13.1 Gravitational Fields

Gravity is a field force, and the strength of the gravitational field at any point is equal to the the acceleration that would be caused on any object at that point.
At the surface of the earth, the strength of the gravitational field is equal to familiar gravitational acceleration constant, which is g = 9.8 (m/s^2)

In order to find the gravitational field strength (g) at any point a distance (r) from the center of mass of a planet of mass (m) one would use a modification of the universal gravitation equation

  • g = G(m/r^2)
when G = 6.673 × 1011(N·m^2)/(k·g^2)

13.2 Gravitational Field Inside a Planet

The above equation implies that all of the mass of the planet is on one side of you, if you burrow down into the planet, some of the planet’s mass will be on the other side of you. For this reason that mass will partially cancel the force from the rest of the mass and reduce the effect of gravity.

If one were to burrow into the earth as to reach the exact center of the planet they would feel absolutly no gravitational forces (i.e. weightlessness).

  • This is due to the balance of math between both sides of the planet.

13.3 Weight and Weightlessness

Gravity, just like any other force, causes acceleration.
We do not always think of gravity in this manner due to the fact that the only noticable effect of gravity is when it is pressing us against the surface of the earth.

If you are inside of an enclosure that is being accelerated (such as an elevator) you will feel a change in your apparent weight. This is not a change in you weight, yet it is just an effect of the enclousure changing speed.
  • Moving up will give the sensation of gaining weight.
  • Moving down will give the sensation of losing weight

If somehow the cables supposrting the enclosure were to break then, you and the elevator car would both fall at the same rate and you would feel no weight relative to the elevator.

13.4 Ocean Tides

Issac Newton discovered that the ocean tides are caused by differences in the gravitational pull of the moon on opposite sides of the earth.
  • On a solid planet, these wouldn't be noticeable but for a planet with liquid such as the water in the oceans, the water is pulled more on the side which is closer to the moon and less on the side which is away from the moon.

This results in a tidal bulge on the side closest to the moon (pulled there by the moon), On the side away from the moon (where there is a smaller pull from the moon and the oceans move away) there is the opposite affect.

There are also similar tidal bulges produced by the sun yet since the sun is much farther away they are less than one half of the size of those that are produced by the moon.

13.5 Tides and the Earth and Atmosphere

The majority of earth itself is not a solid object, it is made from a slightly flexible crust which lies on top of a molten inside.
Earth's layers

Because of thie flexibility of the earth's curst itself, the earth is affected by the tidal forces.

It’s not noticeably effected due to the fact that everything on the surface moves with the surface, but it is measurable.

  • It has been found that each day the earth rises and falls by as much as 25 cm!

13.6 Black Holes

Stars are constantly being affected by two forces; the force of gravity, which pulls the gas in toward the center and they are affected by nuclearfusion in the core of the star which pushes the gas back out.

Occasionally the nuclear fusion weakens over time, this weakening of the nuclear fusion will lead to the gravitational force pulling the gas inward.

  • If there is enough gas there to pull inward then eventually the star will collapse inward onto itself and form what is known as a black hole.

The amount of mass in a black hole is equal to that of the star that collapsed.
  • 750px-Black_Hole_Milkyway.jpg
    Projected view of a black hole outside of the milky way galaxy.
    Anything that was orbiting the star will now orbit the black hole instead.
    • In effect, the star is totally replaced

The only difference between the star and the black hole is size — since the black hole it is much smaller than the star, it is possible to get much closer to the center than when the body was a star.
  • Getting closer to the center will greatly increase the gravitational force to an unbelievably large amount.
    • Eventually the pull of gravity will become so large that even light is unable to escape from the center.

Works cited:
Conceptual physics 3rd edition
Images have hyperlink work cited things attached