Science Blog: How do astronomers know the mass of Jupiter?

I (Rob) love science and I don't know that much about planetary sciences, and this is one question and answer that I've wondered about. EarthSky.org put together this great, easy-to-understand explanation.
I think you'll find the answer interesting:
How do astronomers know the mass of Jupiter?


Jupiter is the largest planet in our solar system and boasts of more than twice the mass (heaviness) of all the other solar system planets, dwarf planets, moons and asteroids combined. But how do astronomers even begin to know Jupiter’s mass? If a planet has an observable moon (or moons), astronomers can figure out that planet’s mass. Jupiter has four major moons – Io, Europa, Ganymede and Callisto – that’ve been watched and studied with great intensity, ever since Galileo first discovered them through an early telescope in the year 1610. Follow the links below to learn more about finding the mass of Jupiter, using its moons.

How can an orbiting moon reveal its planet’s mass? The more massive the planet, the more swiftly its moons revolve around it. Because Jupiter’s moons move in orbit around Jupiter so very swiftly, astronomers know right off the bat that Jupiter is an exceedingly massive world. Jupiter’s moons – Io, Europa, Ganymede and Callisto – lie more distant from Jupiter than our moon does from Earth. Yet these moons orbit Jupiter in far less time than our moon orbits Earth.  If Earth were as massive as Jupiter, our moon’s orbital period would be some 1.5 days, instead of its present 27.322 days!
     By orbital period, we mean the period of time that it takes the moon to go full circle in front of the constellations of the Zodiac. This time period is known as the sidereal month.



TRY TO UNDERSTAND THIS:
Computing Jupiter’s mass with Jupiter’s moon Callisto. Yes, we can compute Jupiter’s mass, relative to the mass of Earth, with Jupiter’s moon Callisto. All we need to know is Callisto’s mean distance from Jupiter, or semi-major axis, in Lunar Distances (LD), and Callisto’s orbital period relative to the moon’s orbital period (sidereal month).

 Left to right: Io, Europa, Ganymede and Callisto

One Lunar Distance (LD) = 384,400 kilometers (238,855 miles)
Moon’s orbital period = 27.322 days.
Callisto’s mean distance from Jupiter is 1,882,700 kilometers (1,169,856 miles) and its orbital period is 16.689 days. Converting Callisto’s mean distance and orbital period into lunar figures:
a = Callisto’s mean distance = 4.898 lunar
p = Callisto’s orbital period = 0.611 lunar
We plug these numbers into the equation below. Voila! We have Jupiter’s mass in Earth masses.
Mass of Jupiter = a³/p²
Mass of Jupiter = a x a x a/p x p
Mass of Jupiter = 4.898 x 4.898 x 4.898/0.611 x 0.611
Mass of Jupiter = 314.756 Earth-masses

SOURCE: http://earthsky.org/space/how-do-astronomers-know-the-mass-of-jupiter?utm_source=EarthSky+News&utm_campaign=36901a1e0d-EarthSky_News&utm_medium=email&utm_term=0_c643945d79-36901a1e0d-307928925#how