Universal Gravitation

ISAAC NEWTON (1642 – 1727) The rate of acceleration due to gravity at the Earth’s surface was proportional to the Earth’s gravitational force on the Moon. The Earth’s gravitational force on the moon was inversely proportional to the square of the Earth’s distance from the moon. F g  1/r 2

LAW OF UNIVERSAL GRAVITATION F g = G (m 1 m 2 ) / r 2 m 1 and m 2 = masses of the 2 objects (kg) r = center-to-center distance between the objects G = universal gravitational constant G = 6.67 x N  m 2 / kg 2

HENRY CAVENDISH ( ) 1798: Using a torsion balance, Cavendish measured the gravitational attraction between small objects, and calculated the value of the Universal Gravitational Constant.

Gravity Near Earth’s Surface The force of gravity is the weight of the object. Near Earth’s surface, F g = G (m m E ) / r E 2 = mg G (m E ) / r E 2 = g The mass of the Earth can be calculated from this: m E = g r E 2 / G

Gravity Near Earth’s Surface The value of g on Earth can vary due to: –Elevation and latitude (distance from center of Earth) –Variations in densities of rock. This may indicate the presence of mineral or oil deposits. These variations are small, but can be measured with a gravimeter

Satellites Satellites are placed in orbit by “throwing” them with enough velocity that they fall around the earth.fall around the earth. –If you give it enough speed, a satellite will escape, never to return (escape speed).

TYCHO BRAHE ( ) Danish astronomer. Became astronomer to the King of Denmark, and made highly detailed observations of planetary movements for over 20 years.

JOHANN KEPLER ( ) German mathematician 1609: Kepler publishes a book which describes the motion of the planets. – Kepler’s 1 st Law: Planets move around the sun in elliptical orbits, with the sun at one focus.

JOHANN KEPLER ( ) Kepler’s 2 nd Law: A straight line connecting the sun and a planet sweeps out equal areas in equal time intervals.

JOHANN KEPLER ( ) Kepler’s 3 rd Law: The ratio of the squares of the periods T of any two planets revolving around the Sun is equal to the ratio of the cubes of their mean distances s from the Sun. (T 1 /T 2 ) 2 = (s 1 /s 2 ) 3 Kepler’s 3 rd law applies to any two bodies orbiting a common center.

Kepler’s Laws and Newton’s Synthesis Newton was able to show that: –Kepler’s Laws could be derived from universal gravitation and the laws of motion –Only an inverse-square relationship for gravitation would explain Kepler’s laws. Deviations in the orbits predicted by Kepler’s laws (perturbations) can be used to locate undiscovered planets.

Types of Forces in Nature Four fundamental forces: –Gravitational –Electromagnetic –Strong nuclear –Weak nuclear Physicists have unified the electromagnetic and the weak nuclear forces (electroweak force), but still seek a Grand Unified Theory Everyday forces are due to electromagnetic and gravitational forces.