Gravitational Forces

What is Gravity? Gravity is the tendency of all objects (with mass) to attract one another. We often refer to this as a gravitational force. Which is the attractive force one mass places on another. The idea of a gravitational force came from Sir Isaac Newton.

Developing the Idea of Gravitational Forces Newton’s did not discover that when you let go of a object held above the ground, it falls to the floor. – Mankind knew that back since its beginning Newton did make this following piece of logic that united the Earth with the universe, and establish the means to unravel the mysteries of space.

The Logic If you drop an object it falls because of a gravitational force. If you fire a cannon ball it Arcs its path because it is Accelerated at same way as the dropped. It too is falling because of a gravitational force. But the faster the ball is fired The large the ball’s range.

On Top of The World Now lets say we have a cannon on the top of the world and it fires a series of balls horizontally. With each shot being faster then the previous one. At some speed the ball will never reach the ground because it out runs the curve of the Earth. It is however still falling because of the Gravitational Force.

Expanding to the universe The Moon orbits the Earth in this manner. All the planets of our solar system orbit the Sun in this manner. All objects in space are falling towards one another. Gravitational Forces are everywhere (just like on earth) The universe must object the same physical laws as objects on earth do. – Until this point people believed the laws for the universe and life on earth were different.

The factors that influence gravitational Forces Newton realized that the gravitational force acting on an object just did not depend on it’s mass, but the mass of the object pulling it. Also the mass of at least one of the two objects must be very large for the force to be noticed. – You don’t often see a person stuck to a wall because of the gravitational force between them. He also realized that the distance of separation has a huge affect (inverse squared) on the gravitational force between the objects.

Newton’s Gravitational Law Is often shown as the equation: (Mass 1 )*(Mass 2 ) (Distance of separation) 2 (Universal Gravitational Constant)* FgFg = m1m2m1m2 r2r2 G FgFg = Newton’s only problem is the fact he did not know what the universal gravitational constant was equal to.

Enter Henry Cavendish Henry Cavendish used an enclosed device consisting of suspended lead balls. By placing different masses inside the device and measuring the Deflection of the suspend lead balls, he was able to find the value of G

Newton’s Gravitational Law Is often shown as the equation: (Mass 1 )*(Mass 2 ) (Distance of separation) 2 (Universal Gravitational Constant)* FgFg = m1m2m1m2 r2r2 G FgFg = G = 6.67* Nm 2 /kg 2

Orbital speeds V orbit FgFg  F satellite = (m satellite )a c (V orbit ) 2 F g = (m satellite )* R R G(m planet)(m satellite ) (V orbit ) = (m satellite )* R 2 R G(m planet ) V orbit = R

Period and radius Circumference of 1 orbit Period = Orbital speed 2  R T = V orbital G(m planet ) R 2  R T =   R  T 2 = G(m planet ) R []

4   R  T 2 = G(m planet ) R [] G(m planet ) [] R G(m planet ) [] T 2 4   = R  G(m planet ) 4   R  T 2 = G(m planet ) T = Constant R  T A 2 T B = R A  R B 

Gravitational Fields Because gravitational forces do not required contact, but act over a distance of separation gravitational forces are a field force A gravitational field is simply how much gravitational force acts one 1 kg of mass Gravitational Field = F g /m g = F g /m The unit for a gravitational field is a N/kg The gravitational field and gravitational acceleration have the same equation so the are numerically equal. But they are not the same thing. m r2r2 G g=

Gravitational Field Vectors Because gravitational forces are always attractive all gravitational field vectors point toward the object who is making them.