Fomalhaut B and Newton's General Solution to Kepler's Third law

1. Fomalhaut B and Newton’s General Solution To Kepler’s Third Law Professor Madigan

2. Fomalhaut

3. Fomalhaut is only 25 light years distant, is the brightest star in Piscis Australis, The Southern Fish and is visible during the late summer Fomalhaut is twice the mass of the sun, over 17 times its luminosity and a productive life span of only 10% of the sun’s Results published in March of 2009 by Paul Kalas and Eugene Chiang of UC, Berkeley show that Fomalhaut B is the first exoplanet directly imaged and orbit around its host star confirmed by direct observation

4. Fomalhaut is only 25 light years distant; is the brightest star in Piscis Australis, The Southern Fish, and is visible during late summer Fomalhaut is twice the mass of the sun and over 17 times its luminosity Results published in March of 2009 by Paul Kalas and Eugene Chiang of UC, Berkeley show that Fomalhaut B is the first exoplanet directly imaged and orbit around its host star confirmed by direct observation

5. Fomalhaut is only 25 light years distant; is the brightest star in Piscis Australis, The Southern Fish, and is visible during late summer Fomalhaut is twice the mass of the sun, over 17 times its luminosity and a productive life span of only 10% of the sun’s Results published in March of 2009 by Paul Kalas and Eugene Chiang of UC, Berkeley show that Fomalhaut B is the first exoplanet directly imaged and orbit around its host star confirmed by direct observation

6. Fomalhaut is only 25 light years distant; is the brightest star in Piscis Australis, The Southern Fish, and is visible during late summer Fomalhaut is twice the mass of the sun, over 17 times its luminosity and a productive life span of only 10% of the sun’s A study published in March 2009 by Paul Kalas and Eugene Chiang of the University of California, Berkeley: Fomalhaut B is the first exoplanet directly imaged whose orbit around its host star is confirmed by direct observation

7. Fomalhaut is only 25 light years distant; is the brightest star in Piscis Australis, The Southern Fish, and is visible during late summer Fomalhaut is twice the mass of the sun, over 17 times its luminosity and a productive life span of only 10% of the sun’s A study published in March 2009 by Paul Kalas and Eugene Chiang of the University of California, Berkeley: Fomalhaut B is the first exoplanet directly imaged whose orbit around its host star is confirmed by direct observation

11. A quick review of Kepler’s laws 1. All orbits are elliptical. Why? Gravitation 2. Equal areas in equal times Why? Gravitation 3. The orbital period of any body in orbit about another varies as the 3/2 power of its semimajor axis Why? Gravitation These laws are universally applicable and are not restricted to any system

12. A quick review of Kepler’s laws 1. All orbits are elliptical Why? Gravitation 2. Equal areas in equal times Why? Gravitation 3. The orbital period of any body in orbit about another varies as the 3/2 power of its semimajor axis Why? Gravitation These laws are universally applicable and are not restricted to any system

22. Using the Hubble Space Telescope, Fomalhaut B was directly imaged and its orbit empirically measured over a 2 year period

24. We thus certify the veracity of all Kepler’s Laws and their inexorable link to gravity as the universal driving principal and the generality of Newton’s Universal Law of Gravitation

25. We choose Kepler’s 3rd law and, using Newton’s original derivation, provide an empirically demonstrable solution for Fomalhaut B’s orbital characteristics

26. 2 3 1 P A  2 3 P A

27. What is the significance of the “1” in this expression?

28. It represents the total mass of the system

29. 2 ( )3 Tot P M A  In terms of Solar Masses and Earth Years, we find:

30. 2 3 ( )TotP A M

31. 3 ( )TotP A M

32. Using the empirically determined distance of 115 AU from Fomalhaut to Fomalhaut B, we compute the period of Fomalhaut B to be: 3 (115) 2 1 1744 872 2 P x SolarMass P x yrs        

33. Deriving Newton’s General Form for Kepler’s Third Law, equating the force of gravity of the two bodies to the centripetal force of the planet in orbit around the center of mass, we find: 1 2 ( ) 2 2 2 ( ) 2 1 2 2 2 G Cent M M F G a M v F a M M M v G a a   

34. 22 2 1 2 2 2 1 2 2 2 1 3 2 3 2 1 2 1 2 4 4 4 4 M v a a G a a a p p M a G a p M G a p a GM p                

35. 3 2 1 2 4a GM p   Newton’s General Form Of Kepler’s 3rd Law

36. Solving this general equation for the period, we find: 2 3 10 1 10 7 1 4 2.751 10 sec 2.751 10 sec 872 3.156 10 sec a P x GM x yrs x yr      

Fomalhaut B and Newton's General Solution to Kepler's Third law

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