Unformatted text preview: UCSD Physics 10 Rockets, Orbits, and Universal Gravitation UCSD Physics 10 Some Questions We'll Address Today What makes a rocket go? How can a rocket work in outer space? How do things get into orbit? What's special about geosynchronous orbit? How does the force of gravity depend on mass and separation? Spring 2008 2 UCSD Physics 10 What does a rocket push against? Cars push on the road Boats push on the water Propellers push against air Jet engines push air through turbines, heat it, and push against the hot exhaust (air) What can you push against in space? Spring 2008 3 UCSD Physics 10 Momentum is conserved! Before
M m v = 0 so p = 0 After
1 2 after 1 2 v M m v p
1 = Mv + mv = 0 as well so
2 Spring 2008 v =  (m/M) v 4 UCSD Physics 10 A Rocket Engine: The Principle Burn Fuel to get hot gas hot = thermally fast more momentum Shoot the gas out the tail end Exploit momentum conservation to accelerate rocket Spring 2008 5 UCSD Physics 10 A Rocket Engine: The Principle Burn Fuel to get hot gas Shoot the gas out the tail end Exploit momentum conservation to accelerate rocket Spring 2008 6 UCSD Physics 10 Rockets push against the inertia of the ejected gas! Imagine standing on a sled throwing bricks. Conservation of momentum, baby! Each brick carries away momentum, adding to your own momentum Can eventually get going faster than you can throw bricks! In this case, a stationary observer views your thrown bricks as also traveling forward a bit, but not as fast as you are Spring 2008 7 UCSD Physics 10 What counts? The "figure of merit" for propellant is the momentum it carries off, mv. It works best to get the propulsion moving as fast as possible before releasing it Converting fuel to a hot gas gives the atoms speeds of around 6000 km/h! Rockets often in stages: gets rid of "dead mass" same momentum kick from propellant has greater impact on velocity of rocket if the rocket's mass is reduced
Spring 2008 8 UCSD Physics 10 Spray Paint Example Imagine you were stranded outside the space shuttle and needed to get back, and had only a can of spray paint. Are you better off throwing the can, or spraying out the contents? Why? Note: Spray paint particles (and especially the gas propellant particles) leave the nozzle at 100300 m/s (several hundred miles per hour) Spring 2008 9 UCSD Physics 10 Going into orbit Recall we approximated gravity as giving a const. acceleration at the Earth's surface It quickly reduces as we move away from the sphere of the earth Imagine launching a succession of rockets upwards, at increasing speeds The first few would fall back to Earth, but eventually one would escape the Earth's gravitational pull and would break free Escape velocity from the surface is 11.2 km/s
Spring 2008 10 UCSD Physics 10 Going into orbit, cont. Now launch sideways from a mountaintop If you achieve a speed v such that v /r = g, the Spring 2008 11 UCSD Physics 10 4 km/s: Not Fast Enough.... Spring 2008 12 UCSD Physics 10 6 km/s: Almost Fast Enough....but not quite! Spring 2008 13 UCSD Physics 10 8 km/s: Not Too Fast, Nor Too Slow....Just Right Spring 2008 14 UCSD Physics 10 10 km/s: Faster Than Needed to Achieve Orbit Spring 2008 15 UCSD Physics 10 Newton's Law of Universal Gravitation
The Gravitational Force between two masses is proportional to each of the masses, and inversely proportional to the square of their separation. F = GM1M2/r2 Newton's Law of Universal Gravitation a1 = F/M1 = GM2/r2 acceleration of mass #1 due to mass #2
(remember when we said grav. force was proportional to mass?) G = 6.674 1011 m3/(kgs2) Earth: M = 5.976 1024 kg; r = 6,378,000 m a = 9.80 m/s2
Spring 2008 16 UCSD Physics 10 What up, G? G is a constant we have to shove into the relationship to match observation Determines the strength of gravity, if you will Best measurement of G to date is 0.001% accurate Large spheres attract small masses inside canister, and deflection is accurately measured Spring 2008 17 UCSD Physics 10 Newton's classic picture of orbits Lowearthorbit takes 88 minutes to come around full circle Geosynchronous satellites take 24 hours The moon takes a month Can figure out circular orbit velocity by setting Fgravity = Fcentripetal, or:
GMm/r2 = mv2/r, reducing to v2 = GM/r M is mass of large body, r is the radius of the orbit
Spring 2008 18 UCSD Physics 10 Space Shuttle Orbit Example of LEO, Low Earth Orbit ~200 km altitude above surface Period of ~90 minutes, v = 7,800 m/s Decays fairly rapidly due to drag from small residual gases in upper atmosphere Not a good longterm parking option! Spring 2008 19 UCSD Physics 10 Other orbits MEO (MidEarth Orbits) Communications satellites GPS nodes halfday orbit 20,000 km altitude, v = 3,900 m/s Elliptical & Polar orbits Spy satellites Scientific sunsynchronous satellites
GPS Constellation
Spring 2008 20 UCSD Physics 10 Geosynchronous Orbit Altitude chosen so that period of orbit = 24 hrs Altitude = 36,000 km (~ 6 R), v = 3,000 m/s Stays above the same spot on the Earth! Only equatorial orbits work That's the direction of earth rotation Scarce resource Cluttered! 2,200 in orbit Spring 2008 21 UCSD Physics 10 Rotating Space Stations Simulate Gravity Just like spinning drum in amusement park, create gravity in space via rotation Where is the "floor"? Where would you still feel weightless? Note the windows on the face of the wheel From 2001: A Space Odyssey rotates like bicycle tire Spring 2008 22 UCSD Physics 10 Summary Rockets work through the conservation of momentum "recoil" the exhaust gas does not "push" on anything F = GMm/r for the gravitational interaction Spring 2008 23 UCSD Physics 10 Assignments HW for 2/17: 7.E.42, 7.P.9; 6.R.16, 6.R.19, 6.R.22, 6.R.23, 6.E.8, 6.E.12, 6.E.43, 6.P.6, 6.P.12, 8.R.29, 8.E.47, 8.P.9, plus additional questions accessed through website Spring 2008 24 ...
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 Fall '10
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 Physics, Orbits, Work, General Relativity

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