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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