For centuries, people believed that Earth was at the center of the universe. This is known as the Geocentric Model.
The Geocentric Model was devised by Claudius Ptolemy, an Alexandrian astronomer who lived in the second century C.E.
The Geocentric Model places Earth at the center of the universe.
Ancient Greeks believed circular motions were "perfect" and the sky should be governed by perfect geometry.
In this model, the Sun, Moon, and Stars orbit Earth in a circular motion.
The Planets orbit in small circles (epicycles) that themselves orbit the Earth.
Problems with the Geocentric Model
The geocentric model had several problems:
Why does Venus look bigger when farther from its full phase?
Why do we never see Mercury and Venus on the opposite side of the Earth from the Sun?
Why do some stars vary in their position in the sky throughout the year (Parallax)?
Parallax
Parallax is the apparent shift in the position of a foreground object relative to background objects as the viewing location changes.
Parallax can be used to measure the distance to astronomical objects.
Nicolaus Copernicus and the Heliocentric Model
Nicolaus Copernicus, a Polish astronomer from the 15th century, proposed that the Sun was at the center of the universe, which is known as the Heliocentric Model.
The Heliocentric Model places the Sun at the center.
In this model, the Moon orbits the Earth in a circular motion.
All the planets (including the Earth) orbit the Sun in a circular motion.
Copernicus retained the concept of circular motion from the Geocentric model.
Tycho Brahe
Tycho Brahe made astoundingly precise measurements of the sky, accurate to 2 arcmin.
He measured the sky every night for years.
Brahe died 10 years before Galileo's telescope.
He believed in the geocentric model.
His observations didn't improve predictions much.
He also studied parallax.
Stellar Parallax
Some stars would experience the Parallax effect but some wouldn’t.
Turns out some of those stars are just really far away!
Johannes Kepler
Johannes Kepler was Tycho's former assistant.
Kepler came up with empirical rules to describe the orbits.
Empirical science describes how something works, not why.
Kepler’s First Law
Planet orbits are ellipses.
Each ellipse has two foci.
The Sun is at one focus of a planet’s elliptical orbit.
Ellipses
An ellipse has a size, described by the semi-major axis.
The longest length is twice the length of the semimajor axis.
Each orbit has a shape and a size.
The eccentricity describes how elongated the ellipse is, and how far the foci are separated.
Kepler’s Second Law
Kepler's Second Law is often called the Law of Equal Areas.
The line between the Sun and the planet “sweeps” out equal areas in equal times.
Consequences:
A planet will go fastest when closest to the Sun.
It will go slowest when farthest from the Sun.
Applies to only one planet at a time.
Kepler’s Third Law
It relates the orbital period to the size of the orbit.
Let A be the length of an orbit in AU.
Let P be the period in years.
P^2 = A^3
Consequences:
Distant planets take longer to orbit the Sun.
Distant planets travel at slower speeds.
Galileo Galilee
Galileo Galilee was the first to make scientific discoveries about the heavens with a telescope.
He observed:
Moon craters
Sunspots
4 Moons of Jupiter (Galilean Moons)
Phases of Venus
But did NOT invent telescope!
Found that an object left in motion remains in motion
Newton’s Laws
Used Galileo’s insights
Newton discovered laws that apply to all objects.
Basis of classical mechanics
Physical laws, not empirical science
Newton’s Discoveries
Gravity
Optics
Most of classical physics
Forces
Inertia
Acceleration
Calculus
Most of which he did before his 24th birthday!
Newton’s First Law
Galileo’s law of inertia
A moving object will stay in constant motion
“Constant” motion means at a constant speed and in a constant direction.
Newton’s Second Law
Unbalanced forces cause changes in motion.
Examples:
Speeding up with the gas pedal
Slowing down with the brake pedal
Turning counts too!
Speed and Velocity
Velocity: the speed and direction of an object’s motion.
Speed: driving 60 miles/hour
Velocity: driving 60 miles/hour east.
Acceleration
A change in velocity is called acceleration.
Acceleration measures how quickly a change in motion takes place.
Newton’s Second Law (Revisited)
Acceleration is force divided by mass
Or: F = m*a
Mass resists changes in motion
Greater forces mean greater accelerations.
Newton’s Third Law
For every force there is an equal and opposite force.
The two forces have the same size.
The two have opposite directions.
Use: finding exoplanets!
Gravitational Acceleration
All objects on Earth fall with the same acceleration, g.
g = 9.8 m/s^2
Gravity
Gravity is an attractive force between any two objects with mass.
It depends on the objects’ masses.
It depends on the distance between them.
The Force of Gravity
F = G \frac{m1 m2}{r^2}
G is the universal gravitational constant.
The m terms are the two masses.
More mass = more force
Forces and Orbits
Uniform circular motion: moving on a circular path at constant speed.
In order to go in a circle, you need a centripetal force
Gravity provides the centripetal force that holds a satellite in its orbit.
Elliptical Orbits
For planets in real-world orbits:
Gravity changes both the direction and the speed of the planet.
Results in Law of Equal Areas
Implications of Gravity
Kepler’s laws of orbits and Newton’s laws of motion and gravity are only the beginning.
Internal forces
Tides
More gravitational phenomena
Internal Forces
Gravity works on every part of every body.
Therefore self-gravity exists within a planet.
This produces internal forces. These hold the planet (or star!) together.
Tidal Forces
Tides are a consequence of gravity.
Something closer to an object experiences a stronger gravitational pull than something else further away.
Tidal Forces on Earth
Parts of Earth are closer to the Moon than other parts.
This produces a stretch on the Earth, called a tide.
Oceans and Tidal Forces
Earth’s oceans flow in response to the tidal forces.
The oceans have a tidal bulge: they are elongated in a direction that is nearly pointed at the Moon.
Earth rotates under the tidal bulge.
We get two high and two low tides each day.
The behavior is complicated by Earth’s landmasses and solar tides.
Tidal Effects on Solid Bodies
Tides can affect the solid part of Earth, too.
A gravitational pull can stretch and deform a solid body.
Results in friction, which generates heat.
Friction also opposes the rotation of Earth, causing Earth to very gradually slow its rotation.
Days lengthen by about 0.0015 seconds every century.
Tides on the Moon
Earth’s mass is large, so tidal forces on the Moon are strong.
Cause tidal braking
Moon’s rotation and orbital period are locked.
Tidal locking
This means the Moon’s rotation period equals its orbital period.
Lunar Recession
Due to tides, Earth is not a perfect sphere.
Earth’s leading edge creates an acceleration of the Moon in its orbit, resulting in a bigger orbit.
The lunar month increases by 0.014 s/century.
Moon is slowly moving away from us!
Tides and the Roche Limit
Tidal (stretching) forces are stronger when closer toward a planet.
There is a limit in orbital distance, called the Roche limit.
Inside the Roche limit for a planet, tides would shatter a moon.
Example: passage of comet Shoemaker-Levy 9 within Jupiter’s Roche limit.
Origin of Rings
Rings are made of swarms of particles.
Each particle or moon orbits the planet, and gravitational interactions between them force them to conform to uniform orbits.
Gravity and Rings
Shepherd moons of Saturn help keep the rings crisp and create gaps such as the Cassini Division.