# Why does the sun and gas planets in our solar system weigh more than the earth?

I was reading a space.com article about What Is The Sun Made Of? The article says that the sun is made of plasma and gas. If this is the case, how is it that the earth which is solid weighs less than the sun and the gas planets in our solar system?

For example, the boulder in the picture alone weighs 1.4 million pounds, to have 1.4 million pounds of gas, I assume that a lot of gas would be needed and it would need to occupy a lot of space.

• The sun is big,. Look hyperphysics.phy-astr.gsu.edu/hbase/Solar/sun.html – anna v Apr 20 at 10:46
• You assume that plasma and gas must be less dense than solid matter, but at the temperatures and pressures that exist in the core of the Sun, that is not necessarily true. – Solomon Slow Apr 20 at 11:12
• Also , while hydrogen and helium are by far the major components of the sun by mass and volume, they're not the only ones. There's roughly a Jupiter mass of iron in the Sun, for instance. – notovny Apr 20 at 15:16

Mass can be calculated by equation: $$m=V\rho\space\space\space\space \text{where V is volume and }\rho\space\text{is density of object}$$ Crude calculations show, that sun mass is: $$m_{sun}=4/3\pi(6.9334 \times 10^8m)^3\times 1410 kg/m^3\approx1.97\times10^{30}kg$$ Meanwhile the for the Earth: $$m_{earth}=4/3\pi(6371m)^3\times5510kg/m^3\approx5.97\times10^{15}kg$$ We see that although density of Earth is approximately 3.9 times as big as sun (by calculating ratio of densities for two bodies) the volume of the Sun is 1.29 x 10^15 as big.

Or to better see it: 1288890294000000 as big!)

The densities I have used are average densities available online. Let us take even less sophisticated example, and treat Sun as hydrogen atoms (which is 73,46% true), orbiting in Sun's volume at absurd STP conditions (Standard Temperature and Pressure) $$m_{sun}'=4/3\pi(6.9334 \times 10^8m)^3\times0.08988kg/m^3\approx1.25\times10^{26}kg>m_{earth}$$

$$Mass = Density . Volume$$ The Sun is not only more dense but also has more volume than those of the earth. Gas planet such as the Saturn is even less dense (average) than water on earth but has very high volume that makes it massive than the earth.