ehrenfest said:OK here are the details:
38.5654 = (T^2/(4 pi^2) * G * (Ms))^(1/3)/(1.4*10^11)
where T is the period in seconds, Ms = 1.991*10^31 and G = 6.674 * 10^(-11)
what am I doing wrong?
Dick said:You beat me! I just figured that out. But, ehrenfest, for solar orbits if you work in AU and years, the constant proportionality k in R^3=k*T^2, is one.
Dick said:Funny, my training is in cosmology, so I know it's like to ten the fifty some proton masses. And fifty plus what I forget. Good job.
ehrenfest said:30 minutes of frustration...
Kepler's Third Law, also known as the "law of harmonies," states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
Halley's Comet is used as a case study to test the accuracy of Kepler's Third Law. This is because it has a highly elliptical orbit and can be observed over multiple orbits, making it a good candidate for studying orbital mechanics.
By using Halley's Comet to test Kepler's Third Law, scientists can refine and improve our understanding of orbital mechanics and the laws governing the motion of celestial bodies.
Astronomers use a combination of ground-based observations and spacecraft data to track the position and movement of Halley's Comet. They measure its orbital period and semi-major axis, and then compare these values to what is predicted by Kepler's Third Law.
Scientists have been able to confirm the accuracy of Kepler's Third Law through their observations of Halley's Comet. They have also been able to use this information to make more precise calculations and predictions about the motion of other celestial bodies in our solar system.