Universal Gravitation

Gravity

• Isaac Newton is first credited for the idea of mass being attracted to other mass.

• He saw the moon after the famous apple fell from the tree and decided both are in motion because of the Earth’s gravity

Gravity

• While Newton developed a formula that was highly accurate in predicting the motion of objects due to gravity, he had NO idea how gravity worked exactly

• Newton’s Law of Universal Gravitation

Gravity• F = Force between the two massive

objects• M = mass 1• m = mass 2• r = distance between the two objects • G = universal gravitational constant G =

• The further the two objects the weaker the force between them

Gravity

• The reason why the Moon doesn’t fall into the Earth, or the planets aren’t forced into the Sun is because of Newton’s 1st law.

• These objects are traveling at the escape velocity of the bigger object, so that they try to maintain motion in a straight line but the gravity of the bigger object tries to pull them in, so they move in a circle.

Gravity

Escape velocity equation

Gravity• Remember that weight is relative. If

you are in an accelerating frame, your weight can change.

• If you are in the center of a shell of mass, (and no where near the Earth) you will NOT feel any force of gravity.

• Ocean tides are caused by the Moon pulling on the Earth’s oceans.

Gravity

• Worksheet problems

Gravity

• Albert Einstein’s Theory of General Relativity solved many of the problems that Newton’s theory couldn’t.

• He considered the idea that space time is a grid. Mass creates dips in the grid.

Gravity

• Video on Newton vs Einstein

Gravity

• A black hole is a incredibly compact object where not even light can escape from it. Therefore it has an escape velocity equal to the speed of light

• Consider it a hole in the space-time grid in Einstein's theory.

Gravity

• Derivation of the Schwarzschild Radius

Gravity

• Book Problems:

• Pg 180 #7, 9, 11, 15, 22

• Pg 196 #6, 20, 25