Chapter 12 Universal Gravitation

What is gravity?

• We are all familiar with gravity. We see and feel the effects of gravity every day, but what is it?

• Isaac Newton made several important observations about gravity:

a) gravity extends throughout the universe

b) objects in motion normally follow a straight-line path. Therefore objects that follow circular or elliptical paths must have a force that constantly causes them to deviate that straight line path

What is gravity?

Newton compared the falling apple with the moon and wondered why it did not fall out of the sky. Newton realized that if the moon did not fall out of the sky, it should continue moving in a straight line and leave its orbit:

What is gravity?

“His idea was that the moon must be falling around Earth. Thus the moon falls in the sense that it falls beneath the straight line it would follow if no force acted on it.” p. 169

Newton’s original drawing showing a projectile fired at different velocities from a mountain top:

• In the 20th century, Albert Einstein discovered that gravity arises from the “warping” of space and time. Neither space and time are perfectly smooth.

What is gravity?

What is gravity?

• Einstein’s explanation of gravity is not complete and it does not describe the mechanism of why space-time is warped by objects with mass.

• Physicists' have been looking for a quantum theory of gravity.

• LIGO (Laser Interferometer Gravitational Wave observatory) looks for gravitational waves produced by massive, rapidly rotating objects in space

Laser Interferometer Gravitational Wave Observatory (LIGO)

Newton’s Law of Universal Gravitation

• Newton’s law of Universal Gravitation states that every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object.

• Newton deduced that the force decreases as the square of the distance between the centers of mass of the objects increases.

• This relationship can be expressed as:

m1m2

d2F ~

Newton’s Law of Universal Gravitation

• “the proportionality form of the law of universal gravitation can be expressed as an exact equation when the constant of proportionality G, called the universal gravitational constant, is introduced. Then the equation is:

m1m2

d2

…where the value G is .0000000000667 or 6.67 x 10-11

• This means that gravity is a very weak force, and in fact is the weakest of the four fundamental forces.

F = G

Does standing on a mountain top change your weight?

“ In addition to your mass, your weight also depends on your distance from the center of Earth. At the top of a mountain your mass is the same as it is anywhere else, but your weight is slightly less than at ground level. Your weight is less because your distance from the center of the Earth is greater.” p. 174

The Inverse Square Law• When a quantity varies as the inverse square of its distance from its source, it follow an inverse-square law

• Things that follow the inverse-square law include gravity, light, sound, and radiation

The Inverse Square Law

Why is the earth round?• The earth is ground because of gravity.• All mass attracts all other mass • The most efficient shape of a three dimensional object

under the effect of gravity is a sphere• Any “corners” and jagged points like mountains over

time will be pulled into a spherical shape due to erosion

Planetary Perturbations• If everything pulls on everything else, then the planets must pull on each other

• The net force that controls jupiter, for example, is not just from the sun, but from the planets also

• When a planet pulls on another planet and disturbs its orbit, this deviation is called a perturbation

• in the 1840’s Urbain Le Verrier predicted the position of the undiscovered planet Neptune after analysing perturbations in the orbit of Uranus

• Pluto was discovered in 1930 using this same method