Astro110-01 Lecture 12 30