1. Universal Gravitation
Chapter 9
Universal Gravitation
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2. The Falling Apple and the Falling Moon
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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3. How Gravity Affects Objects in Space
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
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4. Universal Gravitation
Every object is gravitationally attracted to every other object in the Universe
F = Gm1m2/d2
G = universal gravitation constant
6.67 x N•m2/kg2
M1, M2 = mass of each object
R – distance between the objects
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5. Gravity and Distance: The Inverse Square Law
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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6. Weight and Weightlessness
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”
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7. Tides
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.
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8. Universal Gravitation and Astronomy
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.
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9. Universal Gravitation and Astronomy
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.
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10. Universal Gravitation and Astronomy
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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11. Chapter 10
Part 2: Satellites
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12. Fast Moving Projectiles: Satellites
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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13. Kepler’s Laws Kepler studied planetary motion. He found:
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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14. Escape Speed
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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