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How to Calculate the Density of a Planet

Calculating the density of a planet requires knowledge of both the planet's mass as well as its size because density represents the ratio between and object's mass and volume (see reference 1). Astronomers measure the masses of planets indirectly by observing their gravitational effects on nearby objects, such as moons in orbit around the planets (see reference 2). Astronomers measure the sizes of planets directly by the phenomenon of stellar parallax (see reference 3). Unfortunately, many of these measurements require equipment beyond the reach of amateur astronomers, but professional astronomers have published their findings and made their measurements of planetary masses and sizes available to everyone.

Things You'll Need

Scientific calculator

Instructions

- 1
  Find the mass and diameter of the planet for which the density calculation will be performed. Numerous websites provide this information, such as the Windows to the Universe website given in the Resources section. As an example, astronomers have measured the mass and diameter of Neptune as 17 Earth masses and 49,528 km, respectively.
- 2
  Convert the mass of the planet to grams by multiplying by 5.98 x 10^27. This represents the mass of the earth in grams (see reference 4). Thus, if Neptune possesses a mass equal to 17 earth masses, then it weighs 17 x (5.98 x 10^27 g) = 1.02 x 10^29 g.
- 3
  Convert the planet's diameter to centimeters by multiplying the mass in kilometers by 100,000. In this case, 49,528 km * 100,000 = 4.95 x 10^9 cm.
- 4
  Calculate the planet's volume by first dividing the diameter by 2 to obtain the radius, r. In this case, r = 4.95 x 10^9 / 2 = 2.48 x 10^9 cm. Then use the equation for the volume of a sphere, V = 4/3 * pi * r^3, to calculate the planet's volume. For the example of Neptune, V = 4/3 * 3.14 * (2.48 x 10^9)^3 = 6.39 x 10^28 cm^3.
- 5
  Calculate the planet's density by dividing the mass from step 2 by the volume from step 4. Continuing the previous example, d = 1.02 x 10^29 / 6.39 x 10^28 = 1.59 g/cm^3.

Astronomy