Transcript File
Satellite Motion Warm Up: Given that the centers of the Earth and Moon are 3.85 x 108 m apart and the mass of the moon is 7.36 x 1022 kg, a) calculate the force of gravity between them. b) find the gravitational field strength of the moon felt at the center of the earth. This is a huge amount of force! Why doesn’t the Moon get pulled into the Yeah, that's great, but how does it Earth??? get into orbit? The moon is in orbit around the Earth. Orbit: perpetual motion, usually elliptical, around a celestial body. Consider this: If you throw a baseball at different speeds it will travel forwards, but eventually fall to the ground. Newton's Cannon: Now imagine that you are standing on top of a very high mountain (ignore air friction) and you just happened to bring your trusty baseball cannon. The baseball is still bei Notice that at all times the baseball is being pulled towards the Earth by gravity. Because of this we say that objects in orbit are in free fall – always falling towards the center of the Earth, but never reaching it. Centripetal Force Recall that Fc is any force that keeps objects moving in a circle. In the case of a satellite or orbiting spaceship (or moon), gravity provides the centripetal force. F c= F g Orbital Speed F c= F g This relationship allows us to find the speed necessary for an object to achieve orbit: 2 mv G M m = 2 r r GM 2 v = r √ GM v= r Orbital Speed Ex 1. So just how fast does your cannonball have to go? Let's say the peak of your mountain is at an altitude of 3.0 km above Earth's surface. Orbital Speed Ex 2.The International Space Station orbits at an altitude of 350 km. What is its orbital speed? Orbital Acceleration Recall: Orbital velocity is can also be found using: d 2 πr v= = t T We can put our formula for v together with our formula for ac: Orbital Acceleration Ex 3. Find centripetal acceleration necessary to keep Neptune orbiting around the Sun every 164.97 Earth years. Two Orbital Accelerations? Recall: Orbital acceleration is also the acceleration due to gravity: GM g= 2 = ac r Combining our two formulas for ac: 2 G M 4π r ac = 2 = 2 r T Orbit Ex 4. How long does it take the ISS to orbit the earth (alt = 350 km)? Orbit Ex 5. Calculate the radius of the earth's orbit around the sun? Formula Recap F g= G m1 m2 r 2 F g= m g T= GM g= 2 = a c r v 4π r ac= = 2 r T 2 mv F c= r 2 √ 2 4π r GM √ 2 3 GM v= r d 2 πr v= = t T Try It: 1) Find the period of Pluto's orbit around the sun. 2) Find Mercury's speed as it orbits the sun. 3) Find strength of the Sun's gravitation field on Venus.