Universal Gravitation Physics Mr. Padilla

Falling Apple hits Newton on the head. According to the law of inertia, it would not fall unless acted upon by an outside force. Apple hits Newton on the head. According to the law of inertia, it would not fall unless acted upon by an outside force. If the moon did not fall, it would move off in a straight line and leave orbit. If the moon did not fall, it would move off in a straight line and leave orbit. The moon is, therefore just a projectile circling Earth under the attraction of gravity The moon is, therefore just a projectile circling Earth under the attraction of gravity

Newton & Gravity Newton did not discover gravity. Newton did not discover gravity. Newton showed that the gravity of a regular sphere is the same as if the mass were concentrated at its center. Newton showed that the gravity of a regular sphere is the same as if the mass were concentrated at its center. Developed the law of universal gravitation. Developed the law of universal gravitation. This theory confirmed the Copernican theory of the solar system. This theory confirmed the Copernican theory of the solar system.

Law of Universal Gravitation Everything pulls on everything else. Everything pulls on everything else. This pull involves only an objects mass and their distance apart. This pull involves only an objects mass and their distance apart. Law of universal gravitation – every object acts on every other object with a force that for any two objects is proportional to the mass of each object.

Law of Universal Gravitation The force decreases as the square of the dist. between objects increases. The force decreases as the square of the dist. between objects increases. The greater the distance the less the force. The greater the distance the less the force. Universal Gravitational Constant – G Force of gravity between two objects F g = G m 1 m 2 r 2

Gravitational Constant The gravitational constant was first calculated by Henry Cavendish, 150 years after Newton’s discovery, and then again later by Phillip von Jolly The gravitational constant was first calculated by Henry Cavendish, 150 years after Newton’s discovery, and then again later by Phillip von Jolly

Example Problem The Earth has a mass of 5.98x10 24 kg and rotates around the Sun at a distance of 1.50x10 11 m. If the sun has a mass of 1.99x10 30 kg, what is the force of gravity the Sun exerts on the Earth? The Earth has a mass of 5.98x10 24 kg and rotates around the Sun at a distance of 1.50x10 11 m. If the sun has a mass of 1.99x10 30 kg, what is the force of gravity the Sun exerts on the Earth? Force of gravity = 3.53x10 22 N Force of gravity = 3.53x10 22 N

Sample Problem 7I Find the distance between a kg billiard ball and a kg billiard ball if the magnitude of the gravitational force is 8.92 x N.

Gravity and you Estimate your mass. Estimate your mass. If the radius of the Earth is 6.67x10 6 m, can you calculate the force of gravity exerted on you by the Earth? (Do it) If the radius of the Earth is 6.67x10 6 m, can you calculate the force of gravity exerted on you by the Earth? (Do it) Is there another way to do it? Is there another way to do it?

Gravity Gravity is considered to be a very weak force. Gravity is considered to be a very weak force. We sense gravity only when large masses like the Earth are involved. We sense gravity only when large masses like the Earth are involved. Is your mass the same at sea level as it is on a high mountain? Is your mass the same at sea level as it is on a high mountain? Is your weight the same? Is your weight the same?

Inverse Square Law This law applies to the weakening of gravity with distance This law applies to the weakening of gravity with distance The quantity varies as the inverse square of its distance from its source. The quantity varies as the inverse square of its distance from its source.

Inverse Square The greater the distance from the Earth the less it will weigh. No matter how great the distance Earth’s gravity does not drop to zero. The gravitational influence of every object is exerted through all space.

Universal Gravitation Particles exerting gravity on each other created round planets. Particles exerting gravity on each other created round planets. Planets exert gravity on each other. When these planets are close enough, they can disturb each others orbits. Planets exert gravity on each other. When these planets are close enough, they can disturb each others orbits. This deviation is called a perturbation. This deviation is called a perturbation.

