Universal Universal GravitationGravitation

PhysicsPhysics

Mr. PadillaMr. Padilla

FallingFalling

Apple hits Newton on the head. Apple hits Newton on the head. According to the law of inertia, it would According to the law of inertia, it would not fall unless acted upon by an not fall unless acted upon by an outside force. outside force.

If the moon did not fall, it would move If the moon did not fall, it would move off in a straight line and leave orbit.off in a straight line and leave orbit.

The moon is, therefore just a projectile The moon is, therefore just a projectile circling Earth under the attraction of circling Earth under the attraction of gravitygravity

Newton & GravityNewton & Gravity

Newton did not discover gravity.Newton did not discover gravity. Newton showed that the gravity of a Newton showed that the gravity of a

regular sphere is the same as if the regular sphere is the same as if the mass were concentrated at its center.mass were concentrated at its center.

Developed the law of universal Developed the law of universal gravitation.gravitation.

This theory confirmed the Copernican This theory confirmed the Copernican theory of the solar system.theory of the solar system.

Law of Universal Law of Universal GravitationGravitation

Everything pulls Everything pulls on everything on everything else.else.

This pull involves This pull involves only an objects only an objects mass and their mass and their distance apart.distance apart.

Law of universal Law of universal gravitation – every gravitation – every object acts on object acts on every other object every other object with a force that with a force that for any two for any two objects is objects is proportional to the proportional to the mass of each mass of each object.object.

Law of Universal Law of Universal GravitationGravitation

The force The force decreases as the decreases as the square of the dist. square of the dist. between objects between objects increases.increases.

The greater the The greater the distance the less distance the less the force.the force.

Universal Universal Gravitational Gravitational Constant – GConstant – G

Force of gravity Force of gravity between two between two objectsobjects

FFgg = G = G mm11mm22 rr22

Gravitational ConstantGravitational Constant

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

2

2111067.6kg

NmG

Example ProblemExample Problem

The Earth has a mass of 5.98x10The Earth has a mass of 5.98x102424 kg and rotates around the Sun at a kg and rotates around the Sun at a distance of 1.50x10distance of 1.50x101111 m. If the sun m. If the sun has a mass of 1.99x10has a mass of 1.99x103030 kg, what kg, what is the force of gravity the Sun is the force of gravity the Sun exerts on the Earth?exerts on the Earth?

Force of gravity = 3.53x10Force of gravity = 3.53x102222 N N

Sample Problem 7I

Find the distance between a 0.300 kg billiard ball and a 0.400 kg billiard ball if the magnitude of the gravitational force is 8.92 x 10-11 N.

Gravity and youGravity and you

Estimate your mass.Estimate your mass. If the radius of the Earth is If the radius of the Earth is

6.67x106.67x106 6 m, can you calculate the m, can you calculate the force of gravity exerted on you by force of gravity exerted on you by the Earth? (Do it)the Earth? (Do it)

Is there another way to do it?Is there another way to do it?

GravityGravity

Gravity is considered to be a very Gravity is considered to be a very weak force.weak force.

We sense gravity only when large We sense gravity only when large masses like the Earth are involved. masses like the Earth are involved.

Is your mass the same at sea level Is your mass the same at sea level as it is on a high mountain?as it is on a high mountain?

Is your weight the same?Is your weight the same?

Inverse Square LawInverse Square Law

This law applies This law applies to the weakening to the weakening of gravity with of gravity with distancedistance

The quantity The quantity varies as the varies as the inverse square of inverse square of its distance from its distance from its source.its source.

Inverse SquareInverse Square The greater the The greater the distance from the distance from the Earth the less it Earth the less it will weigh.will weigh.

No matter how No matter how great the distance great the distance Earth’s gravity Earth’s gravity does not drop to does not drop to zero.zero.

The gravitational The gravitational influence of every influence of every object is exerted object is exerted through all space.through all space.

Universal GravitationUniversal Gravitation

Particles exerting gravity on each Particles exerting gravity on each other created round planets.other created round planets.

Planets exert gravity on each Planets exert gravity on each other. When these planets are other. When these planets are close enough, they can disturb close enough, they can disturb each others orbits.each others orbits.

This deviation is called a This deviation is called a perturbation.perturbation.

