Astronomy 1010 Planetary Astronomy Fall_2015 Day-13

Course Announcements SW chapter -2 due: Mon. 9/21; 2pm

Definitions & Terms -1 Season: A time of year characterized by a general weather pattern (meteorological) or a location of the Earth in its orbit around the Sun (astronomical). Solar Day: 24 hours. The average time between successive meridinal transits of the Sun. Sidereal Day: 23h 56m. The time between successive meridinal transits of a star.

Useful Information for Next Lab Scientific Notation Lunar Phase Simulations ClassAction Web Site (Link from apsu.edu/astronomy) Print the instructions BEFORE you come to class!

 From our perspective on Earth, it appears that everything in the sky moves and orbits us.  Early astronomers and philosophers therefore crafted mostly geocentric models of the universe to reflect this.

 These models became greatly fixed in the minds of astronomers for millennia.  Politics and science can clash when cultural mindsets refuse to be changed.  Another point unwilling to be conceded was the idea of “uniform circular motion.” Objects moved in perfect circles at uniform speeds.  As astronomers viewed the motions of the planets, the models did not match the observations.

 Complicated models were needed to explain phenomena such as retrograde motion.  Ptolemy developed a system with epicycles in 150 CE that remained accepted for about 1,500 years.

 Copernicus was the first to create a mathematical model with the Sun at the center.  Heliocentric model with circular orbits.  Could estimate relative distances of the planets from the Sun and each other.

 Copernicus’s model could explain the behavior of objects in the Solar System.  The ordering of the planets could explain how they sometimes interrupt their prograde motion with retrograde motion.

Lecture – Tutorial Observing Retrograde Motion Law: pg 99 Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask one of us for help.

 Tycho Brahe spent decades collecting astronomical data after building his own observatory.  Created his own geocentric model with the other planets orbiting the Sun, but with the Sun orbiting Earth.

 Using Tycho’s data, Johannes Kepler came up with empirical rules to describe planetary orbits in a heliocentric system.  Empirical science describes how something works, not why.

Johannes Kepler

Known for - 1. First telescope observations of the sun 2. First sun centered scientific model of the solar system or universe 3. Being the world’s best naked-eye astronomer 4. Creating first a theoretical model to explain planetary motions 5. Creating first a theoretical model for explaining gravity

Eccentricity, e how squashed or out of round the ellipse is a number ranging from 0 for a circle to 1 for a straight line e = 0.02 e = 0.7 e = 0.9

Kepler’s Three Laws of Planetary Motion

Kepler’s First Law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

What is the shape of Earth’s orbit around the Sun? Earth, e = Nearly circular

SECOND LAW A line drawn from the planet to the Sun sweeps out equal areas in equal times orbital speed is not constant for an ellipse only for a circle planets move faster when near the Sun (perihelion) planets move slower when they are far from the Sun (aphelion)

Kepler’s Second Law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

SECOND LAW The speed a planet travels during its orbit is related to the distance from the star When the planet is near the sun the planet goes faster than when the planet is farther from the sun Planet travels fast here Planet travels slow here

Lecture – Tutorial Kepler’s 2 nd Law: pg 21 Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask one of us for help.

Course Announcements Smartworks Chapter 3: Mon. 9/29 Read chapters 3 & 4 Dark Sky Observing - TONIGHT Wednesday Sept. at the Observatory  Weather dependent. 1 st Quarter night – Wed. Oct. 1 – 7:30pm in the Archwood parking lot or SSB atrium depending on weather.

Kepler’s First Law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus.

Kepler’s Second Law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

According to Kepler’s second law, a planet with an orbit like Earth’s would: A. move faster when further from the Sun. B. move slower when closer to the Sun. C. experience a dramatic change in orbital speed from month to month. D. experience very little change in orbital speed over the course of the year. E. none of the above.

Kepler’s second law says “a line joining a planet and the Sun sweeps out equal areas in equal amounts of time.” Which of the following statements means nearly the same thing? A. Planets move fastest when they are moving toward the Sun. B. Planets move equal distances throughout their orbit of the Sun. C. Planets move slowest when they are moving away from the Sun. D. Planets travel farther in a given time when they are closer to the Sun. E. Planets move the same speed at all points during their orbit of the Sun.

THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun p = 1 year p = ~ 12 years

THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun MASS DOES NOT MATTER Both have p = 1 year

THIRD LAW The size of the orbit determines the orbital period planets that orbit near the Sun orbit with shorter periods than planets that are far from the Sun a 3 AU = P 2 years

 Kepler’s third law in its simplest form utilizes nonstandard units—the periods are in years, while the distances are in AU.  The relationship does not change if standard units are used.  The equation is just more complicated. MATH TOOLS 3.2

 Consequences: Distant planets take longer to orbit the Sun. Distant planets travel at slower speeds.

Lecture – Tutorial Kepler’s 3 rd Law: pg 25 Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask one of us for help.

Which of the following best describes what would happen to a planet’s orbital speed if it’s mass were doubled but it stayed at the same orbital distance? A. It would orbit half as fast. B. It would orbit less that half as fast. C. It would orbit twice as fast. D. It would orbit more than twice as fast. E. It would orbit with the same speed.

