How do scientist measure the mass of the planets?
A planet’s defining physical characteristic is that it is massive enough for the force of its own gravity to dominate over the electromagnetic forces binding its physical structure, leading to a state of hydrostatic equilibrium. This effectively means that all planets are spherical or spheroidal. Up to a certain mass, an object can be irregular in shape, but beyond that point, which varies depending on the chemical makeup of the object, gravity begins to pull an object towards its own centre of mass until the object collapses into a sphere. Mass is also the prime attribute by which planets are distinguished from stars. The upper mass limit for planethood is roughly 13 times Jupiter’s mass, beyond which it achieves conditions suitable for nuclear fusion. Other than the Sun, no objects of such mass exist in our Solar System; however a number of extrasolar planets lie at that threshold. The Extrasolar Planets Encyclopedia lists several planets that are close to this limit: HD 38529c, AB P
The largest mass in the Solar System is the Sun, and the motion of planets in elliptical orbits by Kepler’s laws is most of the motion of the planets. But there are small deviations from these motions, due to the gravitational attraction between planets. By making accurate measurements of the positions of planets, the relative amounts of these “perturbations” can be calculcated, and the relative masses of the planets (i.e. Earth is 1/318 of the mass of Jupiter). To calculate the mass absolutely (as opposed to relatively) you have to know two other things: the distance to the planets, and the value of Newton’s gravitational constant, G. The distance to the planets is best measured by radar, or by laser ranging. The gravitational constant is measured in the laboratory. As mentioned elswhere, if you know Newton’s constant, then the mass of planets with moons can be determined by measuring the orbital periods of the moons.
A combination of Kepler’s Laws and the physics behind it from Newtons laws gives us: P^2 = [4 pi^2 /GM] a^3 where M is the mass of the star or planet around which planet or moons orbits (this is a simplification and assumes that a planet is much less massive than the star; likewise for the relative masses of moons and planets) Since we can observe the distance a moon is from a planet and how long it takes to orbit the planet, the only unknown is the mass of the planet. This method only works for planets with moons.
