In space there exists points in which the combined gravitational effects of larg

Question

In space there exists points in which the combined gravitational effects of large bodies, such as the Earth and the Sun cancel out. These are known as Lagrange points. Ideally if you were to place an object of mass 'm' at one of those points, the object would not have any gravitational attraction to these large bodies. In a simplistic case assume the Sun and the Earth are the only objects in space Determine the point in between the Earth and the Sun where the gravitational attraction is zero Express this as either the distance from the Earth to the object or from the Sun to the object Distance from Sun to Earth (d_sE = 149.6 times 10^9m) Mass of the Sun 1.989 x 10 kg) Mass of the Earth (5.972 times 10^24 kg) Distance from Sun to point (d_sp 149.34 times 10^9 m) Distance from Earth to point (d_Ep 258.77 times 10^6 m)

Explanation / Answer

let the point is x m from earth

GMearth/x^2=GMsun/(149.6*10^9-x)^2

Mearth/Msun=(x/(149.6*10^(-9)-x)^2

taking square root both side

1.732*10^(-3)=x/(149.6*10^(9-x)

we get x=2.587*10^9 m =258.7*10^6 m

so from sun it is

(146.6*10^9-x)=149.34*10^9 m

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