At 02:05 PM 12/19/02 +0000, Alberto Monteiro wrote:
Erik Reuter wrote: > >Orbits are more complicated than simply boosting in the direction you >want to go. > Yep. But I think what he wants is a simpler solution, ignoring the gravitational forces. Using a Hohmann transfer orbit to go from 100 AU to 2 AU would require such a long time that when the ship arrived, it would be populated by the grandchildren of the original crew.
The applicable formula in this case is Newton's version of Kepler's Third Law:
P^2 = (M+m)*a^3,
where P is the period in years, M and m are the masses of the two bodies in solar masses (except when describing a binary star system, m is usually negligible), and a is the semi-major axis of the orbit in AU.
Just doing the calculations in my head� gives somewhere in the vicinity of 150 years if the star in the system is the same mass as our Sun. If the planet at 2AU is supposed to get the same total amount of radiation as Earth, that would imply a hotter, brighter, more massive star, whose greater gravity would cut the time down to about 125 years. (The latter scenario does not take into account the increased ultraviolet radiation the planet would receive from its hotter star in comparison to what Earth receives from the Sun, which would not affect the orbits, but might call into question its habitability . . . )
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�FWIW, my estimate of the star's mass was 1.50 solar masses, and Alberto's program gives 1.49 solar masses . . .
-- Ronn! :)
Ronn Blankenship
Instructor of Astronomy/Planetary Science
University of Montevallo
Montevallo, AL
Disclaimer: Unless specifically stated otherwise, any opinions contained herein are the personal opinions of the author and do not represent the official position of the University of Montevallo.
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