Download Escape Velocity:

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).
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Escape velocity
For object to escape gravity must have:
Ek≥Ep
½ m v2 ≥ m g h
Or for Earth, h = R
vesc ≥ √2 g R ≥ √ 2 G M/R
 independent of mass of object
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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
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Escape velocity: Illustrated
Escape velocity from Earth ≈
11 km/s from sea level
(about 40,000 km/hr)
Escape velocity from Earth
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 Escape and orbital velocities don’t
depend on the mass of the cannonball.
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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.
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Tides and Phases
Size of tides depends on the
phase of the Moon.
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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.
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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 Habbal Astro110-01 Lecture 12
18/02/09
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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.
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