Transcript Chapter 12 - AJRomanello

Chapter 9
Universal Gravitation
Herriman High Physics
The Falling Apple and the
Falling Moon
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Legend has it that Newton hypothesized
about gravity when he watched an apple fall.
He developed this idea further by comparing
the falling apple to the falling moon.
He proposed that a projectile, fired fast
enough would fall around the earth rather
than to the earth and would become a
satellite like the moon.
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How Gravity Affects Objects in
Space
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The lines shown are tangent
to the circle. They
demonstrate the direction a
satellite would move if gravity
were turned off.
•Since the satellite is actually a
projectile, which has gravity
acting on it, it actually moves in
a curved path which allows it
to fall around the earth.
Without
Gravity
With
Gravity
Herriman High Physics
Universal Gravitation
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Every object is gravitationally attracted
to every other object in the Universe
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F = Gm1m2/d2
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G = universal gravitation constant
6.67 x 10-11 N•m2/kg2
M1, M2 = mass of each object
R – distance between the objects
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Gravity and Distance:
The Inverse Square Law
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Gravity is reduced as distance increases, but
this is not linear it is exponential
If you double distance, gravity is reduced by
the square of two, i.e. ¼
If you triple distance, gravity is reduced by
the square of three, i.e. 1/9 and so on.
It is also important to remember that
distances in this law are measured from the
center of one object to the center of the
second object.
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Weight and Weightlessness
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As we learned earlier, weight is due to the
acceleration of gravity on a mass.
Scales do not actually measure weight, but rather the
support force exerted on the scale.
Hence when an elevator is accelerating downward,
the support force is less and your weight appears to
decrease
When the elevator is accelerating upward, the
support force increases and your weight appears to
increase.
Weightlessness is not a result of moving far from
earth, but rather the result of being in a constant
state of “free fall”
Herriman High Physics
Tides
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Ocean tides are the result of the difference in gravitational
pull between the earth and the moon on the opposites of
the earth.
This difference accounts for a high tide on either side of the
earth, and a low tide one quarter turn from the high tide.
Hence high tide occurs once every 12 hours and low tide
occurs mid-way between high tides.
Higher than usual tides occur when the Sun, Moon, and
Earth align (new or full moon) – these are spring tides
When the moon is at right angles to the sun with respect to
the earth, the gravitation affects cancel somewhat, which
results in a somewhat higher low tide, and somewhat lower
high tide – these neap tides occur ½ way between a full or
new moon.
Herriman High Physics
Universal Gravitation and
Astronomy
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We all know the earth is round, but why is it round?
Universal Gravitation!
Since everything is attracted to everything else, the
earth “pulled itself together” before it became solid.
Any “corners” have been pulled in so that earth (and
most other celestial objects) are basically spheres.
This also means that the earth is not just affected by
the Sun’s gravity, but the gravity of other planets as
well. This has important implications for astronomers
and actually led to the discovery of the last two
planets in our solar system.
Herriman High Physics
Universal Gravitation and
Astronomy
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When Saturn is near Jupiter its pull disturbs the otherwise
smooth path of Jupiter. This deviation is called a
perturbation.
When Uranus was discovered, it appeared to deviate from
Kepler’s Laws of Planetary motion – something no planet
before it had done.
When studying this deviation two scientists, working
independently, proposed that another planet, outside
Uranus’ orbit, could be the cause – Hence Neptune was
found.
Similar problems with Neptune’s orbit were the motivation
which led to the discovery of Pluto.
Scientific work in one field often affects the work in all
other fields.
Herriman High Physics
Universal Gravitation and
Astronomy
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Einstein defined gravity differently than Newton. He
envisioned that a gravitational field was a warping of
4 dimensional space.
This warping would cause and object to be attracted
toward the center of the warp.
A black hole is the result of the gravitational collapse
of a star. This collapse causes the star to shrink,
making its mass more condensed. This increases the
effect of gravity according to the law of Universal
Gravitation.
Gravity becomes so strong, that light cannot escape –
hence the name “black hole.”
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Chapter 10
Part 2: Satellites
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Fast Moving Projectiles:
Satellites
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A satellite is a fast moving projectile
Since the projectile moves in a curved path,
and the earth is a curved surface, if the
projectile moved fast enough its motion
would follow the curve of the earth
Such a projectile would fall around the
earth rather than to the earth
Such a projectile becomes a satellite and
orbits the earth.
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Kepler’s Laws
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Kepler studied planetary motion. He
found:
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All planetary bodies move in elliptical orbits
Planetary objects sweep equal areas in
equal amounts of time
If two satellites revolve around the same
object they are related by the equation:
(t1/t2)2 = (r1/r2)3
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Escape Speed
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Escape Speed is the critical speed at
which an object can escape a bodies
gravitational pull. At this speed the
object will not fall back to the planetary
body, but will escape into space.
For earth, escape velocity is 11.2 km/s
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