II) Modern Concepts

A) Mass versus weight

To understand gravity, we must first understand the difference between mass and weight. To most people this seems like a difference without a difference, since we use the terms almost interchangeably. To a scientist, however, it is of crucial importance. Loosely speaking, mass is the amount of material in an object. A large object with low density (say a boulder made of Styrofoam) might have the same amount of mass as a small object of high density (a small lump of lead). The mass measures how hard it is to start an object moving or to slow it down again. Pushing a car is hard work (even on a flat road) because it is very massive.

So what is weight? Weight is the force of attraction between an object and whatever astronomical body it is on. Notice that the mass is simply a property of the object itself, but the weight is a property of the object and its location. The important thing is that moving a car in zero-gravity would be just as hard work as it is on Earth, because the car's mass isn't any different, even though its weight would be zero. It would take a great deal of work to get the car moving in the first place, due to its mass. Astronauts routinely complain that it is awfully hard work to move around or work on the satellites they have to deal with even though they and their tools are weightless—they are not mass-less; therefore, they still require effort to move.

B) Newtonian Gravity is still correct

Although we now know that Newtonian Gravity is only an approximation, we still use it all the time. Why is this? The reason is that it is a superb approximation for almost all uses in the Solar System. Spacecraft are sent to the moon and back, probes are put into orbit around Jupiter, and mile-long bridges are built-- all using Newtonian Gravity with only the smallest of errors. Newtonian gravity works unless the speeds involved are close to that of light, the masses are tremendous, or both.

C) Gravity pulls things together

Gravity is a "together" force, not a "down" force. We only think of it as down because we have only very local experience with it. On the Earth, the force of gravity is everywhere towards the center of the Earth. A beautiful example of this "together" quality of gravity is the formation of the Sun and Solar System. The Solar System formed out of a huge cloud of gas and dust that was many times larger than it is presently. Slowly, over time, the cloud contracted under the influence of gravity.

D) All objects have gravity

Mass is an intrinsic property of matter. It is the amount of "stuff". Every object exerts a gravitational attraction on every other object in the Universe. And this means everything...every grain of sand, every drop of water, every atom of hydrogen in interstellar space... everything.

E) The more massive an object, the stronger its pull on other objects and the more strongly other objects pull on it

Objects with greater mass (usually larger objects, but not always!) attract others more strongly. In turn, these more massive objects are attracted with more force.

F) The closer two objects are to each other, the stronger their gravitational pull on each other

Example: Your weight on different planets depends on both the mass and size of the planet. While Jupiter is 318 times more massive than the Earth, a person would weigh only 2 1/2 times as much, not 318 times as much. This is because Jupiter is bigger than the Earth and so the person would be much more distant from Jupiter's center of mass.

G) Gravity is proportional to mass, not any other property

Only the mass is important to gravity. It doesn't matter what else is true about an object. It doesn't matter if it is pink with purple polka-dots, if it looks vaguely like Elvis, or if it is made of Swiss cheese. The only thing that determines the gravitational force is the mass.

H) Orbits, center-of-mass, and escape velocity

Almost everything in the Universe orbits around something else. Moons orbit around planets, planets around stars, stars around galaxies, galaxies in clusters. As an example, the Moon orbits around the Earth because it keeps falling towards the Earth but missing it (see above description in the history section). The important thing is that the object in orbit has a bit of motion, so it doesn't just smack into the other object but misses it instead. If two objects are released from at rest then they will fall towards each other and collide.

A circular orbit occurs when sideways motion is balanced with the gravitational force. But what if the motion is too fast? Then the object will not only miss the central object but it will fly off into space. The strength of gravity will not be strong enough to keep the two bodies together. The speed an object needs to go to fly away forever is called escape velocity. From the surface of the Earth escape velocity is 7 miles a second. From the surface of the Sun it is 387 miles per second!

But remember the gravitational force is reciprocal. If the Earth attracts the Moon, the Moon also attracts the Earth. So the Earth should also move. Of course the Earth is much more massive than the Moon, so it doesn't move as much. The movement of the Earth-Moon system is like a parent swinging a child around. The child (Moon) moves in a large circle, while the parent (Earth) moves in a small circle. This is the principle through which planets around other stars have been found. We think of planets orbiting stars; in reality, planets and their stars orbit the "center of mass" of the stellar system, so orbiting planets cause their stars to wobble slightly. This wobble can be detected as a periodic Doppler shift in the star's spectral lines or by directly measuring the star's proper motion wobble across the sky. Both methods require very precise measurements over long periods of time.

I) Weightlessness is experienced in free fall - not just in space

Weightlessness is not the absence of gravity. It occurs anytime one is falling! In orbit one is falling continuously (but missing the Earth!) and so one doesn't feel the gravity. But it is there: otherwise one would fly off into space. Gravity does not end outside of the Earth's atmosphere.

