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.