1. Universal Gravitation
Chapter 8

2. Isaac Newton and Gravity
Newton realized an apple falls because of force
Moon follows circular path, force needed
Newton first to realize gravity causes both.
Moon is actually “falling” towards earth
Tangential velocity (sideways) keeps it going around earth instead of into it

3. Law of Universal Gravitation
Newton extended gravitation theory to all objects,
Realized gravitational attraction is property of all mass
Attractive force is directly proportional to product of two masses
Inversely proportional to square of distance between them

4. Law of Universal Gravitation
F ~ m1 m2/d2
Proportionality constant G must be used to make quantities equal
F = Gm1 m2/d2
G = force between 2 1-kg masses, 1 m apart
Its value is G = 6.67 x Nm2/kg2
Henry Cavendish first to measure G

5. Law of Universal Gravitation
Gravity very weak force
Force of attraction with earth is weight
Weight depends on distance from center of earth
On top of high mountain, you weigh less
Using G and radius of earth we can calculate mass of earth = 6 x 1024 kg

6. An Inverse-Square Law
Force of gravity varies inversely with square of distance between objects
For a spherical body, distance is measured from its center
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.

7. An Inverse-Square Law
Other inverse-square relationships: light and sound intensity, magnetic and electric force.
Force of gravity weakens rapidly with distance due to spreading of force into surrounding space, but never really zero, even in deep space.

8. Gravitational Fields
Gravitational force acts over a distance without contact
Caused by interaction with gravitational field
Field can be thought of as lines of force radiating from objects
Strength of field is force per unit mass exerted on object: g = F/m

9. Gravitational Fields
Earth’s grav. field strength is actually acceleration due to gravity at any location
Combining g = F/m and F = G mM/R2, we find g = GMe/ R2, where Me = mass of the earth and R = distance from center of earth.
g for any planet can be found using this formula.

10. Gravitation and the Universe
Planets, moons, stars are spherical due to gravity
All planets affect each other, can cause perturbations (wobbles) in orbits
Neptune and Pluto were discovered because of perturbations in Uranus’ orbit.
Perturbations of distant stars have led to discoveries of planets, double stars

11. Gravitation and the Universe
“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.

12. Gravitational Field Inside Earth
If hole were drilled through earth and you fell in, what would happen?
As you fall, 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.

13. Satellites--Circular Orbits
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 of revolution is 24 hours, satellite remains over same point on earth--communication satellites do this (geosynchronous orbit)

14. Geosynchronous Orbit
Altitude: 36,000 km

15. Satellite Web

16. Satellites--Elliptical Orbits
If speed is faster than needed for circular orbit, elliptical orbit can result
Ellipse is oval with two focal points (foci)
Speed varies in elliptical orbit
Faster speed close to earth, slower when farther away
All planets follow elliptical orbits around sun

17. Elliptical Orbit

18. Tides
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.

19. Tides
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

20. Eclipses 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.

21. Black Holes
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.

22. Black Holes
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 (except small amounts of radiation).
Edge of black hole is called event horizon

23. Black Holes
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.