Unit 06 “Circular Motion, Gravitation and Black Holes” “Gravitation and Black Holes”

Unit 06“Circular Motion, Gravitation and Black

Holes”

“Gravitation and Black Holes”

What would happen to the Earth if the Sun suddenly disappeared?

• What if the Sun suddenly disappeared? • Would the Earth …

…keep moving in a circle?

…move out in a straight line?

…stop moving &stay in one place?

…spiral out into space

The Gravitational Force• We learned about Gravity previously.

– We learned gravity on Earth pulls all objects down to Earth.

– The force of gravity accelerates all objects at the rate of a=-9.8m/s2.

• But WHY does Earth attract these objects?– Newton realized that the force attracting objects

toward Earth is the SAME as the force pulling the Moon around the Earth … or the Earth around the Sun! GRAVITY!

The Gravitational Force• Definition: The force of attraction between

ANY two masses.

• Examples:– The Earth is gravitational attracted to the Sun– The moon is gravitational attracted to the Earth– You are gravitational attracted to the Earth!– You are gravitational attracted to the table!– ANY two masses have a gravitational attraction between

then!

We are attracted to ANY object?• YES! Any two masses

have a gravitational attraction to one another!

• Obviously the attraction between you and the table is much less than you and the Earth… why?

• The force of gravity depends on….• The masses of the objects (more mass, more gravity)• The distance the objects are apart (closer objects, more gravity)

– Since the Earth is HUGE the force between You and Earth is much BIGGER than between You and the Table.• This is why you don’t “fall into the table” or get “pulled into another

person” due to the gravitational force between you.• If there were no other forces … like in outer space, YOU WOULD!

(slowly, but you would!)

Gravitational ForceEquationFG = G m1m2

r2

FG = Gravitation Forcem1 = mass of object 1m2 = mass of object 2r = distance between the objects (“r” is measured center to center)G = constant of universal gravitation

Mass and Fg are “directly proportional” m Fg

m Fg

Example:m increases by factor of 2 … Fg increases by factor of 2

m decreases by factor of 4 … Fg decreases by a factor of 4

distance and Fg are “inverse square proportional” r Fg

r Fg

Example:r increases by factor of 2 … Fg decreases by factor of 4 (22)

r decreases by factor of 4 … Fg increases by a factor of 16 (42)

How do you Escape Gravity!?!?In the picture, 4 cannon balls are shot with different velocities…

Ball B has a small velocity and drops back to earth.

Ball C has a bigger velocity and falls farther but still back to earth.

Ball A has such a big velocity is actually escapes Earth’s gravitational field! This is called “escape velocity”

Ball D has a big velocity so that when it falls “down” it actually curves around the Earth! This is an ORBIT, this is a SATELLITE!(imagine if the Earth was flat, this wouldn’t happen, since the Earth is round the Earth curves under the ball as it falls – CIRCULAR MOTION!!!!)

What would happen to the Earth if the Sun suddenly disappeared?

…keep moving in a circle?

…move out in a straight line?

…stop moving &stay in one place?

…spiral out into space

Escape VelocityCannon ball A “escaped” how?

If your velocity is greater than

the “Escape Velocity” you can escape the gravitational field of an object!

Vesc = 2GMplanet

Rplanet√

The Escape Velocity of a Black Hole is GREATER THAN the Speed of Light!Not even LIGHT can escape a Black Hole!

Gravity is what is responsible for the formation of our Universe

• Universe Galaxies Solar System Earth

Our Galaxy The Milky Way

Our Solar System

Relative Sizes of the Planets to the Sun

Black HolesSome definitions (see Black Holes Lab Worksheet)

1. Singularity: A Singularity is a point of infinite density … meaning a HUGE mass but VERY SMALL (too small and massive to even imagine!)

The center of a black hole is a “singularity in space-time”2. Speed of Light: The Speed of Light is 300,000,000m/s (3.00x108m/s)

It’s called the “cosmic speed limit” because nothing is known to travel faster than light!

3. Light year (ly): A light year is a DISTANCE, it’s the distance light can travel in one year.The sun is 8 light minutes away from us … it takes 8 minutes for the sun’s light to get to us. If something is 8 light YEARS away, it would take 8 years for that light to get to us.Starts and galaxies are millions and billions of light years away from us!

4. Escape Velocity (Vesc): Velocity needed to escape the gravitation pull of a planet.

Black Holes “Internet Based Lab”• Download and complete the Black Holes Lab

– Using the videos on the websites as the worksheet explains, you will learn about Black Holes, how they form and why!

Some artist images of “black holes” and the space around them…

Completed Lab?

Black Hole Basics• Black Holes form when a star runs out of fuel

and dies. • Not all stars turn into Black Holes, only stars

about 20-30 times more massive than our sun.• They first expand as they run out of fuel into a

Supernovae. Then they collapse in on themselves, creating a point of huge density – a black hole.

Black Holes Continued…• Black Holes are not dangerous unless you reach the

“Event Horizon” (aka Schwarzchild radius)– This is the distance from the center of a black hole from

which you can’t escape (the gravitational force is too strong, not even light can escape)

• This is why they are called “Black Holes”– Because not even light can escape them – so there is

nothing to “see”.

• This is why if the Sun was replaced with a Black Hole of the same mass it wouldn’t affect the Earth! – We still wouldn’t be CLOSE enough to get pulled in!!!

How Do We Know They Exist?

• There are many pieces of evidence – so even though we can’t “see” a Black Hole – we know they are there! Two pieces are…– As stars near a Black Hole they experience a strong

gravitational pull which accelerates them, we can see the star moving faster around the this area.

– As matter in the Universe is pulled into the Black Hole the matter accelerates, speeds up and thus gets HOT – we can see this heat in the form of radiation, X-rays are detected.

What’s the Dilly?• Gravity warps time and space….

Black holes warp is SO much, nothing can escape – and scientists wonder if there is more to the story….

Watch part of “The Elegant Universe”for more explanation…..

And Homer in 3D