Gravity & Tides
The Study of Gravity Astronomers are gravity experts because heavenly motions are dominated by gravitation. Isaac Newton gets the credit for discovering gravity, but even Newton couldn’t explain what gravity was. Einstein proposed that gravity is a curvature of space, but that only pushes the mystery further away. “What is curvature?” Astronomers continue to study Einstein’s theory, Is there an even better way to understand the motions of the heavens. What is gravity? Why does it exist? Gravity is universal. It is one of 4 essential forces that create the Universe in which we live.
Mathematics as a tool for understanding physics A New Era of Science Mathematics as a tool for understanding physics
Isaac Newton (1643 - 1727) Major achievements: Building on the results of Galileo and Kepler Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler Major achievements: Invented Calculus as a necessary tool to solve mathematical problems related to motion Defined the three laws of motion Defined the universal law of mutual gravitation
Velocity and Acceleration Acceleration (a) is the change of a body’s velocity (v) with time (t): a a = Dv/Dt Velocity and acceleration are directed quantities (vectors)! v Different cases of acceleration: Acceleration in the conventional sense (i.e. increasing speed) Deceleration (i.e. decreasing speed) Change of the direction of motion (e.g., in circular motion)
Acceleration of Gravity independent of mass All objects of the same SHAPE fall at the same rate Wood ball Iron ball
Newton’s Laws of Motion (1) A body continues at rest or in uniform motion in a straight line unless acted upon by some net force. An astronaut floating in space will continue to float forever in a straight line unless some external force is accelerating him/her.
Newton’s Laws of Motion (2) The acceleration a of a body is inversely proportional to its mass m, directly proportional to the net force F, and in the same direction as the net force. a = F/m F = m a
Newton’s Laws of Motion (3) To every action, there is an equal and opposite reaction. M = 70 kg V = ? The same force that is accelerating the boy forward, is accelerating the skateboard backward. m = 1 kg v = 7 m/s V = 0.1 m/s
The Universal Law of Gravity Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance: Mm F = - G G = 6.67300 × 10-11 m3/kgs2 r2 (G is the Universal constant of gravity.)
Tides on Earth Tidal Force = the difference in gravity from one side of a body to the other that is exerted by a 2nd object. The Moon’s tidal force on Earth causes the oceans facing the Moon to bulge out toward it the oceans on the opposite side of the Earth to bulge out away from the Moon. These varying ocean levels are called the tides.
Tides on Earth The Sun also causes tides on the Earth, but they are smaller than the Lunar tides. When the Moon and Sun are aligned, their tidal forces combine, and the resulting tides are largest.
Tides on Earth
Tidal Friction The Earth is constantly rotating, pulling the tidal ocean bulge out of alignment. As a result, the water is continually moving in the opposite direction of the Earth’s rotation.
Tidal Friction The movement of the water on Earth has two effects: It slows down the Earth’s rotation (few milliseconds per century). When dinosaurs roamed the Earth, a day was 22 hours long. Eventually, the Earth will rotate once in the same time the Moon orbits once. So the Earth and Moon will always have the same faces toward each other.
Tidal Friction The movement of the water on Earth has two effects: It pulls the Moon along a bit faster, slinging it out further from the Earth (about 4 cm per year). So in the distant past, the Moon was much closer to the Earth.
Tides on Moon Lunar tidal forces are slowing the Earth’s rotation it will keep the same face toward the Moon Earth is about 80 times more massive than the Moon its tidal force is 80 times greater. Tidal friction of flowing rocks (lava) has already locked the Moon to the Earth. THIS is why the Moon always keeps the same side facing the Earth. Remember…from the Earth, we never see the far side of the Moon.