A student asked me today, how they come up with the masses of the planets
listed in the front of our text.
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Simple answer: Kepler's "Laws," in particular the third one:
let a = orbital radius (formally, semi-major axis, measured in astronomical
units (mean Earth-Sun distance)
let T = orbital period measured in years.
Observe satellite orbits, assume that the satellite mass is small compared
to the primary, and the ratio a^3/T^2 turns out to the the mass of the
planet in solar mass units. Use other units (like SI) and you need to pop
in a factor of 4*pi*G, if you can't neglect the mass of the satellite,
you'll get the total mass of the system.
Note, that you'll need the distance to the planet to obtain the orbit size
from its angular measure on the sky, but the distance scale in AU is
inherent in the Copernican model.
While this relation was determined empirically, it can be derived as a
necessary consequence of Newtonian gravitation, as can Kepler's first and
second "laws."
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"Whatever one's religion or lack of it, it is an
irresistible metaphor to speak of the final laws
of nature in terms of the mind of God."
- Steven Weinberg
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George Spagna
Department of Physics
Randolph-Macon College
P.O. Box 5005
Ashland, VA 23005-5505
phone: (804) 752-7344 FAX (804) 752-4724
e-mail: gspagna@rmc.edu http://www.rmc.edu/~gspagna/