Weightlessness is a fascinating phenomenon. Once one gets over the initial fear of falling, it is like flying. Astronauts love the sense of freedom it gives them to be able to float in the air. But weightlessness also has interest beyond the aesthetic. Gravity is a guiding principle behind the organization of life. How does a plant seed know what side is up? How do fish orient themselves in the water? Our own bodies evolved with gravity. Our leg bones are thicker to support our weight, our hearts have extra muscle to pump blood up and down our bodies, our inner ears can detect even small departures from the vertical. If we go for long periods in conditions of reduced gravity, our bones become fragile and brittle. Understanding how our bodies react to being in weightlessness will be essential for long term habitation in space, but it will also help to understand our bodies in general, perhaps leading to new discoveries and cures. In a similar way, observing the effects of weightlessness on plants and other animals will help us understand these organisms.

Another important aspect of weightlessness is its industrial potential. For example, it is possible to grow huge single crystals in space, much larger than is possible on earth. These crystals are valuable in electronics or for super strength materials. Crystal don't grow nearly so large on Earth because the gravity interferes with the growth.

J) Very massive objects (stars, planets etc) are round because of gravity's inward pull

Gravity pulls things together. When there is enough mass the rigidity of the object is insufficient to hold its shape against the force of gravity. All the matter wants to be as close to the center as possible. The shape that allows this is the sphere. To see this imagine any other shape, say a cube. The cube's corners are farther away from the center than the faces. Under intense gravity the corners will be flattened out. Continue this process and you end up with a sphere.

K) All objects at the Earth's surface fall towards the Earth with the same acceleration

When Galileo performed his ground-breaking experiments with falling objects, he noticed a very odd fact: all objects fall at the same rate regardless of the mass. This is very strange... If I hold a heavy object in my hand it clearly is pressed down with much greater force than a light object. Why doesn't it fall faster? To understand what is going on consider again Newton's laws that govern the motion of an object in a gravitational field due to the Earth (see also p. 9). We have the law of gravitation, which gives the force exerted on the object:

Where M is the mass of the Earth, m is the mass of the small object and R is the distance between the center of the Earth and the small object. We also have Newton's laws of motion which tell us how an object moves under the influence of a force:

This says that the acceleration (a) of an object is proportional to the force exerted and inversely proportional to its mass (massive objects are harder to push!). Together these equations will tell us how an object will move in a gravitational field. The first gives us the force and the second tells us how the object moves due to the force. All we have to do is substitute the force (F) from the first equation into the second. The result is:

where the mass of the object (m) has cancelled out! So the acceleration depends only on the mass of the Earth, the distance to the Earth's center and Newton's constant G. This is true because the gravitational force is proportional to the mass but the acceleration is inversely proportional to the mass so the mass cancels out.

This explanation is very clever but it leaves something unexplained: why are the two "masses" occurring in the equations the same? Why is gravity dependent on the same quantity as the motion is? After all motion and gravity seem to be very different things. It is peculiar that they depend on the same quantity. For years no one knew what to make of this until Einstein came along with General Relativity.

In General Relativity, gravity is the curvature of space due to the presence of matter. The path of an object is bent in a gravitational field not because of a force acting on it, but because the space it is travelling in is itself bent (see pp. 9-10). But all objects travel through the same space, so they all move in the same way. The acceleration of an object is due to a property of the space, not of the object. Thus, it must be the same for all objects, regardless of mass or other properties.

A nice exhibit would be to have a steel ball and a feather dropped together in a vacuum (in which there is no air resistance) and see them fall at the same rate. A similar experiment was done by one of the Apollo 15 astronauts on the Moon (see URL http://vesuvius.jsc.nasa.gov/er/seh/feather.html).

L) Acceleration is equivalent to gravity

This is a restatement of the equivalence principle that led Einstein to General Relativity. Simply put, in a closed room, it is impossible to tell whether the room is accelerating or whether it is in a gravitational field. One consequence of this is that acceleration can be used to simulate gravity. Moving rapidly in a circle is a form of acceleration (try doing this in a car and see!). If one rapidly spun a space station, one could produce a feeling of gravity for those inside (this is just how a centrifuge works). This may also be done for trips to Mars to help keep the astronauts healthy.

M) Tides and Roche's limit

When two objects orbit each other, the gravitational force is stronger on the sides facing each other than on the far sides. But the gravitational force is cancelled out by the orbital motion (i.e. the motion of the objects revolving around each other) only precisely at the center of the objects. Thus the forces are unbalanced both on the near sides and the far sides. In the case of the Earth and the Moon, the result on Earth is the ocean tides. Water on the Earth piles up on the sides close to and far away from the Moon (but only by a little bit-- a couple of feet typically).

