Give a order of magnitude. Estimate how many times the Earth fits into the Sun. Radius of the Sun: 6.96x10^8m. Radius of the Earth: 6.55x10^6m.

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Give a order of magnitude. Estimate how many times the Earth fits into the Sun. Radius of the Sun: 6.96x10^8m. Radius of the Earth: 6.55x10^6m.

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## Answers (2)

Order of magnitude means that all that really matters is the powers of 10, it's of course not going to be as accurate but the point is it makes it easy enough to do in your head.

Just take the radius of the sun to be 10^8m and the earths as 10^6m

So, the hard part is figuring out how to use these. Well, if you want to know how many Earths fit in the sun it should immediatly make you think to divide the volume of the sun by the volume of the Earth right?

So just find their volumes and divide. The volume of a sphere is:

(4/3)*pi*r^3

Since we are doing an order of magnitude calculation you can take (4/3) as 1, and also since "pi" is about 3.14 you can just take this is 1 too. So then our equation of a sphere is just:

r^3

So the order of magnitude estimate of their volumes are:

Sun: (10^8)^3 = 10^24

Earth: (10^6)^3 = 10^18

(I left off units to make it easier to read, but they should obviously be m^3)

Then as said above, divide the Suns volume by the Earths:

10^24 / 10^18

(if you don't know how to quickly do this, note that 1/10^n = 10^-n so the fraction above is the same things as (10^24)*(10^-18) and then you just add the powers 24-18=6)

So the answer comes out to:

an order of magnitude of about 10^6 Earths can fit in the Sun.

Determine the volume of each using the volume relationship V = pie r^3. Then divide the volume of the earth into the volume of the sun.