Announcements Quiz #1 is this Friday. Please pick up study guide Readings: Chapters 1-7 in Ferris...

AnnouncementsQuiz #1 is this Friday. Please pick up study

guideReadings: Chapters 1-7 in FerrisLectures 1-8 (don’t forget planetarium)Planetarium EC show moved to next MondayPlease pick up HW #1Please turn off all electronic devicesDon’t forget to sign the attendance sheet

a) The meterb) The poundc) The inchd) The kilograme) The Newton

What is the metric unit of force?

Lecture 8: Gravity

Astronomy 1143 – Spring 2014

Key Ideas:Gravity

• Always attractive• Binds gas into stars; stars, gas, dark matter

into galaxies• Works to slow the expansion of the Universe

Newton’s Law of Universal Gravitation• force of gravity depends on mass and

inversely on distance

Key IdeasGravitational Force used to measure amount

of mass Example of Methods

• Circular velocity• Escape velocity

Freely falling in gravity • resembles weightlessness• everything falls at the same rate

Universal Mutual GravitationIsaac Newton, in his Principia, formulated the Law of Universal Mutual Gravitation:Gravity is an Attractive force:

• Works to bring massive objects closer together.

Gravity is a Universal force:• Works everywhere in the Universe.

Gravity is a Mutual force:• Works between pairs of massive objects.

Gravitational ForceThe Force of Gravity between any two objects depends only upon:The masses of the two objects:

• More massive objects exert a stronger force.The distance between them:

• The force gets stronger as they move closer.• The force gets weaker as they move apart.

It does not depend on the shapes, colors, or compositions of the objects.

The Law of Universal Gravitation

The force of gravitational attraction between any two massive bodies is proportional to their masses and inversely proportional to the square of the distance between their centers.

Example of an “Inverse Square Law Force”

Newton’s Gravitational Force Law

F = Force of GravityM1 = Mass of the first object

M2 = Mass of the second object

d = Distance between their centers G = “Gravitational Force Constant”

1 22

GM MFd

M2M1

1 22

GM MFd

1 2 1 22 2

1(2 ) 4GM M GM MFd d

1 2 1 22 24

( / 2)GM M GM MFd d

M2M2

dd/2 2d

The Gravitational Force is inversely proportional to the square of the distance.

M12M1

1 22

GM MFd

M2d

2M2

1 2 1 22 2

(2 ) 2G M M GM MFd d

1 2 1 22 2

(2 )(2 ) 4G M M GM MFd d

The Gravitational Force is proportional to the masses.

The Gravitational Force ConstantThe force constant, G, is a number that gives the size of the gravitational coupling between two massive objects.

G is very small. In metric units:G=6.6710–11 Newtons meter2 / kilogram2

G=6.6710–11 meter3 / kilogram s2

G has to be measured experimentally.

Calculating the Mass of the SunLet’s use the acceleration needed to hold the

Earth in a circle to determine the mass of the Sun

To have a circular orbit, Earth must have an acceleration of

Therefore, force pulling on Earth is

r

Calculating the Mass of the SunForce is force of gravity

therefore

Calculating the Mass of the Sun

What is the speed of the Earth in its orbit around the Sun?

From HW 1.072x105 km/hr

Calculating the Mass of the Sun

speed of Earth around Sun

radius of Earth’s orbit

Gravitational force constant

Calculating the Mass of the Sun

Escape Velocity

Minimum velocity to escape from a gravitating body (go up and never come down):

2E

GMv r

M is the mass of the object you are escapingr is the distance between the centers

Does not depend of mass of object that is escaping

Calculating escape velocity from Earth

G=6.67x10-11 m3/kg s2 = 6.67x10-11 N m2/ kg2

M=5.97x1024 kgr=6378 km

Escaping from Other PlanetsSun 617.5 km/sMercury 4.3 km/sVenus 10.3 km/sEarth 11.2 km/s Moon 2.4 km/sMars 5.0 km/sJupiter 59.5 km/sSaturn 35.6 km/sUranus 21.2 km/sNeptune 23.6 km/s

Mass-o-meterThe motions that we see in the Universe are very

informative about the force of gravity and therefore the amount of matter pulling on a star, planet, etc.

• If we see orbits – how much matter is needed to keep stars/planets on those orbits?• Mass of Sun

• If we see stars or gas confined to a galaxy – how much matter is needed to keep them?• Highest speeds have to be < escape velocity• Mach 1 = 0.34 km/s

Gravity?

“Zero Gravity” doesn’t existIt is a misnomer (though a very descriptive

one) to refer to astronauts or spacecraft as experiencing “weightlessness” or “zero gravity”

Law of Universal Gravity:

Force of Gravity is never zero, no matter how far away you are

Feeling Earth’s Gravity

Your weight in SpaceWeight is defined as the force of gravity on an

objectHow much less do you weigh on the shuttle?

dearth=6378 km

dshuttle=6378+350 km=6728 km

Your weight in Space

If you weighed 200 lbs on Earth, you would weigh 180 lbs on the space shuttle

Force of Gravity still workingThe force of gravity is truly long-range.This is not true for all forces (such as the

strong nuclear force)Collectively, force of many objects can be

quite powerful – escape velocity of Milky Way is 600 km/s

Everything in the Universe is feeling the force of gravity!

Why do you float in space?The force of gravity from the Earth is still

pulling on you in orbit (in fact, it’s what keeps the shuttle/space station in orbit)

The force of gravity is also pulling on every other part of the spacecraft

No air resistance, no surfaces of planets to add an extra force

Everything is falling at the same rate, therefore nothing falls relative to each other

Everything falling

Gravitational Accelerations

Acceleration because of Earth’s gravity does not depend on mass of object

Weightlessness Movies

Falling ObjectsEverything falls at the same rate in a gravitational field was established by GalileoTook Newton’s laws to understand how the laws of physics explained thisEinstein used this idea to lead him to General Relativity

Mr Galileo was correct

Airplane Weightlessness

“Vomit Comet” in Action

Weightlessness Movies

a) The Gravitational Force Constantb) The speed of lightc) The distance between Earth and Sund) The fifth day of the weeke) The metric unit of distance

What does G stand for?

a) There is no gravitational forceb) More massive objects fall more quicklyc) The gravitational force from the Earth on

objects does not depend on their massd) Your weight is heavier than it is on Earthe) Everything is falling at the same rate

In a space shuttle in orbit

a) Star 1 and Star 3 separated by 5 AUb) Star 2 and Star 3 separated by 1 AUc) Star 1 and Star 2 separated by 1 AUd) Star 1 and Star 3 separated by 1 AUe) Star 1 and Star 3 separated by 5 AU

Star 1 has a mass of 10 solar masses, Star 2 has a mass of 5 solar masses and Star 3 has a mass of 1 1 solar mass. In which setup is the gravitational force between two stars the largest?

a) Sun’s pull on Jupiter is greaterb) They are the samec) Jupiter’s pull on Saturn is greaterd) You need more informatione) The answer depends on the distance

between the Sun and Jupiter

How does the size of the gravitational force of the Sun on Jupiter compare to the force of Jupiter on the Sun?

a) Sunb) Jupiterc) They are the samed) You need more informatione) There is no acceleration, just a circular

orbit

Which has the larger acceleration from the other’s gravitational force, the Sun or Jupiter?

Force of Gravity between A & B

Equal & Opposite

Force of Gravity from Earth on A

bigger than Force of Gravity from

Earth on B

AB