Gravitation

Newton observed falling apple and orbiting moon, saw both were accelerating, so both had net force.
Newton wondered if force on apple was same as force on moon
First to realize force of gravitation is universal, exists between all objects with mass

Force between any two objects is directly prop to product of their masses, inversely prop to square of distance between their centers of mass.
To calculate force, proportionality constant is needed-first measured by Cavendish in his optical lever experiment
F = (Gm₁m₂)/d² ; where F is the force exerted on each body by the other (3rd law), m₁and m₂ are the masses of the two bodies, d is the distance between the centers of mass of the two bodies and G = 6.67 x 10^-11 Nm²/kg², the universal gravitation constant.

Force of gravity varies inversely with square of distance between objects
If distance is doubled, force is one-fourth as much; if tripled, force is one-ninth (1/3)²
If distance is halved, force is 4 times as much; if distance is 1/3 as much, force is 9 times as great.
Due to spreading of force into surrounding space

When G was finally measured, it allowed us to find the mass of the earth by using an object of known mass and weight at one earth radius distance (also known)
Also allowed us to calculate g at any location near any celestial body: g = GM/d²
Gravity depends on distance from center of earth or other planet and its mass

Weight is force due to gravitational attraction, depends on location.
Sensation of weight requires supporting force; feel weightless without it: amusement park rides, astronauts

Force is felt in area surrounding large body
Called gravitational field, can be mapped by measuring force at many locations
Vector field whose direction points to center of planet, magnitude depends on distance

If hole were drilled through earth and you fell in, mass below you pulls down, mass above you pulls up.
No force at center of earth, pull equal in all directions
You would accelerate with decreasing acceleration until you reached the center, then decelerate as you approach opposite surface.

How force acts at a distance is not well understood
Explained by Einstein's general relativity theory: large mass distorts fabric of space-time causing nearby objects to be pulled in
Particle theorists suggest exchange of particles called gravitons carried by gravity waves between objects

Johannes Kepler examined orbits of planets and formulated 3 laws for all satellites
Law of Orbits: all planets move in elliptical orbits with the sun at one focus
Law of Areas: a line that connects a planet to the sun sweeps out equal areas in equal times
Law of Periods: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit
Period is time for one revolution
Semimajor axis is longest radius dimension of ellipse

Satellites are projectiles
Must have enough horizontal velocity so vertical fall matches earth's curvature
Earth's surface drops 4.9 m in 8000 m horizontal distance
Since projectiles fall 4.9 m in 1 second, must travel 8 km/s to be in orbit (29000 km/hr or 18000 mi/hr)

In circular orbit, gravity always pulls perpendicular to velocity
Speed doesn't change, only direction.
Time (period) for close orbit about 90 min., greater for higher orbits
If period is 24 hours, satellite remains over same point on earth--communication satellites do this (geosynchronous orbit)

"Big Bang" theory says universe hurled outward from big explosion
Universe is expanding, only pull of gravitation can stop it.
Unknown whether enough matter exists to stop expansion and begin contraction leading to "Big Crunch" and another big bang-expansion-contraction cycle.

Change in sea level due to difference in gravitational pull between earth and moon on opposite sides of earth.
Causes elongation of earth and moon along line of force, bulging on near and far side.
Earth turns underneath high water levels causing 2 high tides and two low tides per day.
Sun also creates tides but effect is less than moon because distance difference is not as large a part of total distance.
Extra large spring tides caused by sun-moon alignment on same side of earth
Smaller neap tides occur when sun and moon are on opposite sides of earth

When sun-moon-earth alignment is perfect, eclipses occur
When earth is between sun and moon, moon is in shadow and lunar eclipse occurs.
When moon is between sun and earth, parts of earth in moon's shadow see solar eclipse

In stars, expansion forces due to nuclear fusion are balanced by contraction force of gravity.
When solar fuel runs out, stars collapse
Small stars will become dense, cool, black dwarfs.
Large stars will continue collapse to enormous density with gravitational forces too strong for anything to escape
Even light, radio communications are trapped--nothing can escape black hole.
Fabric of space-time is warped by tremendous gravity inside black hole
Mass of black hole is same as star that created it so gravity outside black hole is same as if original star were still there.

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