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'Lagrangian Point’ is a location in space between the Earth and the Sun; where the net gravitational force on any body due to both the Earth and the Sun is zero. Calculate the distance of this point from Earth. The distance between Earth and Sun is approximately 108 km, and the mass of the Sun is 3.24 × 105 times the mass of the Earth.

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Given; distance between Earth and Sun,
r = 108 km = 1011 m
Mass of Sun, Ms = 3.24 × 105Me
The distance of Lagrangian Point from the Earth x =?
A Lagrangian point P,

or x (568.8 + 1) = 1011
or x × 569.8 = 1011
∴ x = \(\frac{10^{11}}{569.8}=\frac{1000}{569.8} \times 10^{8}\)
or x = 1.75 × 108 m

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