Gravity in the Universe The perturbations of Uranus led to other planets being discovered. The perturbations of Uranus led to other planets being discovered. Neptune in 1846 Neptune in 1846 Pluto in 1930 Pluto in 1930 The universe may have been created bill. years ago (big bang) Since then its been constantly expanding Gravity may stop, or even reverse this expansion

Gravitational Interactions Gravitational field – force field that surrounds massive objects = gravity Gravitational field – force field that surrounds massive objects = gravity Outside the planet Outside the planet Inside the planet Inside the planet Weight and weightlessness Weight and weightlessness Ocean Tides Ocean Tides

Orbits Circular – A satellite in a circular orbit, always moves perpendicular to the force of gravity, so it always moves at a constant speed Circular – A satellite in a circular orbit, always moves perpendicular to the force of gravity, so it always moves at a constant speed The time it takes for a satellite to complete one orbit is called the period. The time it takes for a satellite to complete one orbit is called the period. Not all satellites follow a circular orbit. Some will travel along an oval path called an ellipse. Not all satellites follow a circular orbit. Some will travel along an oval path called an ellipse.

Ellipse A closed path taken by a point (satellite) that moves in such a way that the sum of it distances from two fixed points is constant. A closed path taken by a point (satellite) that moves in such a way that the sum of it distances from two fixed points is constant. These points are called foci These points are called foci

Ellipse Satellite speed varies in an ellipse. Satellite speed varies in an ellipse. Satellites speed up as they approach and slow as they go away. Satellites speed up as they approach and slow as they go away. The satellite will continue to orbit unless it reaches escape speed The satellite will continue to orbit unless it reaches escape speed

Planetary motion is caused by, yes you guessed it, gravity. Tycho Brahe ( ) was one if the first to make exact measurements of the position of the planets and stars. He still believed that the Earth was the center of the solar system He still believed that the Earth was the center of the solar system Johannes Kepler, one of his assistants, used Brahe’s data and with the sun as the center of the solar system, and was able to explain the behavior of every satellite and planet.

Kepler’s Laws of Planetary Motion 1. The paths of the planets are ellipses, with the sun at one focus. 1. The paths of the planets are ellipses, with the sun at one focus. 2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. (Planet travels faster when closer to the sun) 2. An imaginary line from the sun to a planet sweeps out equal areas in equal time intervals. (Planet travels faster when closer to the sun)

Kepler’s Laws 3. The square of the ratio of the periods of any two planets revolving around the sun is equal to the cube of the ratio of their average distances from the sun. 3. The square of the ratio of the periods of any two planets revolving around the sun is equal to the cube of the ratio of their average distances from the sun.

Escape Speed: Take off… Speed necessary for an object to escape gravity and not come crashing back down. Speed necessary for an object to escape gravity and not come crashing back down. Escape velocity varies from planet to planet because each planet has a different amount of gravity. Escape velocity varies from planet to planet because each planet has a different amount of gravity. Here are some escape velocities Earth – 11.2 km/s Moon – 2.4 km/s Mars – 5.0 km/s Jupiter – 60.2 km/s Sun’s gravity from Earth – 42.2 km/s Sun – 620 km/s

Stars Produce energy through fusion of Hydrogen Produce energy through fusion of Hydrogen The more fusion, the bigger and hotter the star The more fusion, the bigger and hotter the star Less fusion, smaller and cooler Less fusion, smaller and cooler When a star runs out of fuel, gravity will dominate and the start will collapse When a star runs out of fuel, gravity will dominate and the start will collapse

Sun After Hydrogen is gone After Hydrogen is gone Helium will fuse into carbon Helium will fuse into carbon Causes sun to expand into a red giant Causes sun to expand into a red giant It will expand beyond Earth’s orbit It will expand beyond Earth’s orbit Won’t take place for about 5 billion years Won’t take place for about 5 billion years When Helium is used up… Red Giant will collapse into a black dwarf It will no longer give off heat and light.

Black Holes Happens for stars at least twice as big as ours Happens for stars at least twice as big as ours When gravitational collapse takes over it doesn’t stop. When gravitational collapse takes over it doesn’t stop. Density becomes infinite Density becomes infinite Gravity is so great that nothing can get out. Gravity is so great that nothing can get out. Gravitational field does not change. Gravitational field does not change. Black Holes can not be seen Black Holes can not be seen