Planetary Density From Mass Radius Calculator

Bulk density is a body total mass divided by its total volume, and for an object treated as a sphere it follows from two measurable quantities and nothing else: rho equals M divided by V, with V equal to four thirds pi R cubed, which rearranges to rho equals 3M divided by 4 pi R cubed. No interior model is assumed anywhere in that chain, so the result is a genuine observable rather than an inference. The same two inputs fix two further surface quantities exactly. Surface gravity is g equals GM divided by R squared, which can be rewritten as four thirds pi G rho R, and escape speed is v equals the square root of 2GM divided by R, equivalently R times the square root of eight thirds pi G rho. Expressed in Earth units the constants disappear altogether: the density ratio is the mass ratio divided by the cube of the radius ratio, the gravity ratio is the mass ratio divided by the square of the radius ratio, and the escape speed ratio is the square root of the mass ratio divided by the radius ratio. Because radius enters cubed, a one percent radius error moves the density by three percent while a one percent mass error moves it by only one percent, which is why radius precision dominates the error budget for transiting exoplanets. The number that comes out is the first compositional diagnostic available for any planet. Using NASA fact sheet values in kilograms per cubic metre, Earth is the densest planet in the Solar System at 5514, followed by Mercury at 5429, Venus at 5243, Mars at 3933, the Moon at 3344, Neptune at 1638, Jupiter at 1326, Uranus at 1270 and Saturn at 687, which is less dense than liquid water. Values above roughly 5000 imply a large iron core, 3000 to 5000 indicate a silicate body, 2000 to 3000 point to a rock and ice mixture, and anything near or below about 2000 requires hydrogen and helium or a large ice fraction. Two caveats matter. Bulk density is not material density, because self compression under a planet own weight raises it, and the uncompressed mean density of Earth is estimated near 4000 against a measured 5514. And the radius used must be the volumetric mean radius rather than the equatorial one: substituting the Saturn equatorial radius of 60268 kilometres for its volumetric mean of 58232 would understate its density by about ten percent.

Isaac Newton set the problem in the Principia of 1687, arguing from the density of surface rock and of rock found deeper in mines that Earth was probably five or six times denser than water, a guess that landed within a few percent of the modern 5.51. He also compared the densities of the Sun, Jupiter, Saturn and Earth using the orbits of their satellites, though only as ratios, because fixing the absolute scale required a constant nobody had yet measured. Turning the guess into a measurement took another century. Pierre Bouguer attempted it during the French geodetic expedition to Peru, measuring the deflection of a plumb line near Chimborazo in 1738, but the deflection proved far smaller than expected and the result was crude. The Royal Society then funded the Schiehallion experiment of 1774, in which Nevil Maskelyne measured the deflection of the vertical on either side of a Scottish mountain; Charles Hutton reduced the survey in 1778 to a mean Earth density near 4500 kilograms per cubic metre, inventing the contour line along the way to handle the terrain data. Henry Cavendish closed the question in 1798 using a torsion balance built to a design by the late John Michell, reporting a mean density 5.48 times that of water, within about one percent of the accepted value. Cavendish framed his result as the density of the Earth; the gravitational constant G was written in that form only decades later. Extending the method outward depended on getting masses. A planet with a moon can be weighed through the orbit of that moon, so mean densities for Jupiter and Saturn were available long before anything was known about their interiors, but Mercury and Venus have no satellites and their densities stayed uncertain until spacecraft flew close enough to be deflected measurably. Radio tracking of Mariner 10 during its three Mercury encounters in 1974 and 1975, and of MESSENGER in orbit from 2011, pinned down the gravitational parameter to many digits while radar ranging and imaging pinned down the radius. The unexpectedly high density that emerged is the principal evidence that Mercury carries an iron core filling roughly eighty percent of its radius. The technique reached other stars when HD 209458 b was caught in transit in 1999: the transit depth gave the radius, the radial velocity amplitude gave the mass, and the resulting density of roughly a third that of water was the first ever measured for a planet outside the Solar System and far too low for rock. Kepler mission statistics later exposed a scarcity of planets between about 1.5 and 2.0 Earth radii, reported by Benjamin Fulton and colleagues in 2017, now read as the density divide between rocky super-Earths and volatile-rich sub-Neptunes.