Gravitational Potential Energy
• On Earth, depends on:
Gravitational Potential Energy
• In space, an object or gas cloud has more gravitational energy
when it is spread out than when it contracts.
⇒ A contracting cloud converts gravitational potential energy into
thermal energy.
– object’s mass (m)
– strength of gravity (g)
– distance object could
potentially fall
What determines the strength of gravity?
Newton’s Law of Gravity
How does Newton’s law of gravity extend
Kepler’s laws?
Newton extended Kepler’s first two laws to
apply to all orbiting objects, not just planets.
• Using his laws of motion and
gravitation, Newton demonstrated
that ellipses are not the only
orbital paths. Generally, orbits
can be:
– bound (ellipses and circles)
– unbound
• parabola
• hyperbola
The Universal Law of Gravitation states:
1. Every mass attracts every other mass.
2. Force of attraction is directly proportional to the
product of their masses.
3. Force of attraction is inversely proportional to the
square of the distance between their centers.
Newton generalized Kepler’s Third Law
Newton’s version of Kepler’s Third Law:
IF a small object orbits a larger one and you measure the
orbiting object’s orbital period AND average orbital distance
THEN you can calculate the mass of the larger object.
Examples:
• Calculate mass of Sun from Earth’s orbital period (1 year) and
average distance (1 AU).
• Calculate mass of Earth from orbital period and distance of a
satellite.
• Calculate mass of Jupiter from orbital period and distance of
one of its moons.
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Newton’s version of Kepler’s Third Law
p2 =
4" 2
a3
G(M1+M2 )
!
How do gravity and energy together
explain orbits?
• Orbits cannot change spontaneously.
• An object’s orbit can only change if it somehow gains or
loses orbital energy =
kinetic energy + gravitational potential energy
(due to orbit).
p = orbital period
a = average orbital distance (between centers)
(M1 + M2) = sum of object masses
• If an object gains enough orbital energy, it may
escape (change from a bound to unbound orbit)
⇒ So what can make an object gain or lose orbital
energy?
• Friction or atmospheric drag.
• A gravitational encounter.
•escape velocity from Earth ≈ 11 km/s from sea
level (about 40,000 km/hr)
Escape Velocity
Definition: The minimum velocity that a body must
attain to escape a gravitational field completely.
•
•
•
•
A cannonball fired horizontally at 8
km/s from Newton’s mountain would
find itself in circular orbit around
the Earth (case D).
At greater starting speed, but less
than 11.2 km/s, it will take an
elliptical orbit and return in a
slightly longer time (cases E and F).
When tossed at a critical speed of
11.2 km/s, the cannonball leaves
the Earth and never returns.
Tossed at more than 42.5 km/s, it
will escape the solar system.
Patterns in the Night Sky:
The Celestial Sphere
We had the sky, up there, all speckled with
stars, and we used to lay on our backs and
look up at them, and discuss about whether
they was made, or only just happened.
Mark Twain (1835–1910)
Huckleberry Finn
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What are constellations?
The Celestial Sphere
A constellation is a
region of the sky.
88 constellations
fill the entire sky.
The Celestial Sphere
The Milky Way
A band of light
making a circle around
the celestial sphere.
What is it?
Our view into the
plane of our galaxy.
How do we locate objects in the sky?
We measure the sky in angles.
1. Know your reference points.
2. Locate an object by its altitude (above
horizon) and direction (along horizon)
Angle measurements:
• Full circle = 360º
• 1º = 60′ (arcminutes)
• 1′ = 60″ (arcseconds)
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Why do stars rise and set?
Our view from Earth
• Stars near the north celestial pole are circumpolar and
never set.
• We cannot see stars near the south celestial pole.
• All other stars (and Sun, Moon, planets) rise in east and
set in west.
Earth rotates west to east, so
stars appear to circle on the sky
from east to west.
Celestial Equator
Your horizon
Review: Coordinates on the Earth
Why do not we see the same
constellations throughout the year?
•
•
• Latitude: position north or south of equator
• Longitude: position east or west of prime meridian
(runs through Greenwich, England)
Depends on whether you stay home:
Constellations vary with latitude.
Depends on time of year:
Constellations vary as the Earth orbits the Sun.
The sky varies with latitude but not longitude.
altitude of the celestial pole = your latitude
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The sky varies as Earth orbits the Sun
• As the Earth orbits the Sun, the Sun appears to move eastward
along the ecliptic.
• At midnight, the stars on our meridian are opposite to the Sun in
the sky.
Summary
What are constellations?
• A region of the sky; every
position on the sky
belongs to one of the 88
constellations.
How do we locate objects
in the sky?
• By its altitude above the
horizon and its direction
along the horizon.
Special Topic: How Long is a Day?
• Solar day = 24 hours
• Sidereal day (Earth’s rotation period) = 23hr, 56min
Summary (Cont.)
Why do stars rise and set?
• Because the Earth rotates around
its axis.
Why do not we see the same
constellations throughout the
year?
• Because the night sky changes as
the Earth orbits the Sun.
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