But this differential force can have much more major consequences. There exists a critical distance between two massive objects where this tide-raising force is sufficient to tear the smaller object apart. This distance is known as the Roche Limit, after its discoverer Edouard Roche (1850), a French mathematician. A beautiful example of this was the disruption of comet Shoemaker-Levy 9 as it rounded Jupiter for the first time. Do you recall the beautiful Hubble images (the necklace) of SL9 just before impact? Before the tidal forces from Jupiter acted, the comet was a single object.

N) Gravity is the weakest of the four fundamental forces

There are four fundamental forces in the Universe. They are: the electromagnetic force, the "weak" force, the "strong" force, and gravity. The electromagnetic force is perhaps the most common force. It is what holds atoms together, drives chemical reactions, and keeps objects from floating through each other. You have perhaps heard that most of matter is empty space. So why don't objects pass right through each other? The electromagnetic force is the reason. All the chemical reactions are also consequences of the electromagnetic force (taste, touch, smell). The very light we see with our eyes is a consequence of the electromagnetic force. Light is, after all, electromagnetic radiation.

The "weak" and "strong" forces are both only important in the atomic nucleus. Among other things, the weak force is responsible for radioactive decay. The strong force is what keeps nuclei and nucleons together. Without it, all matter would disintegrate in the tiniest fraction of a second. When huge "atom smashers" (more correctly particle accelerators) are used to probe the constituents of matter, they are probing the strong and weak forces.

The strong force is, reasonably enough, the strongest of the four forces, next comes the electromagnetic force, followed by the weak force. Gravity is by far the weakest force. The electromagnetic force between an electron and a proton is about 10,000,000,000,000,000,000,000,000,000,000,000,000,000 (10^40) (ten thousand trillion, trillion, trillion) times stronger than the gravitational force!

O) Gravity is nevertheless the main mover and shaper in the Universe

So why don't the other forces dominate the Universe? There are two reasons. The first deals with the range of the forces. Gravity and electromagnetism have infinite range. However, the forces weaken with distance, but not very quickly. By contrast, the weak and strong forces are limited to distances small compared to atoms. At distances farther than a hundred thousandth of a nanometer, the weak and strong forces are negligible. Still, electromagnetism is infinite in range and so much stronger than gravity. Why isn't it more important? The reason is that electric charge comes in two types, positive and negative. Like charges repel, and opposite charges attract. So imagine a lonely positive charge sitting in the Universe, perhaps a proton. It will exert a tremendous force on any loose negative charges nearby, and they will move towards it. But as soon as the first negative charge reaches it, then taken together they have a net charge of zero, so they stop attracting other particles! Any free charge quickly cancels out with an opposite charge, so most of the Universe is neutral and hence exerts no electromagnetic forces. This leaves gravity, which is always attractive and never cancels itself out.

P) Gravity determines the fate of the Universe

How will the Universe end? We know now that the Universe began about 12-16 billion years ago, when the size of the Universe was zero and the density tended towards infinity. Since then, the Universe has been expanding. If the Universe continues to expand, it will eventually freeze as the temperature drops to absolute zero and the stars burn out. On the other hand, if the expansion stops, the Universe will re-collapse, and the world will end in fire as we return to a state much like the initial Big Bang.

But what controls whether the expansion stops or not? Gravity! As the Universe expands, the galaxies are getting farther and farther away from each other. But remember, gravity tries to pull galaxies together. So the expansion is slowed down by gravity. The same is true if I throw a ball into the air. The away-from-the-Earth motion is slowed by gravity, and eventually the ball will come to a stop and then reverse its course and return down... That is, unless I throw the ball very, very hard indeed, and it reaches escape velocity! Then it will continue to travel farther and farther away. Getting back to the Universe, if the initial expansion is fast enough, then the Universe is "open," and it will expand forever. If the Universe is expanding too slowly, then it will slow more and finally stop and then re-collapse. Another way of saying this is to consider the mass of the Universe. If the Universe is too massive, then it has a lot of gravity, and it will re-collapse. If it is light, then the Universe's expansion will be able to overcome its gravity, and it will continue to expand.

Q) Gravity permits the detection of invisible stuff (stars, planets, galaxies, structure in the Universe, black holes etc.)

From an astronomical perspective, one of the most important aspects of gravity is that it gives us a tool to determine the mass of objects forever beyond our reach. Consider a star. It is very difficult to determine the mass of a star. Even if one knows the distance, and hence the absolute brightness of the star, it requires complicated (and possibly incorrect!) computer models of the structure of the star to work back to determine the mass of the star. This is a very unsatisfactory state of affairs. But now consider a binary star system. The two stars orbit each other in accordance with Newton's law of gravitation. The force of gravity depends on the mass of the stars! By making careful observations of the orbits of the binary stars, one can determine the mass directly without modeling. So, Newton's law of gravity is at the very foundation of what we know about stars.

