• # Question: how many times bigger is the sun compared to the earth

Asked by charliet to Hywel, Keith on 25 Jun 2010 in Categories: .
• Hywel Vaughan answered on 25 Jun 2010:

Good question charlie!
It really depends on how you take ‘times bigger’… if you are talking about volume, then the sun is approximately 1,300,000 of the planet Earth. If you were trying to fit the planet Earth into the sun though, then you would have lots of gaps, so you could only fit about 910,000!
The sun is about 93 million miles away, which is why it looks so small in the sky 😀

• Keith Brain answered on 25 Jun 2010:

It’s quite easily to measure the radius of the sun, once it’s distance is know, using a bit of trigonometry (a useful bit of maths) but I’ve just googled it and found it to be about 700,000km. You could measure the radius of the earth in lots of ways, like travelling around the equator to measure the circumference, then calculate the radius. I’m not up for that today ;), so I checked a favourite source and found that the radius was 6,400km. We could just calculate the volumes, then take the ratio, but we don’t have to do so much number crunching. We can just realise that because the volumes are proportional to the cube (power of 3) of the radius, the ratio of the volumes is equal to the cube of the ratio of the radii, or
(700,000/6400)^3. I seem to have misplaced my calculator 😉 so let’s say that 6400 is about 7000, which means that the ratio is about 100^3=10^6=1,000,000. My rounding was a bit severe, and you’ll have to trust my maths (unless you’re really really good at it) when I estimate that the error is about 10%x3 or about 30%, so I’d estimate the sun to be about 1,300,000 times bigger than the earth. These sorts of “back of the envelope” estimates can be quite handy for quickly checking whether something you might be interested in is reasonable.