Density is defined as the property of a substance that determines the mass of a given volume of the same substance. For example, the density of liquid water is 1 gram per cubic centimetre (1 g/cm^{3}). This means that a cube of water measuring 1cm x 1cm x 1cm will have a mass of 1 gram. A cubic metre of water (1m x 1m x 1m) (equal to 1 million cubic centimetres) will subsequently have a mass of 1 million grams or 1000 kilograms (1 metric ton).
The density of any substance can be calculated by dividing its mass by its volume:
DENSITY = MASS ÷ VOLUME
The mass of any major Solar System body, such as a planet, dwarf planet, asteroid, etc. can be looked up in any basic astronomy book or on the Internet:
For this example, we will use the planet Saturn for a reason that will become very apparent soon:
MASS_{Saturn} = 5.7 x 10^{26} kilograms
The volume of Saturn can be calculated using its equatorial and polar radii. Some Solar System bodies are not perfectly spherical but oblate (elliptical) because they spin so fast that they bulge at their equators. Saturn is the most oblate planet in the the Solar System, so the following equation is certainly required to calculate its volume:
VOLUME_{Saturn} = (4/3)pR^{2}_{eq} R_{polar}
The equatorial radius of Saturn can be looked up in any basic astronomy book or on the Internet:
R_{eq} = 60,270 kilometres
The polar radius of Saturn can be determined by using its equatorial radius and its oblateness:
R_{polar} = R_{eq} ( 1 - Saturn's Oblateness )
However, since we can express the polar radius of Saturn as a function of the equatorial radius the volume equation can be rewritten as:
VOLUME_{Saturn} = (4/3)pR^{3}_{eq }( 1 - Saturn's Oblateness )
The oblateness (flattening) of Saturn can also be easily looked up or determined from your images:
Saturn's oblateness = 0.09796
Therefore, the volume of Saturn is:
VOLUME_{Saturn} = 8.27 x 10^{14} km^{3}
Finally, the density of Saturn can be determined:
DENSITY_{Saturn} = MASS_{Saturn} / VOLUME_{Saturn}
DENSITY_{Saturn} = 6.89 x 10^{11} kg / km^{3}
If you expressed this value in units of grams per cubic centimetre (g / cm^{3}):
DENSITY_{Saturn} = 0.689 g / cm^{3}
This number essentially means that if you took a cubic centimetre of the planet Saturn (a 1cm x 1cm x 1cm cube) that cube's mass would be only 0.689 grams (very light).
The density of pure liquid water is:
DENSITY_{Water} = 1 g / cm^{3}
The density of Saturn is LESS than that of water. A substance of lower density will float in a substance of higher density. Ice cubes (solid water) float in liquid water because the density of ice is 0.9 g / cm^{3}. Therefore, if we could place Saturn in a tub of water large enough to hold it, Saturn would FLOAT, showing about 30 percent of its volume above the water! Amazing! The table below illustrates the densities of the other worlds in our Solar System. Note that Saturn is the only floating body of the bunch!
BODY | MASS (kg) | EQ RADIUS (km) | OBLATENESS | VOLUME (km^{3}) | DENSITY (g / cm^{3})* |
SUN | 1.9891 x 10^{30} | 696,000 | 0.000009 |
1.41 x 10^{18} |
1.410 |
MERCURY | 3.3 x 10^{23} | 2,439.7 | 0 | 6.08 x 10^{10} | 5.425 |
VENUS | 4.8685 x 10^{24} | 6,051.8 | 0 | 9.28 x 10^{11} | 5.244 |
EARTH | 5.9736 x 10^{24} | 6,378.1 | 0.0033528 | 1.08 x 10^{12} | 5.514 |
OUR MOON |
7.3477 x 10^{22} |
1,738.14 | 0.00125 | 2.20 x 10^{10} | 3.345 |
MARS | 6.4185 x 10^{23} | 3,396.2 | 0.00589 | 1.63 x 10^{11} | 3.935 |
CERES |
9.43 x 10^{20} |
487.3 | 0.0669 | 4.52 x 10^{8} | 2.085 |
JUPITER | 1.8986 x 10^{27} | 71,492 | 0.06487 | 1.43 x 10^{15} | 1.326 |
SATURN |
5.7 x 10^{26} |
6.027 x 10^{4} | 0.09796 | 8.27 x 10^{14} | 0.689 |
URANUS | 8.681 x 10^{26} | 25,559 | 0.0229 | 6.83 x 10^{13} | 1.270 |
NEPTUNE |
1.0243 x 10^{26} |
24,764 | 0.0171 | 6.25 x 10^{13} | 1.638 |
PLUTO | 1.305 x 10^{22} | 1,153 | 0 | 6.42 x 10^{9} | 2.033 |
ERIS | 1.67 x 10^{22} | 1,170? | 0? | 6.71 x 10^{9}? | 2.489? |
* The densities
published here represent the average densities only. The densities of Solar
System bodies are certainly not uniform throughout.
Planet Density was Last Updated on December 07, 2010 |