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Lagrangian point : net gravitational force due to Earth & Sun is zero.
Let the point be at a distance d km from center of Earth. Then the Lagrangian point is at a distance of (10⁸ - x) km from center of Sun.
Mass of Earth = Me
Mass of Sun = Ms
Gravitational force due to Earth on a body of mass m = G Me m /d²
Gravitational force due to Sun on mass m = G Ms m/(10⁸ - d)²
At L P : G Ms m/(10⁸ - d)² = G Me m/d²
=> Ms/Me = (10⁸ - d)²/d²
=> 3.24 * 10⁵ d² = 10¹⁶ - 2* 10⁸ d + d²
=> 3.24 * 10⁵ d² + 2 * 10⁸ d - 10¹⁶ = 0
=> 3.24 d² + 2000 d - 10¹¹ = 0
=> d = 175373.7 km approx
=> d = 0.00175 th of distance between Earth & Sun, from Earth.
Let the point be at a distance d km from center of Earth. Then the Lagrangian point is at a distance of (10⁸ - x) km from center of Sun.
Mass of Earth = Me
Mass of Sun = Ms
Gravitational force due to Earth on a body of mass m = G Me m /d²
Gravitational force due to Sun on mass m = G Ms m/(10⁸ - d)²
At L P : G Ms m/(10⁸ - d)² = G Me m/d²
=> Ms/Me = (10⁸ - d)²/d²
=> 3.24 * 10⁵ d² = 10¹⁶ - 2* 10⁸ d + d²
=> 3.24 * 10⁵ d² + 2 * 10⁸ d - 10¹⁶ = 0
=> 3.24 d² + 2000 d - 10¹¹ = 0
=> d = 175373.7 km approx
=> d = 0.00175 th of distance between Earth & Sun, from Earth.
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langranian point where the gravitional force is zero
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