Verified Answer :
as i recall, gravity is relative to the square of the distance.
so if the distance is tripled, then the gravitational attraction would be reduced by 3^2 or 1/9.
so F1 = F0/9
if the satellite is 2R from the center, and is moved to 4R (doubled would be 3R, tripled is 4R) then the distance is twice, and gravity would be 2^2 or 1/4.
The gravitational force after the separation between the two particles is tripled will be \(\boxed{\frac{{{f_0}}}{9}}\) .
Further Explanation:
The force of attraction due to gravity is the force which exists between two bodies kept at a distance from each other. This force is given by Newton’s law of gravitation.
The Newton’s law of gravitation states that the gravitational force of attraction between the bodies kept at a certain distance is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
The above explanation can be shown mathematically as:
\(\begin{aligned}F&\propto\frac{1}{{{r^2}}}\hfill\\\frac{{{F_2}}}{{{F_1}}}&=\frac{{r_1^2}}{{r_2^2}}\hfill\\\end{aligned}\)
The proportionality equations can be combined and the formula for the Gravitational force of attraction can be written as:
\(F=\frac{{G{m_1}{m_2}}}{{{r^2}}}\)
Let us consider that in initial distance between the two bodies is \(r\) . Now, if the distance between the two bodies is tripled of its initial distance, then the new separation becomes \(3r\).
Substitute \({f_0}\) for \({F_1}\) , \({f_1}\) for \({F_2}\) , \(r\) for \({r_1}\) and \(3r\) for \({r_2}\) in above expression.
\(\begin{aligned}\frac{{{f_1}}}{{{f_0}}}&=\frac{{{r^2}}}{{{{\left({3r}\right)}^2}}}\hfill\\{f_1}&=\frac{{{f_0}}}{9}\hfill\\\end{aligned}\)
Thus, the new gravitational force of attraction after increasing the separation between the two particles is \(\boxed{\frac{{{f_0}}}{9}}\) .
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Answer Details:
Grade: Senior School
Subject: Physics
Chapter: Gravitation
Keywords:
Gravitational interaction, separated by a certain distance, gravitational force, Newton’s law of gravitation, between the particles, tripled.