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LAB #11

LAB #11. KEPLER’S 3 RD LAW. GOALS. TO BUILD A VIRTUAL SOLAR SYSTEM TO PLACE A SATELLITE IN GEOSYSCHRONOUS ORBIT TO TEST KEPLER’S 3 RD LAW:. T 2 a R 3. = mv 2. GMm. R. R 2. Kepler’s Third Law. T 2 a R 3. Fg is Fc. = 2 p R. v = C. T. T. GM. = 4 p 2 R 2. R. T 2.

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LAB #11

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  1. LAB #11 KEPLER’S 3RD LAW

  2. GOALS TO BUILD A VIRTUAL SOLAR SYSTEM TO PLACE A SATELLITE IN GEOSYSCHRONOUS ORBIT TO TEST KEPLER’S 3RD LAW: T2a R3

  3. = mv2 GMm R R2 Kepler’s Third Law T2a R3 Fg is Fc = 2pR v = C T T GM = 4p2R2 R T2 = 4p2R3 Units?? T2 GM

  4. Kepler’s Third Law Units?? = 4p2 T2 (R3) GM T2= (k) R3

  5. = 4p2R3 = GMT2 T2 Rs3 4p2 GM Geosynchronous Satellites Period (T) = 1 DAY = 86,400s Rs=? M = GMT2 Rs Rs = 4.23 x 107 m 3 4p2 ~300 Satellites

  6. NASA Satellite Website http://science.nasa.gov/Realtime/JTrack/3D/AppletFrame.html

  7. http://science.nasa.gov/Realtime/JTrack/3D/AppletFrame.html RGEO VGEO

  8. Kepler’s Third Law

  9. Geosynchronous Proof Screen Shot: Animation stopped at t ~ T

  10. PROCEDURE • Build your IP virtual solar system • Constants • G = 5 • M = 4 • T = 30 s • Position 5 satellites at radii given in data table • Calculate orbital speeds of each satellite • Start simulation. Time the orbital period of each satellite and record • Create a 6th satellite. Place in geosynchronous orbit • Check to see if this satellite is geosynchronous • Stop sim at one revolution, screen dump to lab report

  11. DATA TABLE G = 5 M = 4kg T = 30 s Constants: 1 2 3 4 5 ?

  12. GRAPH #1: T vs R ORBITAL PERIOD (s) ORBITAL RADIUS (m)

  13. GRAPH #2: T2 vs R3 SLOPE = 4p2 T2 (R3) (PERIOD)2 (s2) GM (RADIUS)3 (m3)

  14. LAB 11 WRITE-UP • ABSTRACT: • BACKGROUND • METHOD • IP PRINTOUT OF 3RD LAW • At time = T (Geosync at one revolution) • SHOW PROOF OF 3RD LAW EQUATION • DATA TABLE • GRAPHS • TRENDLINES • GRAPH ANALYSIS • CONCLUSION

  15. LAB #11 DATA ANALYSIS

  16. GRAPH #1: T vs R T a Rn n = 1,2,? ORBITAL PERIOD (s) ORBITAL RADIUS (m)

  17. GRAPH #2: T2 vs R3 4 p2 T2a R3 T 2= R3 GM Slope = ? 4 p2 G M (PERIOD)2 (s2) p = (slope) G M 4 (RADIUS)3 (m3)

  18. = mv2 GMm R R2 GM R Planetary Motion Fg is Fc m R Fg M V = (See IP sims)

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