How Do We Calculate the Weight of Celestial Bodies in the Solar System?

[Blahness]

Figuring out the weight of celestial bodies in the solar system, please.

Algebra-representations also requested.

Oh, politeness. Um... please?

 

[LURCH]

This is mostly done by just observing the rate at which things accelerate when approaching a planet. This tells us the gravitational "pull" of the planet, which is a direct function of its mass.

 

[Creator]

More specifically, monitor the orbital period, T, and orbital radius, d, of a small moon or satellite, around a planet of mass, M, and use Kepler's 3rd Law:
M = (4pi^2/G)(d^3/T^2)
(Caveat: the orbital mass must be relatively negligible campared to the gravitating body).
It is universal, so you can also find the sun's mass using a planet's orbit.
Launch a satellite around Earth and use the same eqn. to get the Earth's mass. The ratio of orbital radius cubed to orbital period squared will be approx. constant for any satellite about earth.
If the orbit is eccentric, the same eqn. applies if you simply substitute the semi-major axis for radius d.
This is rather simplistic and there are other methods but this is enough to get you started.
Creator

 

[tony873004]

And once you know the mass, and you can observe the size, then you can compute the density, and you can make some good guesses as to the composition.

 

[geoorge]

Celestial mechanics

Newton's universal law of gravitation is:

F :: Force between two bodies. (in Newtons)

M :: Mass of larger body

m :: Mass of smaller body

r :: Distance beween centers of mass of two bodies

G :: 6.674 e-11 N*m2*kg -2


F =
GMm / r2

Kepler's three laws of planetary motion can be derived from Newton's law of gravitation and his laws of motion.

Kepler's third law gives:

T :: Period (in sec)

r :: Distance (between centers)

C :: (Kepler's constant; G * mass of body being orbited)

T2 = C*r3.