Author: Jesse Voltin

Students will be able to explain tangential velocity and gravitational acceleration.

Students will learn about Newton's hypothesis of universal gravitation.

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Falling Objects

Isaac Newton is credited for the 'discovery' of gravity. What he did was really give the idea of gravitational force on objects on Earth an actual name, something that people would more easily conceptualize and use to explain the concept to others. The classic story goes that Newton was sitting under an apple tree on the campus of Cambridge University. While he was pondering the forces of nature he was struck upon the head with an apple. He then began studying why it is that things fall down. Newton knew that for an object to change its motion or position it must be acted on by an unbalanced force. Therefore a force must be present that pulls objects towards the center of the Earth.

During his investigation he looked back to the study of inertia that Galileo had already undertaken and had established that there was an unseen force that drew the apple toward the ground. As he looked up into the apple tree he gazed threw the branches and say the moon above in space. He knew that there was a force acting upon the apple but he began wondering why the moon did not just fall into the planet.

Circular Motion

Newton was familiar with circular motion and that as an object revolves around a source (much like whirling a ball that is attached to a string around your head) there is an acceleration towards the middle of the orbital path. Newton believed that the moon was attracted to the Earth in the same way an apple would be.

Newton believed that the moon was indeed falling towards the Earth. However, the apple, unlike the moon, was stationary when it began its journey to the ground. The moon is moving very fast around the planet. This is called its tangential velocity. The arrow illustrated on the right show the instantaneous velocity of the moon at any given moment. As the moon is pulled toward the Earth the direction of the moon's path is changed. The pull from Earth's gravity will provide the moon with an endless force that will continue to pull it inward. And with nothing in space to slow the movement of the moon it will be able to continue to circle the planet for a very long time.

Newton dropped an apple from 5 meters and measured the time it took for the apple to strike the ground. He believe that, much like a light source, the closer you are to the source the move powerful of an affect there is felt or seen. So the moon was a much further distance away meaning that gravity did not have as large of a hold on the moon as it did on the apple. The smaller gravitation affect and the tangential velocity of the moon is what permits it to remain the same distance away.

Newton was satisfied with his understanding of why the moon orbited the  Earth but the academic community demanded more concrete explanation. So he simply invented a new focus of mathematics that explained universal gravitation laws.

Earth Falls Too

Around the time of Copernicus the world believed that the Earth was the center of the solar system and the universe. As shown on the right it was believed each planet and star revolved around the Earth as the central focus point. We know this now not to be the case and it is thanks in large part to Newton.

Newton claimed that the Earth was simply not massive enough to be the center of the solar system. Using telescopes and methodical observations astronomers at the time had a good idea of how much mass each of the planets were and using Newton's new gravitational law he was able to prove that the Earth was in fact revolving around the sun. The Earth was actually traveling at its own tangential velocity, much like the moon does relative to Earth, as it orbited the sun. His law further proves that the moon revolves around the Earth and not the sun because the moon is more attracted to Earth than it is to the sun.