What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction? Do you need to know the lunar distance to solve this problem? b. How many thousand kilograms of hydrogen would be needed to provide the positive charge calculated in part
Answers
To neutralize their gravity, the force of repulsion must equal the force of attraction.
Universal Gravitational force = (G * m1 * m2) ÷ d^2
G = 6.67 * 10^-11
m1 = mass of earth = 5.98 * 10^24 kg
m2 = mass of moon = 7.36 * 10^22 kg
d = distance from earth to moon
Force caused by charges = (k * q1 * q2) ÷ d^2
k = 9 * 10^9
q1 = charge on earth
q2 = charge on moon
d = distance from earth to moon
Force caused by charges = Universal Gravitational force
(k * q1 * q2) ÷ d^2 = (G * m1 * m2) ÷ d^2
Multiply both sides by d^2
(k * q1 * q2) = (G * m1 * m2)
Divide both sides by k
q1 * q2 = (G * m1 * m2) ÷ k
The charges are equal, so q1 * q2 = q^2
q^2 = (G * m1 * m2) ÷ k
q = √ (G * m1 * m2 ÷ k)
q = √ (6.67 * 10^-11 * 5.98 * 10^24 * 7.36 * 10^22 ÷ 9 * 10^9)
q ≈ 3.26 * 10^27 Coulombs
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