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Home , Gravity, Motion, Vertical and horizontal

Chapter 6: &

Sun at Center are Circular Tycho Brahe 1546-1601

Tycho was the greatest observational astronomer of his . Tycho did not believe in the Copernican model because he didn’t believe that the Moved. Kepler worked for Tycho as his mathematician. Kepler derived his laws of planetary motion from Tycho’s observational data.

Orbits are Elliptical Kepler’s 3 Laws of Planetary Motion

1: The of each about the is an ellipse with the sun at one focus.

2. Each planet moves so that it sweeps out equal areas in equal .

22 Tr11 3. 22= Tr22 Isaac (1642 -1727) UniversalUniversal LawLaw ofof GravityGravity Every in the attracts every other particle with a along a line joining them. The force is directly proportional to the product to their and inversely proportional to the of the between them. M d m mM F ~ d 2 Gravitational Force is Universal

The same force that makes the apple fall to Earth, causes the to fall around the Earth. UniversalUniversal LawLaw ofof GravityGravity

Nm2 Gx= 6.67 10−11 kg 2 M d m GmM F = d 2 Measuring G: Cavendish

mM GmM F ~ 2 F = d d 2

Nm2 Gx= 6.67 10−11 kg 2

G is the same everywhere in the Universe. Inverse Square Law

GmM F = d 2 Gravitational Force How would the force of gravity and the due to gravity change as you fell through a hole in the Earth? Problem Calculate the acceleration of gravity acting on you at the surface of the Earth.

Gmyou M E F = Fma= you d 2 GM a = E d 2 ()6.673xNmkgxkg 10−11 2 / 2 () 5.98 1024 a = 2 ()3.84xm 108

ams= 9.81 / 2 Problem Calculate the force of gravity between the Earth and the Moon. Assume a . GmM F = d 2

(6.673xNmk 10−11 2 /g 2 )( 6.00xk 1024 g)( 7.4xk 1022 g ) F = 2 ()3.84xm 108

FxN= 2.01 1020 Problem Calculate the acceleration of the Earth due to the Earth-Moon gravitational interaction. F a = m

2.01x 1020 N a = 5.98x 1024 kg

axms= 3.33 10−52 / Problem Calculate the acceleration of the Moon due to the Earth-Moon gravitational interaction. F a = m 2.01x 1020 N a = 7.35x 1022 kg

axms= 2.73 10−32 / Problem

The acceleration of gravity at the Moon due to the Earth is:

axms= 2.73 10−32 /

The acceleration of gravity at the Earth due to the moon is: axms= 3.33 10−52 / Why the difference?

FORCE is the same. Acceleration is NOT!!! Force is not Acceleration!

FFEarth on Moon= − Moon on Earth

The are equal but the are not! Gravitational forces produce the and keep the same side of the Moon always facing the Earth in a Synchronous . The gravitational force between Earth and Moon results in tides

Large spring tides occur when the Sun and Moon are aligned such that they BOTH pull on the Earth’s .

Smaller neap tides occur when the Sun and Moon are misaligned such that they pull on the Earth’s water in different directions. Earth’s Ocean Tides

Neap Tides Spring Tides How many High and Low Tides per ? Earth- Moon System: Tidal Lock Moon pulls on Earth and causes tidal bulges in Oceans. Earth pulls on moon causing tidal bulge in Moon such that the CM is off from CG.

Earth’s pull on the moon at its center of gravity produces a which rotates it. The moon is ‘tidally locked’ so that it rotates at the same rate at which it revolves, showing Earth only one face. Questions! Which exerts a greater gravitational force on the Earth, the moon or the Sun? Which has a greater effect on the Earth’s tides? Why?

The Sun exerts a greater force on the Earth. It also causes tides, though it has about half the effect as the moon. Tides are due to differences in force on opposite sides of the Earth. The sun is so far away relative to the of the Earth that the difference in force is not as significant as the difference due to the Moon since it is closer! Spring

Spring

Neap Bouncing laser beams off the Moon demonstrates that it slowly moving away from the Earth ~.25 cm/month Earth- Moon System is Changing!

•Earth Rotation Slowing due to of ocean on bottom •.0023 s per century: 900 Million yrs ago, Earth day was 18 hrs! •Decrease of Earth’s angular , increases the orbital of the Moon! •Earth is slowing down and Moon is moving further away! Eventually the Earth's will be identical to the Moon's orbital period. This situation is called synchronous (1:1) rotation. In the distant future (many billions of from now), the Earth will have a day which is 47 current days long, and the Moon will only be visible from one side of the Earth!! Projectile Motion Ignore Air Resistance!

Most Important: X and Y components are INDEPENDENT of each other! Zero at the Top! Y component of is zero at the top of the path in both cases!

You know they have the y component of velocity is the same in both cases because they reached the same height! Projectile Motion

Horizontal and vertical components are independent of each other!

Gravity acts in the vertical direction but not in the horizontal direction!!

Speed in vertical direction up! in horizontal direction stays the same! First the SIMPLE Case: Horizontal Launch (Ignore Air Resistance)

The x-component doesn’t change (no acceleration in x-direction.) The y-component changes (a = -g.) Projectile Motion

No Change

ax = 0

Actual path is a vector sum of horizontal and vertical .

change agy = Dropping From Moving Frame Plane and Package

An airplane traveling at a constant speed and height drops a care package. Ignoring air resistance, at the the package hits the ground, where is it relative to the plane?

a) Behind the plane. b) Under the plane. c) In front of the plane.

