How We Know Where They’re Going

 Geocentric Model  Earth is the center of the universe  Philosophy at the time leads to the idea of perfection and harmony in the heavens, thus orbits are perfect circles  The Problem? Retrograde Motion: Mars Uranus

 He still has a geocentric model  BUT Earth not exactly at the center  Planets move in circles called epicycles  Able to predict future locations  Explains retrograde motion (90-168)

 Proposes heliocentric model to explain retrograde motion  The Sun is at the center of the solar system now  Still assumes perfect circles  Able to calculate periods and relative distances  Not better than Ptolemaic predictions. ( )

 Recognized the need for new model and dedicated his life to making more precise measurements  Built first modern observatory  Recorded planetary positions from 1576 – 1591  2.5x more accurate than any previous records! ( )

 Continued the work of Brahe by trying to use his data to prove the Copernican model  Now recognizes that planetary orbits are elliptical  Developed 3 Laws of Planetary Motion  Answered “what” but not “why” ( )

 Challenges the belief that the heavens are perfect  In 1604, he observes a nova. Why can new stars appear if everything is perfect as it is?  1609 refines the telescope (didn’t invent it)  1610, publishes findings:  The surface of the moon isn’t perfect  Stars found in Pleiades that are “invisible” to naked eye ( )

 Discovers Galilean moons (1610) ( ) Telescope Photograph of Jupiter and the Galilean Moons

 Venus has phases like the moon  In 1613, publishes a letter documenting sun spots! ( )

 Isaac Newton ( )  Formulated 3 Laws of Motion and 1 Law of Universal Gravitation ▪ Now we’ve answered the question of “why” ▪ Theory matches observation, so we must reexamine our beliefs  Happened again with Einstein in 1911 ▪ General Relativity offers new explanation of gravity and explain phenomena that couldn’t be explained by past theories. ▪ Verified experimentally

 The Law of Orbits  “The orbit of every planet is an ellipse with the Sun at one of the two foci”  The eccentricity of an orbit tells you have elliptical it is ▪ An eccentricity of 0 is a circle ▪ The further from 0, the more elliptical the orbit

Mercury0.2056Jupiter0.0489Ceres Venus0.0067Saturn0.0565Pluto Earth0.0167Uranus0.0457Haumea Mars0.0935Neptune0.0113Makemake Eris Copy Into Planet Packets

 The Law of Areas  “A line joining a planet and the Sun sweeps out equal areas during equal intervals of time.”  Planets move faster when they are closest to the Sun, and slower when they are farther away ▪ Closest approach is called perihelion ▪ For Earth, it occurs on January 3 when we’re 1.46 x 10 8 miles from the Sun! ▪ Furthest point is called aphelion ▪ For Earth, it occurs on July 4 when we’re 1.50 x 10 8 miles from the Sun!

If it sweeps out equal areas in equal times, does it travel faster or slower when it is far from the Sun?

If is sweeps out equal areas in equal times, does it travel faster or slower when far from the Sun?

Same Areas

The farther away a planet is from the Sun, the longer it takes for that planet to go around the Sun once

 While gazing at the planets that are visible with the naked eye, you tell a friend that the farther a planet is from the Sun, the longer its solar year is. Your friend first asks what a solar year is. After explaining that it’s the time required for a planet to return to its same position relative to the Sun, your friend then asks, “Why does it take longer for the outermost planets to orbit the Sun?” What is your reply?

 “An object at rest will remain at rest, and an object in motion will remain in motion with a constant speed and in a straight line unless acted upon by an external force.” An astronaut floating in space will continue to float forever in a straight line unless some external force is changing his/her motion.

Acceleration is a change in velocity or a change in direction of velocity. Newton’s laws classify objects as accelerating or non-accelerating, not as moving or stationary.

 To every action, there is an equal and opposite reaction. The same force that is accelerating the rocket forward, is accelerating the exhaust backward.

 So how did Newton revolutionize our understanding of planetary motion using gravitation?

Planets/Moons have curved paths ↓ Their velocity is changing ↓ They’re accelerating ↓ There must be a force causing the acceleration!

F = gravitational force between two objects m 1 = mass of first object m 2 = mass of second object r = distance between objects G = universal constant of gravitation

 If the bodies are twice as far apart, the gravitational force of each body on the other is ¼ of their previous values.  This is called an “inverse-square law.”

Newton’s description of gravity accounts for Kepler’s laws and explains the motions of the planets and other orbiting bodies

G = universal constant of gravitation M central = mass of central object r = distance between objects

 The Earth exerts a gravitational force on an orbiting satellite. Use Newton’s third law to compare the force of the satellite on the Earth. Draw a picture similar to the ones I drew for object A and object B.  According to Newton’s second law, compare the accelerations of the satellite and Earth as a result of their interaction.

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