# Answer to Question #21549 in Astronomy | Astrophysics for Derek Baker

Question #21549

At what distance from the earth is the gravitational pull of the sun equal to the gravitational pull of the earth?

Expert's answer

The condition for the gravitationalpull of the sun to be equal to the Earth's one is

F1=F2

GmM1/(r1^2)= GmM2/(r2^2)

where r1 is distance to Sun, M1 is mass of the Sun, r2 is distance to Earth and

M2 mass of the Earth.

From this we can find, what relation between distances toEarth and to the Sun should be

r1/r2 = sqrt(M1/M2)

knowing also, that their difference should give distancebetween Sun and Earth

r1^2-r2^2 = R^2

we can find r1:

r2= r1/sqrt(M1/M2)

r1^2+r1^2/(M1/M2) = R^2

r1^2 = R^2/(1+M1/M2)

r1 = R/sqrt(1+M1/M2)

r1 = 149*10^9 m from Earth

F1=F2

GmM1/(r1^2)= GmM2/(r2^2)

where r1 is distance to Sun, M1 is mass of the Sun, r2 is distance to Earth and

M2 mass of the Earth.

From this we can find, what relation between distances toEarth and to the Sun should be

r1/r2 = sqrt(M1/M2)

knowing also, that their difference should give distancebetween Sun and Earth

r1^2-r2^2 = R^2

we can find r1:

r2= r1/sqrt(M1/M2)

r1^2+r1^2/(M1/M2) = R^2

r1^2 = R^2/(1+M1/M2)

r1 = R/sqrt(1+M1/M2)

r1 = 149*10^9 m from Earth

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