Any dropped from a plane has the same initial velocity as the plane! Projectile Motion Which hits the ground first? SAME! Both falling the same height! Horizontal speed doesn’t effect the time to hit the ground!

If it takes 1 second to hit the ground, how tall is the tower? Projectile Motion

dt==55(1)522 = m

If it takes 1 second to hit the ground, how tall is the tower? Same rock, same speed, same angle. Which rock hits the water first? a) Rock 1 b) Rock 2 c) same

Which rock hits the water with the greatest speed? a) Rock 1 b) Rock 2 c) same Same rock, same speed, same angle. Which rock hits the water first? a) Rock 1 b) Rock 2 c) same

Which rock hits the water with the greatest speed? a) Rock 1 b) Rock 2 c) same

Spatial Symmetry In G ! Projectile Motion Launched at an Angle (Ignore Air Resistance)

The x-component doesn’t change (no acceleration in x-direction.) The y-component changes (a = -g.) Shooting UP From Moving Frame

Horizontal and vertical components are independent of each other! Horizontal component remains unchanged without air resistance. Only the vertical component changes! Launched at an Angle: The simple case: Δy=0 Question gms=10 / 2

The ball is thrown horizontally at 20 m/s. About how long does it take to hit the ground? 0 1 2 2Δy Δ=y vt + gt ts==1 yi 2 g

d How far does it travel in the horizontal direction? m Δ=x vt =20 1 s = 20 m xi s Question gms=10 / 2

The ball is thrown horizontally at 30 m/s. About how long does it take to hit the ground?

1 2 2Δy Δ=y vt + gt ts==1 yi 2 g Only Δy determines time!

d How far does it travel in the horizontal direction? m Δ=x vt =30 1 s = 30 m xi s Question gms=10 / 2

The ball is thrown horizontally at 100 m/s. How long does it take to hit the ground? 1 Second!! How far does it travel in the horizontal direction?

m Δ=x vt =100 1 s = 100 m xi s of Earth

If you threw the ball at 8000 m/s off the surface of the Earth (and there were no buildings or mountains in the way) how far would it travel in the directions in 1 second? Curvature of Earth

If you threw the ball at 8000 m/s off the surface of the Earth (and there were no buildings or mountains in the way) how far would it travel in the vertical and horizontal directions in 1 second?

horizontal: Δ= x vx t =(8000 m / s)( 1 s)= 8000 m

1 2 vertical : Δ=ygtt22 =5 = 5() 1 s = 5 m 2 Curvature of Earth

If you threw the ball at 8000 m/s off the surface of the Earth (and there were no buildings or mountains in the way) how far would it travel in the vertical and horizontal directions in 1 second?

horizontal: Δ= x vx t =(8000 m / s)( 1 s)= 8000 m

1 2 vertical : Δ=ygtt22 =5 = 5() 1 s = 5 m 2 Curvature of Earth

If you threw the ball at 8000 m/s off the surface of the Earth (and there were no buildings or mountains in the way) how far would it travel in the vertical and horizontal directions in 1 second?

Does the ball ever hit the Earth???? Curvature of Earth Curvature of the Earth: Every 8000 m, the Earth curves by 5 meters! Orbital Velocity If you can throw a ball at 8000m/s, the Earth curves away from it so that the ball continually falls in around the Earth – it is in orbit around the Earth!

Ignoring air resistance.

Above the Orbital Motion| & Escape Velocity

8km/s: Circular orbit Between 8 & 11.2 km/s: Elliptical orbit 11.2 km/s: Escape Earth 42.5 km/s: Escape ! Projectile Motion IS Orbital Motion The Earth is in the way! Circular Orbital Velocity The force of gravity is perpendicular to the velocity of the ball so it doesn’t speed it up – it changed the direction of the ball. It provide a centripetal acceleration the keeps it in a circle!

At a speed of 8km/s Orbital time is ~ 90 minutes Elliptical Orbits Does the force of gravity change the speed of on object in an elliptical orbit?

Because there is a component of force in the direction of motion!

Do Workbook 45-47 Orbits

Circular Orbit Elliptical Orbit

Where does the satellite move faster in the elliptical orbit? Near the Earth or far from Earth? Why? Elliptical Orbit Satellite Orbits Global Geostationary Satellite Coverage

USA USA

Euro

Japan

USSR China With an orbital period of about 100 minutes, these satellites will complete slightly more than 14 orbits in a single day. Sun-Synchronous Near Polar Orbits

Orbiting Trash Man-made debris orbits at a speed of roughly 17,500 miles/hour (28,000 km/h)!

More than 4,000 satellites have been launched into space since 1957. All that activity has led to large amounts of space trash. More than 13,000 objects that are at least three to four inches (seven to ten centimeters) wide. Of those objects, only 600 to 700 are still in use. 95 percent of everything up there that the United States is tracking is trash. There are millions of smaller parts that are too small to track.

Orbiting Space Trash Fast Trash Go Boom

Australia, in 1979. Orbiting Space Trash What Goes Up Must Come Down

This is the main propellant tank of the Skylab crashed onto second stage of a Delta 2 launch vehicle Australia in 1979. which landed near Georgetown, TX, on 22 January 1997. This approximately 250 kg tank is primarily a stainless steel structure and survived reentry relatively intact. Radioactive Space Junk 954

Nuclear in Space Mission to Mars

The NASA Mars Exploration Program (MEP) will launch a spaceflight mission to Mars in late 2009 that will land a nuclear powered roving Mars Laboratory on the surface of the planet.

Our Spaceship Earth

One island in one ocean...from space “...we’re all aboard a little spaceship called Earth” - Bucky Fuller