Gravitation (astronomy)
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In astronomy, the discovery and application of Newton's law of gravity accounted for the detailed information we have about the planets in our solar system, the mass of the sun, the distance to stars and even the theory of dark matter. Although we haven't traveled to all the planets nor to the sun, we know their mass. This is through the study of the law of gravity. In space everything is in an orbit around some massive object. They maintain orbit because of the force of gravity between them. Planets orbit stars, stars orbit galactic centers, galaxies orbit a center of mass in clusters, and clusters orbit in superclusters.
By watching how the position of a planet changes with respect to earth over the course of a year, we can determine by using geometry how far that planet is from the sun compared to how far the earth is, thus getting the distance from that planet to the sun. Copernicus calculated the distances of the inner planets and Kepler noticed a relation between them and their orbits. When Newton formulated his law of gravity, he generalized Kepler's third law to show that the masses of the sun and the planets were involved in the calculation. From Newton's law of gravity, science calculated the mass of the sun basically using Kepler's third law that the sidereal period of an object in orbit around another object cubed is equal to the distance between them, the radius, squared, in conjunction with Newton's law of gravity applying the product of the masses.
From this calculation using Newton's law of gravity any two orbiting objects in the universe could be compared and their masses could be calculated. Where the sidereal period is known then the centripetal acceleration is known given the distance between the objects. Therefore, from a known velocity of an astronomical object orbiting around another astronomical object and from the known distance between them, you can calculate the masses of the objects. This is all due to the law of gravity where the force between objects is proportional to their masses and inversely proportional to the distance between them.
The calculations from Newton's law of gravity are so exact for astronomical measurements (except near black holes and neutron stars) that in 1846 two astronomers, John Couch Adams and Urbain Le Verrier, working independently, located an undiscovered planet later called Neptune simply by mathematical calculations using the law of gravity. (In fact, these calculations have been described as "totally wrong", and the agreement of Neptune's actual position with its calculated position an "accident" [1]. However, this was due to human error, not a flaw in the law of gravity.)
A self-gravitating system is a system of masses kept together by mutual gravity. An example is a binary star.
