Gravity, Orbits & Tides

• Astronomers study gravity to describe and understand the motions of objects in space.

• Isaac Newton • Gets credit for describing gravity

• Could not explain what caused gravity

• Einstein proposed that gravity is a curvature of space and time

• What is gravity? Why does it exist?

The Study of Gravity

Isaac Newton: A New Era of Science

Mathematics as a tool for understanding the physical world.

Isaac Newton (1643 - 1727)

• Building on the results of Galileo and Kepler

• Applied physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler

• Major achievements:• Invented Calculus to solve mathematical

problems related to motion• Defined the three laws of motion• Defined the universal law of gravitation

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

1. Acceleration in the conventional sense (i.e. increasing speed)

a = v/t

Different cases of acceleration:

Velocity and acceleration are directed quantities (vectors)!

3. Change of the direction of motion (e.g., in circular motion)

2. Deceleration (i.e. decreasing speed)

a

v

Acceleration of Gravity

Acceleration of gravity

•independent of mass

•All objects of the same SHAPE fall at

the same rate

Iron ball

Wood ball

Newton’s 1st Law of MotionUnless acted on by an outside force,

1. an object that is not moving will not move

2. an object that is moving will continue to move with the same speed and direction

An astronaut floating in space will continue to float forever in

a straight line unless some external force accelerates

him or her.

Newton’s 2nd Law of Motion

The acceleration, a, of an object is

1.inversely proportional to its mass, m

1.in the same direction and directly proportional to the net force, F

a = F/m F = m a

Newton’s 3rd Law of Motion

To every action, there is an equal and opposite reaction.

The same force that is accelerating the boy forward, is accelerating the skateboard backward.

M = 70 kg

m = 1 kg

v = 7 m/s

V = ?

V = 0.1 m/s

The Universal Law of Gravity

Any two bodies, M and m, are attracted to each other through gravitation. The gravitational force, F, is

1.Proportional to the product of the masses, M x m

2.Inversely proportional to the square of their distance:

F = G Mmd2

G is the Universal Constant of Gravity

G = 6.67300 × 10-11 m3/kgs2

Understanding Orbital MotionThe Universal Law of Gravity

describes the orbital motion:1. According to the 1st law, the moon

would move in a straight line with constant velocity, v.

2. Earth and moon attract each other through gravitational force, F.

3. The Earth has more mass than the moon so the moon’s effect on Earth is small. This shifts the center of the gravitational force closer to the Earth

4. Earth’s gravitational force, F, constantly accelerates the moon towards Earth

5. This acceleration is constantly changing the moon’s direction of motion, Δv, holding it on its almost circular orbit

Earth

Moon

v v’

v

F

Center of Masshttp://en.wikipedia.org/wiki/Center_of_mass

Orbital Motion (2)In order to stay on a

closed orbit, an object has to be within a certain range of

velocities:

Too slow => Object falls back down to Earth

Too fast => Object escapes Earth’s gravity

Newton’s Cannon

Click on the link to see how this works:http://waowen.screaming.net/revision/force&motion/ncananim.htm

Orbital Motion (3)

Geosynchronous Orbits

Geosynchronous Orbit

http://spaceplace.nasa.gov/en/kids/goes/goes_poes_orbits.shtml

Kepler’s 1st and 2nd Laws

1. The orbit of every planet is an ellipse with the Sun at one of the two foci.

2. A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.

Kepler’s 3rd Law … Explained by Newton

Newton described the “Centripetal Force”, a force that balances the orbiting objects circular motion.

Py2 = dAU

3

Kepler’s 3rd Law states that for any orbiting body,

the square of the Period of Revolution in years

=

the cube of the average distance measured in AU

Tides on EarthTidal Force = the difference in gravity from one side of a body to the other that is exerted by a 2nd object.

The Moon’s tidal force on Earth•causes the oceans facing the Moon to bulge out toward it•the oceans on the opposite side of the Earth to bulge out away from the Moon. •These varying ocean levels are called the tides.

Tides on Earth

• The Sun also causes tides on the Earth, but they are smaller than the Lunar tides because the Sun is further from the Earth than the Moon.

• When the Moon and Sun are aligned, their tidal forces combine, and the resulting tides are largest.– Spring Tides - Largest– Neap Tides - Smallest

Tidal Friction

The Earth is constantly rotating, pulling the tidal ocean bulge out of alignment. As a result, the water is continually moving in the opposite direction of the Earth’s rotation.

Tidal FrictionThe movement of the water on Earth has two effects:

It slows down the Earth’s rotation (few milliseconds per century). When dinosaurs roamed the Earth, a day was 22 hours long. Eventually, the Earth will rotate once in the same time the Moon orbits once.

So the Earth and Moon will always have the same faces toward each other.

Tidal FrictionThe movement of the water on Earth has two effects:

It pulls the Moon along a bit faster, slinging it out further from the Earth (about 4 cm per year).

In the distant past, the Moon was much closer to the Earth.

Tides on Moon• Lunar tidal forces are slowing the Earth’s rotation

–it will keep the same face toward the Moon

• Earth is about 80 times more massive than the Moon– its tidal force is 80 times greater. –Tidal friction of flowing rocks (lava) has already locked the Moon to the Earth.

THIS is why the Moon always keeps the same side facing the Earth.

Remember…from the Earth, we never see the far side of the Moon.

Tidal Patterns

Semi-Diurnal: 2 high waters and 2 low waters per day

Diurnal: 1 high water and 1 low water per day

Mixed: A combination of Semi-Diurnal and Diurnal patterns

Tidal Patterns• Tides are described by

TIME and AMPLITUDE• Variations are caused by

– Alignment of Sun and Moon

– Patterns of tides in the deep ocean

– Harmonics of tidal movements

– Shape of Coastline and bathymetry

Size of Tidal Variations