The Science of Orbits (Power Point 04) Image Credit: NASA

Student Learning Objectives Examine the contributions of ancient and modern astronomy to the understanding of gravity and planetary motion. Recall and apply Kepler’s Laws to our solar system Apply Newtonian physics to our solar system Describe gravity and its effects Analyze orbital motion

One More Geocentric Tycho Brahe (late1500’s) Designed and utilized new instruments for measuring precise angles in the sky Although Tycho Brahe believed in a geocentric system, his measurements were later used to provide proof for the heliocentric system. lol https://www.youtube.com/channel/UCgdxVfxpAXcxtka1o3TD2Cg

What are Kepler’s Laws? Kepler (1600’s) Kepler’s 1st Law Used Tycho Brahe’s observations and measurements of planetary positions to develop three laws of planetary motion. Kepler’s 1st Law Planets move in elliptical orbits with the Sun at one focus. (Ellipses) Image Credit: study.com

Kepler’s 2nd Law Planets sweep out equal areas of space in equal time intervals. (Equal Areas) Image Credit: www.wonderwhizkids.com

Kepler’s 3rd Law The orbital period of a planet is related to the semi-major axis of it’s orbit. P2 = a3

Practice 1) Which planet has the longer orbital period? Saturn: a = 9.54 AU Jupiter: a = 5.2 AU 2) How do we measure birthdays? http://www.exploratorium.edu/ronh/age/index.html

The planets in our solar system follow orbits that are nearly circular. Image Credit: NASA

Circles vs Ellipses Eccentricity indicates the elongation of the ellipse. (e = 0 to 1) Image Credit: NASA Earth Observatory

How are the motions of objects described? Average speed is the amount of distance traveled in some amount of time. (65 mph) Velocity is speed in a particular direction. (65 mph South) s = d t

Acceleration Acceleration is the change of velocity in some amount of time. Change in speed or direction All objects on Earth have the same downward acceleration. 9.81 m/s2

Practice How fast would an object dropped from the tower of Pisa be traveling after 2 seconds, in the absence of air? Is the acceleration due to gravity greater on a book or a feather? If a satellite travelled at a constant speed in a circular orbit, it would have zero acceleration (True or False)?

https://www.youtube.com/watch?v=5C5_dOEyAfk

What are Newton’s Laws of Motion? Newton’s 1st Law An object will remain at rest or maintain a constant velocity unless an unbalanced force causes the object’s motion to change. (Inertia) Inertia is the tendency of an object to maintain its motion. https://www.youtube.com/watch?v=d7iYZPp2zYY

Newton’s 2nd Law of Motion An unbalanced force acting on a mass gives the mass an acceleration in the same direction as the unbalanced force. (F = ma) http://www.physicsclassroom.com/mmedia/kinema/stl.cfm

Mass vs Weight Mass is a fundamental quantity. Mass is the amount of material contained in an object. Weight is the gravitational force acting on a mass. (W=mg) Average Man 73 kg Sun 1.989 x 1030 kg Earth 5.972 x 1024 kg http://www.exploratorium.edu/ronh/weight/index.html

Practice 1) Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct? 2) Would your mass be different if you were on the moon right now? 3) What would a 75 kg person weigh on Earth? What would this person weigh on Mars where the acceleration due to gravity is 3.72 m/s2?

Newton’s 3rd Law of Motion When two objects interact, they create equal and opposite forces on each other. (Action-Reaction) Same Pull Opposite Directions Stock Image

Space X

Practice Apply each of Newton's laws to observations within our solar system. State an example of each law. Do all of Newton’s Laws apply to an object at the same time? Explain.

F = GMm d2 What is Gravity? Gravity is a property of mass. Newton’s Universal Law of Gravitation Every object with mass attracts every other object with mass with a force. F = GMm d2

Newton’s Mutual Force of Attraction Both masses pull the same on each other!

Force decreases with the square of the distance. Inverse Square Law Force decreases with the square of the distance.

Practice 1) Is the gravitational force zero in space? 2) If Earth had twice as much mass, would this change your weight? Would it change your mass? 3) If the distance changes between two objects, does the acceleration due to gravity change?

What is Einstein’s description of Gravity? https://www.youtube.com/watch?v=LoaOHvy5AcA Image Credit: Kurdistan Planetarium

Mass & Space Einstein’s Theory of Gravity Every object with mass creates a curvature of space-time. Mass does not create a force Mass changes space Space alters path of objects and light More Mass = More Curvature

Image Credit: oneminuteastronomer.com

Practice Does an apple cause a curvature of space? Why doesn’t the Moon fall into the gravity well caused by Earth?

Effects of Gravity Orbits Atmospheres Galaxies Star Formation Shapes of Objects Orbital Perturbations Synchronous Motion Weight Tides Motion

Gravity & Tides Credit: NASA

Our Changing System Our Earth-Moon system is changing. Earth’s rotation is slowing (0.0015 seconds/century) Our Moon is drifting away (3.8 cm/year) The synchronous orbit of the Moon (same face) Image Credit: NASA

Image Credit: wired.com Weightlessness The feeling of weightlessness occurs when an object and its reference frame accelerate at the same rate. Objects fall together. Image Credit: wired.com

https://www.youtube.com/watch?v=WMK36dpHIkg

Practice The Sun's tidal affects are weak compared to the Moon. Why? The astronauts on the space station have no weight. (true or false) Does the moon have weight? Explain.

What is the physics of orbital motion? Objects move in a straight line, unless an unbalanced force changes the motion. In circular motion, a centripetal force is causing a change in motion.

Falling into Orbit

Practice If the force keeping an object in a circular orbit is removed, what will be the path of the orbiting object? 2) What is a geosynchronous orbit? 3) What would be the path of an open orbit?

Center of Mass Astronomical objects actually orbit about the center of mass of the system. (Elliptical Orbits) Common Center Of Gravity

Conservation Of Energy Elliptical orbits are maintained by conservation of mechanical energy. GPEMax KEMax Image Credit: Planetary Society India