In a similar way, the existence of planets can be inferred even if the planets themselves cannot be seen. Imagine looking at the Solar System from many light years away. Even Jupiter, the largest planet, would be at least a billion times fainter than the Sun, and it would be lost in the glare. It would be hopeless to try to look for planets directly. So how do astronomers detect extra-solar planets? The key lies with gravity. As a planet orbits a star, it exerts a gravitational force on the star. The star responds to this force by moving slightly. As the planet orbits, the star wobbles slightly. Although we cannot see the planet directly, we can see this wobble!

On a larger scale, gravity allows us to probe the contents of galaxies. By observing the orbits of the stars in galaxies, we can determine the masses of the galaxies. If we compare these masses to the number of stars, we discover something very interesting: There is much more mass in galaxies than can be accounted for by the visible stars and gas. Ninety percent of the mass in galaxies is dark.

R) What is a black hole?

Simply put, a black hole is an object so massive and so dense that not even light can escape. To get a good understanding of a black hole, it is useful to consider how a black hole is formed. A typical black hole is formed from the collapse of a high-mass star. During its life, a star is held up against the force of gravity by the high pressure pushing outward from its center. This pressure is caused by the release of energy from nuclear fusion. Without this energy source, the star would collapse. For a very massive star, at the end of its life, this energy source fails spectacularly when light elements such as helium are no longer produced by fusion and instead iron is the result of the fusion reaction. Fusion cannot progress any farther than iron, and so new energy is not released. Eventually (in a fraction of a second), the pressure is not sufficient to support the star against gravity, and the star collapses. During this collapse, the densities increase dramatically. For intermediate mass stars, it is possible that the collapse can be halted by neutron pressure. If this happens, the star becomes a neutron star. If the star is massive enough, however, even neutron pressure is not sufficient to stop the collapse, and it continues indefinitely until a black hole is formed.

A black hole has two important regions. The first is the singularity. The singularity is all that remains of the star that formed the black hole. All the matter has been crushed down by the force of gravity to a single point where the curvature of spacetime is infinite and the laws of physics breakdown. Surrounding the singularity is the event horizon. This can loosely be thought of as the surface of the black hole. But it isn't a solid surface that one could land on. The event horizon is the point of no return. If one were above it, one could still escape the black hole. If one were to fall below it, then return to the outside world is impossible. Even worse, once past the event horizon, it is impossible to stop one's fall to the center of the black hole where the singularity lurks.

S) Gravitational waves

Remember Newton's theory? The gravitational force was determined by the masses and positions of objects. Let us imagine we change the position of an object. Now the gravitational force will be slightly different. In Newtonian theory, this change takes place instantaneously. But Special Relativity forbids this! Nothing can go faster than light. At best, the change in the gravitational force can propagate outwards at the speed of light. A propagating change? This is just a wave!

But gravitational waves are more than simply the change in the force of gravity from some distant object. In Einstein's GR, gravity is not really a force, it is a warping of space and time. So the change that is propagating out from a perturbed system is a distortion of spacetime! It's like a ripple in spacetime itself. As the ripple goes by, objects are stretched and stressed (very gently). But stretching objects takes energy. Where does this energy come from? It can't just appear because energy is conserved! (Energy is neither created nor destroyed - it may change form, (motion to heat or potential to kinetic) but it can't simply disappear or appear.) The energy comes from the original object. The gravitational wave takes its energy from the source of the wave. So accelerating objects lose energy.

Now for most objects in our experience, this is hardly important. The masses involved are small and the velocities far less than that of light, and so the gravitational radiation is miniscule, almost too tiny to comprehend. Is gravitational radiation important under any circumstances? Yes, but it requires high speeds and large masses. A neutron star is the dead remnant of a massive star that has burned up all its nuclear fuel. It is a little bit more massive than the Sun, but much, much smaller, being only about 10 kilometers across. Usually neutron stars are born in isolation, but occasionally two are produced together. If they are close enough together, then their orbital velocity is very high, and gravitational waves are produced copiously (large mass and large speed). But this means that the system loses energy. But losing energy means that the neutron stars fall closer together. This makes the orbit faster, which in turn increases the gravitational waves! A vicious cycle sets in with the neutron stars spiraling in faster and faster. Eventually, they merge together entirely with a tremendous collision. Some scientists believe that gamma-ray bursts, the most powerful explosions in the Universe, are powered by these collisions of neutron stars in distant galaxies.