At the core of astronomy is gravity, and the theory of gravity first came to us from the genius of physics and astronomy of the 17th century, Isaac Newton. Isaac Newton was an extraordinary figure in the history of science. Early in his life, he came up with a theory of gravity that has stood us in good set for centuries until it got its final adjustment in general relativity from Albert Einstein. Newton came up with his theory of gravity using the telescope, but almost entirely based on mathematics and physical thinking. Even though he developed a very successful theory of gravity, there were things about gravity that Newton didn't understand. When he was asked about this force of nature that apparently operated over the vacuum of space instantaneously and what that meant, he said, "I frame no hypothesis." In other words, even Newton, as brilliant as he was, could not explain all the subtleties of gravity. However, Newton's theory of gravity applies in most of the situations of the universe, which involve relatively weak gravity. It perfectly describes the objects of the solar system, the stars within the galaxy, and most of the motions between galaxies in the larger universe. When Apollo 8 was heading towards the moon, Ed Anders, one of the astronauts, was patched through to his son, and his son asked, "Daddy, who's driving the spacecraft?" Anders said, "Isaac Newton's driving, son." So even though general relativity is a superior and more all encompassing theory of gravity, Newton's theory works for almost all the work that NASA does, sending spacecraft around the solar system, or to the moon, or an orbit of the Earth. Newton's universal law of gravity has a very simple mathematical form. It says that the force between any two objects equals a constant of nature, the gravitational constant, times the mass of the two objects divided by the square of the distance between them. It's a simple equation that says that the force is proportional to each of the masses and inversely proportional to the square of the distance between them. Notice the assumptions, Newton's law of gravity applies only to two objects isolated in space. If you actually add a third or fourth object, Newton's law is no longer exact. It can be solved with infinite precision given a sufficiently powerful computer, but it's basically a numerical approximation. That's why the deterministic view of Newton's theory is simply wrong. Newton's law of gravity is not deterministic in any complex situation. Notice also the extraordinary nature of gravity with its infinite reach. The force of gravity between two objects diminishes with the square of the distance, but the inverse square of a very large number never goes to zero until the number is infinite. In other words, gravity has infinite reach. That has profound consequences for how we deal with gravity, how we do the calculations, and also how we understand the universe. The key attribute of Newtonian gravity is that it's an inverse square law. This is what allows us to calculate the force between objects at different distances. This is a profound realization. Also, we can see that Newton's theory unifies things that happen on the Earth with things that happen in space. It turns out that the apple probably didn't fall on Newton's head. That's just a story. It is nice, however, that his childhood home in Lincolnshire does have an apple orchard in the backyard. Perhaps he was watching an apple fall when he got his insight. If you work this mathematically, it turns out that the motion of an object or an apple dropping is similar to the motion of the moon in the orbit of the Earth, for example. If you do the math, it turns out that the moon is 60 times further away than the Earth surfaces from the center of the Earth, where all the gravity seems to act. Do the math, it turns out that the apple does drop in one second 3,600 times or 60 squared further than the moon deviates from a straight line in its orbit of the Earth. Newton's theory really does unify the motions of all objects operating under gravity. The other thing that was part of his early calculations was how the gravity of an extended object operates. For a spherical object like the Earth, the Earth acts as if all the mass was concentrated at the center. So we can replace the extended mass of the Earth by the sum of its mass located at its center. Newton's simple equation applies to point sources of mass, and for an extended object like a planet or a person, the calculation is actually quite complicated because you need to work out the force of gravity between all parts of the Earth on a person and vice versa to calculate the total gravity. Newton actually developed calculus to do this calculation more easily, and he and Leibniz warred for a decade or more over who invented the calculus. But a specific mathematical technique was required to make these gravity calculations more simple. This idea of gravity means we must distinguish between the concepts of mass and weight. Mass is the amount of stuff in an object, essentially the number of atoms it contains and what the individual mass of those atoms is summed up. Weight is different. Weight depends on local gravity. So you can be weightless if you're free falling in gravity but you always have the same mass. Equally, you could be in an elevator accelerating upward and feel larger than your normal weight, but your mass is unaltered. That is the amount of