Gravity in the UniverseGravity in the Universe

The perturbations The perturbations of Uranus led to of Uranus led to other planets other planets being discovered.being discovered. Neptune in 1846Neptune in 1846 Pluto in 1930Pluto in 1930

The universe may The universe may have been created have been created 10-15 bill. years 10-15 bill. years ago (big bang)ago (big bang)

Since then its Since then its been constantly been constantly expandingexpanding

Gravity may stop, Gravity may stop, or even reverse or even reverse this expansionthis expansion

Gravitational InteractionsGravitational Interactions

Gravitational field – force field that Gravitational field – force field that surrounds massive objects = surrounds massive objects = gravitygravity Outside the planetOutside the planet Inside the planetInside the planet

Weight and weightlessnessWeight and weightlessness Ocean TidesOcean Tides

OrbitsOrbits

Circular – A satellite in a circular Circular – A satellite in a circular orbit, always moves perpendicular orbit, always moves perpendicular to the force of gravity, so it always to the force of gravity, so it always moves at a constant speedmoves at a constant speed

The time it takes for a satellite to The time it takes for a satellite to complete one orbit is called the complete one orbit is called the period.period.

Not all satellites follow a circular Not all satellites follow a circular orbit. Some will travel along an orbit. Some will travel along an oval path called an ellipse.oval path called an ellipse.

EllipseEllipse

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

These points are called These points are called focifoci

EllipseEllipse Satellite speed varies in an ellipse.Satellite speed varies in an ellipse. Satellites speed up as they Satellites speed up as they

approach and slow as they go approach and slow as they go away.away.

The satellite will continue to orbit The satellite will continue to orbit unless it reaches escape speedunless it reaches escape speed

Planetary motion is caused Planetary motion is caused by, yes you guessed it, by, yes you guessed it, gravity.gravity.

Tycho Brahe (1546-Tycho Brahe (1546-1601) was one if 1601) was one if the first to make the first to make exact exact measurements of measurements of the position of the the position of the planets and stars.planets and stars.

He still believed He still believed that the Earth was that the Earth was the center of the the center of the solar systemsolar system

Johannes Kepler, Johannes Kepler, one of his one of his assistants, used assistants, used Brahe’s data and Brahe’s data and with the sun as the with the sun as the center of the solar center of the solar system, and was system, and was able to explain the able to explain the behavior of every behavior of every satellite and satellite and planet.planet.

Kepler’s Laws Kepler’s Laws of Planetary Motionof Planetary Motion

1. The paths of the planets are 1. The paths of the planets are ellipses, with the sun at one focus.ellipses, with the sun at one focus.

2. An imaginary line from the sun 2. An imaginary line from the sun to a planet sweeps out equal areas to a planet sweeps out equal areas in equal time intervals. (Planet in equal time intervals. (Planet travels faster when closer to the travels faster when closer to the sun)sun)

Kepler’s LawsKepler’s Laws

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

32

B

A

B

A

r

r

T

T

Escape Speed: Take off…Escape Speed: Take off… Speed necessary Speed necessary

for an object to for an object to escape gravity and escape gravity and not come crashing not come crashing back down.back down.

Escape velocity Escape velocity varies from planet varies from planet to planet because to planet because each planet has a each planet has a different amount different amount of gravity.of gravity.

Here are some Here are some escape velocitiesescape velocities

Earth – 11.2 km/sEarth – 11.2 km/s Moon – 2.4 km/sMoon – 2.4 km/s Mars – 5.0 km/sMars – 5.0 km/s Jupiter – 60.2 km/sJupiter – 60.2 km/s Sun’s gravity from Sun’s gravity from

Earth – 42.2 km/sEarth – 42.2 km/s Sun – 620 km/sSun – 620 km/s

StarsStars

Produce energy through fusion of Produce energy through fusion of HydrogenHydrogen

The more fusion, the bigger and The more fusion, the bigger and hotter the starhotter the star

Less fusion, smaller and coolerLess fusion, smaller and cooler When a star runs out of fuel, When a star runs out of fuel,

gravity will dominate and the start gravity will dominate and the start will collapsewill collapse

SunSun After Hydrogen is After Hydrogen is

gonegone Helium will fuse Helium will fuse

into carboninto carbon Causes sun to Causes sun to

expand into a expand into a red giantred giant

It will expand It will expand beyond Earth’s beyond Earth’s orbitorbit

Won’t take Won’t take place for about place for about 5 billion years5 billion years

When Helium is When Helium is used up…used up… Red Giant will Red Giant will

collapse into a collapse into a black dwarfblack dwarf

It will no longer It will no longer give off heat give off heat and light.and light.

Black HolesBlack Holes Happens for stars at least twice as Happens for stars at least twice as

big as oursbig as ours When gravitational collapse takes When gravitational collapse takes

over it doesn’t stop.over it doesn’t stop. Density becomes infiniteDensity becomes infinite Gravity is so great that nothing can Gravity is so great that nothing can

get out.get out. Gravitational field Gravitational field does notdoes not change. change. Black Holes can not be seenBlack Holes can not be seen