How far from the earth must a body be along line toward the sun so that the gravitational pull of the sun balances that of the earth? Earth-to-sun distance is 9.3x10^7 mi; mass of the sun is 3.24x10^5 times the mass of earth.

Question

paki · Answer

is this a math question...? please post it in the relevant section, so that it can be guided/answered properly...

anonymous · Answer

Say $x$ is the distance between the body and the sun, so $9.3\times10^7-x$ is the distance between the body and Earth.
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You want to find $x$ such that
$$\large F_{\text{sun}}=G\frac{(3.24\times10^5m)k}{x^2}$$
is equivalent to
$$\large F_{\text{earth}}=G\frac{mk}{(9.3\times10^7-x)^2}$$
where $m$ is the mass of the Earth and $k$ is the mass of the body.

It's been a while since I've worked out a physics problem like this, but I think you'll have to convert your units (miles to meters). The masses are proportional to each other so units won't matter there.

Also note that you want to find the value of $9.3\times10^7-x$, as that's the distance between the body and Earth.