atoms, the amount of stuff you contain. The idea of weight as local gravity means that in different situations in the universe or around the solar system, your weight can vary while your mass never does. Even a massive object like the Earth, you can use Newton's law to work out how fast an object has to go before being liberated from that object. As we see example we looked at earlier where Newton imagined a cannon firing horizontally off a tall mountain, at what speed would be required before the falling of the cannonball in a parabolic trajectory match the rate at which the falling surface of the Earth fell away from that object, an orbit? That's the orbital velocity. He also calculated how much more energy would be required to liberate the object entirely from the gravity of the Earth, essentially send it to an infinite distance from the Earth. For any object, the escape velocity is the square root of two or about 40 percent more than the circular velocity or the velocity required to put in an orbit. These are the fundamental relationships that underlie the entire space telecommunications and space travel business. The energy requirement to create orbital or escape velocities are the basis of almost everything that NASA does. In terms of exploring the solar system or other gravity situations, we can think of terms of the gravity as a potential well, where certain amount of energy, or velocity, or kinetic energy is required to be liberated from that potential well. Being liberated from the Earth's gravity, of course, does not imply being liberated from the solar system because the Earth is an orbit around the sun. So a separate calculation is involved in understanding how much velocity or kinetic energy is required to liberate an object like a satellite from the solar system itself. Quite important in space travel and in sending satellites around the solar system are particular situations where gravity balances. These are called the Lagrange points. They were first theorized by a mathematical physicist in France 200 years ago. The Lagrange points are valuable in space exploration. There are places where gravity balances, so very little energy is required to keep a spacecraft or a probe in these situations. Some of the Lagrange points are unstable, in which case small retro-rockets or ballistics are required to keep a satellite in its position. Only one of them is stable. These are valuable locations and many large space missions of the recent past or future are destined for the Lagrange points. In particular, the second Lagrange point, L2, is a favored location for many NASA and ESA missions, such as the Wilkinson Microwave Anisotropy Probe, WMAP, and Herschel and Planck to current satellites. The James Webb Space Telescope is also destined to be launched there in 2016. Space travel also uses other tricks of gravity such as gravitational assist. Gravitational assist is a nice idea. If you bring a fast-moving object up behind a larger more massive object, then even without them colliding, their gravitational interaction can transfer kinetic energy to the smaller object, the space probe. It's a gravity assist. Doing this sequentially can speed up an object like a space probe to the point where it can reach an outer solar system target much more quickly than if you had to spend that energy on extra propellant. Gravity assist is used routinely to get space probes into the outer solar system. Often, these probes have to do closed pass bys of inner solar system objects, like Venus or the Earth, to be able to push themselves fast into the outer solar system and reach their targets. This is a particular and complex pattern of gravity assist enjoyed by the Cassini Probe as it headed towards the Saturn system. Another important feature of gravity is the tidal force. For an extended object like a planet or a moon, the gravity on the near side of the object from a second object is larger because of the inverse square law than the gravity on the far side of the object. This difference between the gravity force and the near and far side amounts to a stretching force or tidal force. The tidal force dictates how large a moon can be in close proximity to a planet before it's actually ripped apart, and its rocks are destroyed by the tidal force. Tides also operate to cause tides in the oceans on the Earth and actually land tides. Earthquakes are more frequent slightly at new moon and full moon because in that situation, the Earth, Sun, and Moon align to create a slightly larger tidal force on the Earth. The dominant force in the universe is gravity. Even though it's the weakest of the four forces of nature, its infinite range and universal positive attraction means that it governs how structure happens in the universe. The theory behind gravity was first put in place by Isaac Newton. Even though Einstein embellished the theory with the theory that acts better in situations of strong gravity, Newtonian gravity still works perfectly well and it's quite precise for most situations in the solar system and the galaxy. Newton's universal law of gravitation states that the force between any two isolated objects is governed by the mass, and the product of the mass between the two objects, and the inverse square of the distance between them. So gravity is an infinite reach force. The calculation of gravity between extended objects or more than two objects requires computers to generate an accurate result.
