universal gravitation. projectile motion revisited how do the paths of a bullet fired from a gun...

Universal Gravitation

Projectile Motion revisited

• How do the paths of a bullet fired from a gun horizontally and a baseball thrown horizontally compare?

• Which will hit the ground first?• Which will go farther?

What if…

• What if the speed of an object is so great, that it is able to get past the Earth before it “lands”?

• Picture a cannonball being fired from the top of a mountain.

Orbit

• The Moon orbits the Earth because it is really “falling around the Earth”

• It is going so fast, that instead of falling and hitting the surface (like a cannonball), it continues to fall around the Earth.

Isaac Newton

• Supposedly, Newton came up with all of this while sitting under an apple tree

20 years later…

• 20 years later after Newton invented and developed calculus to help explain his theory, he came back to this problem and achieved the final version of the law of universal gravitation.

Newton’s Law of Universal Gravitation

• The force of gravity depends on the mass of the objects and the distance between them.

• The greater the mass, the greater the force• The greater the distance, the less the force

Mathematically

221

r

mGmF

Note: We will NOT be doing any calculations with this formula. We just need to understand the universal force law qualitatively.

Gravitational Constant

• G is the force between two 1 kg masses separated 1 meter.

• The force is 0.000 000 000 0667 Newtons• That is really, really, really small.• In other words, two students will not be

attracted to each other due to gravity because their masses are too small.

How G was found

• Englishman, Henry Cavendish, 150 years after Newton’s discovery used a torsion balance

How G was found a 2nd time

• Phillip von Jolly use a balance hung above a very heavy lead ball.

• The smaller mass was attracted to the larger ball and then the amount of weight used to balance out the scale is equal to the gravitational force.

Field forces

• So far we have only talked about contact forces, ie forces that must be in contact to cause an acceleration.

• Field forces are forces that can act over a distance.

• Gravity is a field force.• Can you name other field forces?

Butter Gun

• Picture working at very busy restaurant.• Image a gun that is able to shoot out a perfect

amount of butter onto all areas of one piece of toast with a thickness of 1mm.

• What if we double the distance of the toast and shoot again?

• The area is 4x as much, but the butter is 1/4mm thick now.

Inverse-square law

• As the distance increases, the strength of the force of a field force will decrease with the square of the distance.

• For example: Triple the distance will be 1/9 the strength.

Never Zero

• Looking at the equation for Universal Gravity, no matter how large the distance is from the object, the force will never be zero!

• That means that even if you are in the farthest reaches of the universe, the force due to the Earth on you would never be zero

• … just very small

Perturbation

• Planets have a nice smooth orbit until they are close to another planet.

• This deviation from normal orbits is called perturbation.