6.5 Newton's Universal Law of Gravitation

The force of gravity causes each.

The force of Earth's gravity on us causes our feet to be strained.
An apple falls from a tree because of the same force above Earth's surface.
The Moon is able to travel at a distance of hundreds of millions of meters because of gravity.
The same force causes planets to circle the Sun, and stars to circle the center of the galaxy.
Another example of simplicity is gravity.
It is the least understood of the four basic forces found in nature.
It is a force that acts at a distance, without physical contact, and is expressed by a formula that is valid everywhere in the universe.

The first scientist to show that the force of gravity could explain both falling bodies and motion in the sky was Sir IsaacNewton.

The force that caused our weight and motion was not the first to be suspected.
Falling bodies and planetary motions have the same cause, according to Galileo Galilei.
Robert Hooke, Christopher Wren, and Edmund Halley all made progress in understanding gravitation.
To show that the motion of heavenly bodies should be conic sections--circles, ellipses, parabolas, and hyperbolas--Newton proposed an exact mathematical form.

It had been known for some time that moons, planets, and comets follow such paths, but no one had been able to propose a mechanism that caused them to follow them.

When he saw an apple fall from a tree, he realized that if the force of gravity could extend above the ground to a tree, it could reach the Sun.

The inspiration ofNewton's apple may be based in fact.
The universal law of gravitation and his laws of motion gave tremendous support to the idea of underlying simplicity and unity in nature.
Scientists expect simplicity to emerge from their inquiries into nature.

The force of gravity is easy to understand.

It depends on the mass of people involved and the distance between them.
The force is proportional to the product of their mass and the distance between them.

The centers of the mass of these two bodies are joined by a line.

The force is the same on each.

The force on each object is the same as the force on the other.

The bodies we are dealing with are large.

The units of are such that a force in newtons is obtained from them.

Two 1.000 kg mass separated by 1.000 m will experience the same attraction.
This force is small.
The small magnitude of the force is not out of the ordinary.
We don't know that mountains exert force on us.
The attraction of the entire Earth on us is due to our body weight.

The acceleration is due to gravity.

The weight of an object is the force between Earth and it.

The mass of the object is the mass of Earth, and the distance between the centers of the object and Earth is 6.42.

This is not related to the body's mass.

Galileo's observation of a force that causes objects to fall with the same acceleration is explained in terms of a universally existing force of attraction between mass.

There are still attempts to understand the force.

Modern physics is looking at the connections of gravity to other forces, space, and time.
General relativity makes us think of gravitation as bending space and time.

We make a comparison similar to one made byNewton.

The centripetal acceleration of the Moon should be equal to the force of gravity if it caused the Moon to go around Earth.

The distance from the center of Earth to the center of the Moon is the same as the acceleration due to gravity at Earth's surface.

The Moon is nearly circular in shape.

The moon's angle of view is 6.48.

The center of the Earth is the direction of the acceleration.

Earth's gravity causes the Moon's centripetal acceleration to differ by less than 1%.

Earth is not stationary because the EarthMoon system rotates about its center of mass, which is 1700 km below the surface.
The implication is that Earth's gravity causes the Moon to go around it.

The effect of the Moon's gravity is clearly shown in Earth.

Similar wiggles in the paths of stars have been observed and are considered direct evidence of planets in those stars.

The reflected light of the planets is too dim to be seen.

The Moon's gravity acting on Earth causes ocean tides.

Because water easily flows on Earth's surface, a high tide is created on the side of Earth nearest to the Moon.

Earth is pulled toward the Moon more than the water on the far side because it is closer to the Moon.

The water on the side closest to the Moon is pulled away from Earth.

The tidal bulge is an effect of the tidal forces between a natural satellite and a primary planet that keeps the Moon's orientation.

The actual tidal period is about 12 hours and 25.2 minutes, but because the Moon moves in its own way, there are two tides per day.

The moon attracts the water on the near side of the ocean more than the water on the far side.

The sizes and distances are not large enough.
Earth rotates under the tidal bulge and there are two high and two low tides per day.

The Sun has less effect on tides than the Moon.

Spring tides occur when Earth, the Moon, and the Sun are all aligned.
neap tides occur when the Sun is at an angle to the Earth-Moon alignment.

This figure is not drawn to scale.

Tides are not unique to Earth.

There are a few likely candidates for black holes.
These are larger than the Sun but have smaller diameters.
They can tear matter from a companion star because of the great tidal forces near them.

Light cannot escape a black hole with its strong gravity.

The black hole was created by a single star.
The black hole tears matter from the companion star.
Light and X-rays are visible from Earth when this matter is sucked into a black hole.

The apparent gravitational field experienced by astronauts is very different from the force caused by black holes.

Weightlessness doesn't mean that the astronauts aren't being acted upon.
There's no "zero gravity" in the space program.
The term means that a person is in free-fall due to gravity.
The passengers inside the elevator will experience weightlessness if the cable breaks.
Some rides in amusement parks have short periods of weightlessness.

The International Space Station has astronauts on it.

Over the past three decades, many interesting biology and physics topics have been studied in the presence of microgravity.
The effect on astronauts of extended times in outer space is of immediate concern.
This environment will cause muscles to atrophy.
There is a loss of bone mass.
The cardiovascular adaptation to space flight study continues.
The higher the column of blood, the higher the pressure in the feet.

When standing, 70% of your blood is below the level of the heart, while in a horizontal position, just the opposite occurs.

The management of diseases on Earth can be influenced by some findings in space.

Experiments in space show that somebacteria grow faster in microgravity than they do on Earth.

Studies show that space-grown cultures can increase the production of antibiotics by a factor of two.
One hopes to be able to understand these mechanisms so that they can be replicated on the ground.
In another area of physics space research, crystals grown in outer space have higher quality than those grown on Earth, so crystallography studies on their structure can yield better results.

Plants have evolved with gravity.

Shoots grow upward.

Plants might be able to provide a life support system for long duration space missions by regenerating the atmosphere, purifying water, and producing food.

There is still uncertainty about structural changes in grown plants in a microgravity environment, despite some studies indicating that plant growth and development are not affected by gravity.

The universal gravitational constant is determined by experimentation.

The first accurate definition was done by Henry Cavendish in 1798, more than 100 years after the publication of the universal law of gravitation.
The strength of one of the four forces in nature is determined by the measurement of.

Knowing that an accurate value for Earth's mass could be obtained was an important consequence.

The mass of the object is the mass of Earth, and the distance between the centers of the object and Earth is 6.52.

The quantities on the right are known from direct measurements.

In Satellites and Kepler's Laws: An Argument for Simplicity, we will see that knowing also allows for the determination of the moon's mass.
The fundamental constants in physics are the least well determined.

Other aspects of gravity are explored in the Cavendish experiment.

One of the most interesting questions is whether the force depends on substance or mass, for example, if one kilogram of lead exerts the same force as one kilogram of water.
Early in the 20th century, a Hungarian scientist pioneered this inquiry.
He found that the force does not depend on the substance.

Experiments have improved upon those of Eotvos.

Experiments such as those of Eric Adelberger and others at the University of Washington have put severe limits on the possibility of a fifth force and have verified a major prediction of general relativity.
Cavendish used a parallel plate to examine how the law of gravitation works over sub-millimeter distances.
No deviation has been observed so far.