Lesson #12 Topic: Satellites, Gravitational PE, & Fields Objectives: (After this class I will be able to) 1. Explain what is meant by a “gravitational field” 2. Describe potential energy based upon universal gravitation 3. Relate circular motion to the motion of satellites 4. Describe the earth’s natural satellite and how it affects the earth 9/19/06 Warm Up: 1. What would be the length of a day if the earth spun fast enough such that objects on the equator were weightless? Earth radius = 6380 km

Warm Up: 2. How much would a 70 kg person weigh when standing on the 40th parallel? Assignment: “ Gravitational Potential Energy ” Hewitt Ch13 RQ # , 19, 20; T&E #7; T&S #2, 3 Hewitt Ch14 RQ # ; T&E #1, 2, 4, 5, 8, 14 Warm Up: 3. If you stepped into a hole bored completely through the earth, what kind of motion would you experience? Halfway to the center would you feel more or less acceleration than at the surface of the earth?

Force Fields Like an invisible shield from Star Trek right? Like an invisible shield from Star Trek right? uhh… no.. not quite The concept of a field helps us keep track of how a particular object will influence another object The concept of a field helps us keep track of how a particular object will influence another object Example: The earth’s gravitational field. Example: The earth’s gravitational field. How will an object be forced if placed somewhere within the earth’s gravitational field? How will an object be forced if placed somewhere within the earth’s gravitational field?

Gravitational Fields Is field strength of an object the same as force? Is field strength of an object the same as force? No… we want field strength to be independent of the affected object’s mass. No… we want field strength to be independent of the affected object’s mass. It should only be dependent on the mass of the original object. It should only be dependent on the mass of the original object. Gravitational field strength is gravitational force per mass: F g /m Gravitational field strength is gravitational force per mass: F g /m g= F g / m 2 or g= F g / m 2 or Where g is in units of N/kg or m/s 2 Where g is in units of N/kg or m/s 2

Gravitational Potential Energy For objects moving close to the surface of the earth, PE g = mgΔr For objects moving close to the surface of the earth, PE g = mgΔr This works because the force of gravity at this distance is relatively constant due to the fact that Δr << r This works because the force of gravity at this distance is relatively constant due to the fact that Δr << r However, at large distances F g changes with respect to r. So our gravitational potential energy equation turns into However, at large distances F g changes with respect to r. So our gravitational potential energy equation turns into

Gravitational Potential Energy But what r do we use in this equation? r i or r f ? But what r do we use in this equation? r i or r f ? Both; r i is the initial separation distance of the two objects, and r f is the final separation distance. Both; r i is the initial separation distance of the two objects, and r f is the final separation distance. This is more commonly written as: This is more commonly written as: Derive the last equation from the previous (2pts) Derive the last equation from the previous (2pts)

Practice Problems A kg space shuttle is approaching the moon. It is 2x10 5 m away from the surface of the moon. Find the gravitational field strength of the moon at this distance. A kg space shuttle is approaching the moon. It is 2x10 5 m away from the surface of the moon. Find the gravitational field strength of the moon at this distance. Moon mass = 7.35x10 22 kg radius = 1.7x10 6 m 2. Find the work done by gravity from this point to where the shuttle finally lands on the surface of the moon. 3. Find the work needed to launch a shuttle from the surface of the earth to infinitely far away. Earth mass = 5.97x10 24 kg Earth Radius = 6.37x10 6 m

Satellite Motion An earth satellite is an object that has a high enough tangential velocity to fall around the earth rather than into it. An earth satellite is an object that has a high enough tangential velocity to fall around the earth rather than into it. If the surface of the earth drops 5 meters below a 8000 m long tangential line, what tangential speed does an object need to become a satellite? If the surface of the earth drops 5 meters below a 8000 m long tangential line, what tangential speed does an object need to become a satellite? How does a satellite following a circular path differ from one following an elliptical path? How does a satellite following a circular path differ from one following an elliptical path?

Earth’s Natural Satellite Create a demonstration to show why the moon goes through phases as it travels around the earth as well as solar and lunar eclipses. Create a demonstration to show why the moon goes through phases as it travels around the earth as well as solar and lunar eclipses. Why do we only ever see one side of the moon? Why do we only ever see one side of the moon? How does having a moon affect life on the earth? How does having a moon affect life on the earth?

Tides Oceans closer to the moon are pulled toward it, creating a bulge on that side of the earth. Oceans closer to the moon are pulled toward it, creating a bulge on that side of the earth. Oceans on the other side of the earth aren’t pulled as much creating a separation or a bulge on the opposite side of the earth. Oceans on the other side of the earth aren’t pulled as much creating a separation or a bulge on the opposite side of the earth. As the Earth rotates the bulges slide up onto shore and down off of shore. As the Earth rotates the bulges slide up onto shore and down off of shore. *Demonstrate* *Demonstrate*

Tides The moon experiences land tides from the pull of the Earth. The moon experiences land tides from the pull of the Earth. This causes the Moon to be slightly oval in shape. This causes the Moon to be slightly oval in shape. The moon’s CG is then in a different spot than its CM. This causes a net torque on the moon, making the same side of the moon always face the earth. The moon’s CG is then in a different spot than its CM. This causes a net torque on the moon, making the same side of the moon always face the earth. What has a stronger force on the Earth, the sun or the moon? Explain the difference. What has a stronger force on the Earth, the sun or the moon? Explain the difference.