GRAVITY

THE UNIVERSAL LAW OF GRAVITY

• Newton had the insight to see that force between the Earth and a falling apple is the same force that pulls the Moon in an orbital path around the Earth, a path similar to a planet’s path around the Sun.

LAW OF UNIVERSAL GRAVITATION

• Every body in the universe attracts every other body with a force that, for two bodies, is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them.

• The greater the masses of m1 and m2, the greater the force of attraction between them

• The greater the distance of separation d, the weaker the force of attraction

UNIVERSAL GRAVITATIONAL CONSTANT, G

• The magnitude of G is identical to the magnitude of the force between a pair of 1-kg masses that are 1 meter apart: 0.0000000000667 newton.

• This small magnitude indicates an extremely weak force.

• Henry Cavendish experiment YouTube Video

GRAVITY & DISTANCE: THE INVERSE-SQUARE LAW

A CAN OF PAINT

• What would happen if you strayed a can of paint from 5 m away? What about 10m? 15m?

• What changes would you see in the spray of the can?

INVERSE-SQUARE LAW

• A law relating the intensity of an effect to the inverse square of the distance from the cause:

• Gravity follows an inverse-square law

• As do the effects of all phenomena wherein the effect from a localized source spreads uniformly throughout the surrounding space.

• Such as electric, magnetic, light, sound, and radiation phenomena.

OCEAN TIDES

• Newton showed that the ocean tides are caused by differences in the gravitational pull between the Moon and the Earth.

• Gravitational force between the Moon and the Earth is stronger on the side of the Earth that is farther from the Moon

• This is because the gravitational force is weaker with increased distance

• To understand the difference in gravitational pulls by the moon. Imagine that you have a large ball of jell-o. If you were to exert the same amount of force on the entire ball then it would remain spherical as you accelerated, but if you were to pull harder on one side than the other there would be a difference in acceleration and the ball would become elongated.

• This is what happens with the Earth and the Moon

• Both the Earth and the Moon undergo centripetal acceleration. Since both the Moon and the Earth are elongated there is a bulge of nearly 1 m above the surface level of the ocean.

• The Earth spins once per day, so a fixed point on Earth passes beneath both of these bulges each day.

• This produces two sets of ocean tides per day

• High and Low tide

• We actually experience two high and two low tides each day. This is experienced every time the Earth makes a quarter turn.

• The two-high-tide cycle is actually at 24 hour and 50 minutes.

• This why tides do not occur at the same time everyday.

• The Sun also contributes to ocean tides, although it is less than half as effective as the Moon in raising tides.

• The Sun doesn’t have a large affect on the ocean tides because of the great distance of the Sun, the difference in its gravitational pull on opposite sides of the Earth is very small.

• Look at figure 9.15

• The Sun does produce tides but they are only about half as much

• When the Sun, Earth, and Moon are aligned, the tides due to the Sun and the Moon (this is also when we experience lunar eclipse). Then we experience higher than average high tides and lower than average low tides.

• These are called spring tides

• The Earth and the Moon have elliptical obits.

• Highest spring tides occur when the Moon and Sun are closest to the Earth

• When the Moon is halfway between a new Moon and a full Moon, the tides due to the Sun and the Moon partly cancel each other out.

• Then the high tides are lower than average and the low tides are not as low as average low tides.

• These are called Neap Tides

• The tidal effects in the ionosphere produce electric currents that alter the magnetic field that surrounds the Earth.

• These are magnetic tides

TIDES ON THE MOON

• There are two tidal bulges on the Moon for the same reason there are two tidal bulges on Earth.

• Unlike Earth, the tidal bulges remain in a fixed location.

• The Moon takes 27.3 days to make a single revolution about its own axis.

• The Moon always shows the Earth the same face because whenever the Moon’s long axis is not lined up toward Earth, Earth exerts a small torque on the Moon.

• This tends to twist the Moon toward aligning with Earth’s gravitational field.

GRAVITATIONAL FIELDS

• A gravitational field is an example of a force field, for any body with mass experiences a force in the field space.

• Another example of this would be a magnetic field

• Look at figure 9.21 on p.172

EINSTEIN’S THEORY OF GRAVITATION

• Einstein’s perceived a gravitational field as a geometrical warping of four-dimensional space and time.

• He realized that bodies put dents in space and time somewhat like a massive ball placed in the middle of a large waterbed dents the two-dimensional surface.

• The more massive the ball, the greater the dent or warp.