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Key Figures in Gravitational Science

Brahe.jpgTycho Brahe and Johannes Kepler

Tycho Brahe made observations of the motions of the planets from his great observatory on the Danish island of Hven from 1576 to 1597.  He introduced many innovations in technology and observing techniques, and understood the importance of random and systematic errors in his observations.  In 1600 Tycho Brahe employed Johannes Kepler, the most distinguished mathematician in Europe, to work on the problem of the orbit of Mars.  After Brahe died in 1601, Kepler set about analysing Brahe’s magnificent data.  Kepler fully appreciated the significance of these precise observations.  In his words:

“Divine providence has granted us a diligent observer in Tycho Brahe that his observations convicted this Ptolemaic calculation of an error of 8 arcmin; it is only right that we should accept God’s gift with a grateful mind… because the 8 arcmin could not be ignored, they alone have led to a total reformation of astronomy.”

Brahe’s observations were 10 times more accurate than all previous observations and they led to Kepler’s laws of planetary motion.

Kepler 1: The orbits of the planets are ellipses with the Sun at one focus.

kepler.jpgKepler 2: The line joining the Sun to a planet sweeps out equal areas in equal times.

Kepler 3: The square of the period T of the planet about the Sun is proportional to the cube of the length of its semi-major axis r: T2 α r3


Kepler's Third Law can be demonstrated using the average distance of planets from the Sun and their average period of revolution around the Sun.
 

Isaac Newton

newton_1_.jpgIn 1687, Isaac Newton published the Principia in which he set out his concept of the universal nature of gravity and also his law of gravity.  The line of thought leading to his mature theory of gravity started with an exchange of letters with Robert Hooke in 1679-80, but it did not become precise until after a visit from Edmund Halley in 1684. Halley, like Hooke before him, asked about the trajectory of a body under the influence of inverse-square law forces directed towards a given centre.

The Principia contains Newton’s contributions to mechanics and celestial dynamics.   He formulated the concepts of mass and centripetal force and set forth his three famous “Laws of Motion”.

Newton also showed the physical significance of Kepler’s laws by relating them to centripetal forces.  Today we write this as:

F=GM1M2/r2

principia.jpgwhere G is the gravitational constant, M1­ and M­2 are the masses of the objects and r is their separation.

The third book of the Principia lays out the Newtonian “System of the World”, a celestial dynamics system based on the action of universal gravity.  Newton presented results on the shape of the Earth and the variation of its surface gravity with latitude, showed that the complex motion of the Moon arises from the action of the Sun’s gravity superposed on that of the Earth’s, explained the way that the gravitational forces of the Sun and Moon act together to produce the ocean tides, and provided the first method for determining the trajectories of comets from limited observations.  It is not an exaggeration to say that modern astronomy, and modern science, began with the publication of the Principia.





Albert Einstein

albert_einstein_young_1_1_.jpgAlbert Einstein’s great papers on Special Relativity and General Relativity, written at the beginning of the 20th Century, extend Newton’s theory of gravitation to much more extreme physical conditions.  In his Special Theory of Relativity, published in 1905, Einstein showed that we live in a four-dimensional space-time.  His famous formula E=mc2 is a consequence of this. 

His General Theory, completed in 1915, showed that matter bends space-time and that matter moves along paths in bent space-time, making the theory somewhat complex.  In theory, the idea of gravity being a mysterious force is replaced by the idea of curved space-time.  General Relativity predicted that the perihelion of Mercury would advance faster than predicted by Newtonian theory by a tiny but measurable rate.

It also predicted that the paths of light rays would be bent by the Sun, which was first observed during the total eclipse of 1919.  This effect is now seen much more dramatically in gravitational lenses.  Einstein also showed that moving clocks would run more slowly, an effect that has been demonstrated by clocks placed in artificial satellites circling the Earth and by the greatly increased lifetimes of particles circling in accelerators.

Gravitational radiation
Einstein predicted that when two masses rotate about each other they will emit gravitational radiation, causing the bodies to move closer together and the period of rotation to decrease.  This has been observed in the binary pulsar PSR 1913 + 16, in which two neutron stars, each no more than 20 km in diameter, orbit each other every 7.7 hours.  Eventually, the two stars will merge, releasing an intense burst of gravitational radiation and more energy than the supernova explosion that formed them.  Gravitational wave detectors have been built in laboratories but, so far, no detections have been made.