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.

Fg 1/r2

LAW OF UNIVERSAL GRAVITATION

 Fg = G (m1 m2) / r2

• m1 and m2 = masses of the 2 objects

(kg)

• r = center-to-center distance between the objects

• G = universal gravitational constant

• G = 6.67 x 10 -11 Nm2 / kg 2

HENRY CAVENDISH (1731-1810)

• 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,

Fg = G (m mE) / rE 2 = mg

G (mE) / rE 2 = g

• The mass of the Earth can be calculated from this:

mE = g rE 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.– If you give it enough speed, a satellite will

escape, never to return (escape speed).

TYCHO BRAHE (1546 - 1601)

• Danish astronomer.• Became astronomer to the

King of Denmark, and made highly detailed observations of planetary movements for over 20 years.

JOHANN KEPLER (1571 - 1630)

• German mathematician •1609: Kepler publishes a book

which describes the motion of the planets.–  Kepler’s 1st Law: Planets move

around the sun in elliptical orbits, with the sun at one focus.

JOHANN KEPLER (1571 - 1630)

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

JOHANN KEPLER (1571 - 1630)

• Kepler’s 3rd 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.

(T1/T2)2 = (s1/s2)3

• Kepler’s 3rd 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.