Re: Mass of Jupiter

[Rondo JEFFERY <RJEFFERY@WEBER.EDU>]

  This post by Paul Johnson (and a few others that came before it) continues to make the same mistake I mark students off for on similar questions on homework in astronomy.  The mass of the planet can NOT be determined from information about the planet's orbit about the sun.  The only way to determine the mass of the planet is by looking at the orbit(s) of its moon(s).  The formua Paul gives (below) was first derived by Newton, and is often referred to as Newton's version of Kepler's third law.
  The mass that is determined is the sum of the masses of the two bodies.  To get the individual masses you need to know the ratio of masses, as you find from locating the center of mass.  In the case of the sun-planet orbit, the sum of M-sun and M-planet is so dominated by the sun that you would need accuracy to better than one part in 10,000 to get Jupiter's mass to even 10%, since the sun's mass is 1000 times the mass of Jupiter.  On the other hand, by knowing the orbital parameters (size and period of orbit) of at least one moon of the planet, the mass of planet plus moon comes out.  Only if the moon's mass is a significant fraction of the planet's mass, as in the case of the earth's moon (1/81.3 of earth's mass), do you then need to take the moon's mass into consideration.
  Please, let's stop saying that "Kepler's third law" lets us determine the mass of the planets by the size and period of the planets' orbits around the sun. It only comes from Newton's version of K3 (N/K3, so to speak).
  There are two planets in the solar system that have no moons, and so this can't be used.  One of those (Venus) has had artificial satellites placed around it, so you use that.  Mercury's mass is calculated from the deflection of spacecraft that have flown by, or the deflection of comets before space probes.  It is only the last two or three decades that the mass of Pluto has been known, since its moon was only recently discovered.
  One more thing, N/K3 lets us determine the masses of double star systems.  It those cases the masses are more similar, and so you have to take the center of mass into consideration to get the ratio.  That gives you two equations in two unknowns - the sum and the ratio of the masses.
Rondo Jeffery
Weber State University
Ogden, UT 84408-2508

> > > pojhome@SWBELL.NET 01/29/01 01:51PM >>>
> The mass of any satellite orbiting a central object (M) is proportional to
> the cube of the orbital radius (r) and is inversely proportional to the
> square of the orbital period (T). The relationship is
>        M = 4(pi)*2 r*3/G T*2
> where G is the universal gravitational constant.
> This is derived by equating the centripetal and gravitational forces acting
> on the satellite
> So the mass of any planet can be calculated from measured values of its
> average distance from the sun and its orbital period.
>
> Paul O. Johnson
> Collin County College

----- Original Message -----
From: "Ron Curtin" <curtin@CCDS.CHARLOTTE.NC.US>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, January 29, 2001 2:10 PM
Subject: Mass of Jupiter


> A student asked me today, how they come up with the masses of the planets
> listed in the front of our text.  I couldn't answer him.  Can anyone out
> there?  Thanks.
>
>
> --------------
> Ron Curtin
> Physics Instructor
> Charlotte Country Day School
> Charlotte, NC  28226
> (704) 943-4690 Ext. 6159