If a small weather satellite and the large International Space Station are orbiting Earth at the same altitude above Earth’s surface, which of the following is true? A. The large space station has a longer orbital period. B. The small weather satellite has a longer orbital period. C. Each has the same orbital period

 Copernicus was able to use right-triangle trigonometry and observations of planets at opposition or conjunction to very accurately find their distances relative to the Earth–Sun distance. CONNECTIONS 3.1

 These distances were very accurate compared to our modern values.  He was not able to discern our distance from the Sun this way, so the distances are expressed in units of our distance (1 AU). CONNECTIONS 3.1

 The synodic (S) and sidereal (P) periods of the planets can be related to Earth’s (E) sidereal period ( days).  Inferior planets:  Superior planets:  Synodic periods are measurable from Earth. MATH TOOLS 3.1

 Kepler’s third law in its simplest form utilizes nonstandard units—the periods are in years, while the distances are in AU.  The relationship does not change if standard units are used.  The equation is just more complicated. MATH TOOLS 3.2

 Proportionality and inverse proportionality are ways to understand how one quantity behaves relative to another quantity.  It lets you get the gist of how the relationship works between those two quantities.  Sometimes, you need to know more than just the gist—you need to know the constant of proportionality, which exactly relates the quantities. MATH TOOLS 3.3

 Galileo Galilei was the first scientist to observe the sky with a telescope.  Found four moons in orbit around Jupiter.  Saw that Venus had phases. In a geocentric model, Venus’s phase would not change.

Isaac Newton (1642 – 1727) The Baddest Dead White Guy of Them All

Isaac Newton (1642 – 1727) 1. Probably died a virgin 2. Was a priest and Lawyer 3. Had artificial wooden and silver noses 4. Probably died of Mercury poisoning 5. Rumored to have died when his bladder burst 6. Was blind at the time of his death 7. Was labelled a heretic by the church

Isaac Newton (1642 – 1727) 1. Probably died a virgin 2. Was a priest and Lawyer 3. Had artificial wooden and silver noses 4. Probably died of Mercury poisoning 5. Rumored to have died when his bladder burst 6. Was blind at the time of his death 7. Was labeled a heretic by the church

 Using observations and investigations from Galileo, Isaac Newton discovered laws that apply to all objects.  Basis of classical mechanics.  Physical laws, not empirical science.

Course Announcements Smartworks Chapter 3: Wed. 10/01 Smartworks Chapter 4: Mon. 10/06 Read chapters 4 1 st Quarter night – Wed. Oct. 1 – 7:30pm in the Archwood parking lot or SSB atrium depending on weather.

 Using observations and investigations from Galileo, Isaac Newton discovered laws that apply to all objects.  Basis of classical mechanics.  Physical laws, not empirical science.

Newton’s First Law of Motion A body remains at rest or moves in a straight line at a constant speed unless acted upon by an outside (net) force. A rockets will coast in space along a straight line at constant speed. A hockey puck glides across the ice at constant speed until it hits something

Newton’s Second Law of Motion (net)Force = mass x acceleration or F net = m x a Acceleration is the rate of change in velocity – or how quickly your motion is changing. Three accelerators in your car!!

 Acceleration is force divided by mass, or  Mass resists changes in motion.  Greater forces mean greater accelerations.

 Proportionality and inverse proportionality are ways to understand how one quantity behaves relative to another quantity.  It lets you get the gist of how the relationship works between those two quantities.  Sometimes, you need to know more than just the gist—you need to know the constant of proportionality, which exactly relates the quantities. MATH TOOLS 3.3

 Knowing the unbalanced force an object experiences allows you to find its acceleration, and vice versa. MATH TOOLS 3.4

Newton’s Third Law of Motion Whenever one body exerts a force on a second body, the second body exerts an equal and opposite force on the first body. Don’t need a rocket launch pad! The Bug and the Windshield – who is having the worse day?

 Newton’s third law of motion: For every force, there is an equal and opposite force.  The two forces have the same size.  The two have opposite directions.

Newton’s Law of Gravitation Newton’s law of gravitation states: Two bodies attract each other with a force that is directly proportional the product of their masses and is inversely proportional to the square of the distance between them. What the ….? I thought I understood gravity?

Newton’s Law of Gravitation To figure out the gravitational force just multiply the mass of the two things together then divide by the distance they are apart (squared). m1m1 m2m2 d

Newton’s Law of Gravitation Newton’s law of gravitation states: Two bodies attract each other with a force that is directly proportional the product of their masses and is inversely proportional to the square of the distance between them. g ~ 10 m/s 2 “the acceleration of gravity” & g x m is your weight!

 The gravitational acceleration at the surface of Earth, g, can be solved for by using the formula for the gravitational force and Newton’s second law.  The m cancels.  g is the same for all objects at the same R. MATH TOOLS 4.1

 Gravity works on every part of every body.  Therefore, self-gravity exists within a planet.  This produces internal forces, which hold the planet together. CONNECTIONS 4.1

 There’s a special case: spherically symmetric bodies.  Force from a spherically symmetric body is the same as from a point mass at the center. CONNECTIONS 4.1

Lecture – Tutorial Newton’s Law of Gravity: pg 29 Work with a partner! Read the instructions and questions carefully. Discuss the concepts and your answers with one another. Come to a consensus answer you both agree on. If you get stuck or are not sure of your answer, ask another group. If you get really stuck or don’t understand what the Lecture Tutorial is asking, ask one of us for help.