Sure! Let's find the positive value of [tex]\( r \)[/tex] in terms of [tex]\( F_g \)[/tex], [tex]\( G \)[/tex], [tex]\( M_1 \)[/tex], and [tex]\( M_2 \)[/tex]. We start with the formula for gravitational force:
[tex]\[ F_g = \frac{G M_1 M_2}{r^2} \][/tex]
Our goal is to solve this equation for [tex]\( r \)[/tex]. Here are the steps:
1. Isolate [tex]\( r^2 \)[/tex] on one side of the equation:
[tex]\[
F_g = \frac{G M_1 M_2}{r^2} \implies F_g \cdot r^2 = G M_1 M_2
\][/tex]
2. Rearrange the equation to solve for [tex]\( r^2 \)[/tex]:
[tex]\[
r^2 = \frac{G M_1 M_2}{F_g}
\][/tex]
3. Solve for [tex]\( r \)[/tex] by taking the square root of both sides:
[tex]\[
r = \sqrt{\frac{G M_1 M_2}{F_g}}
\][/tex]
Since we are interested in the positive value of [tex]\( r \)[/tex]:
[tex]\[
r = \sqrt{\frac{G M_1 M_2}{F_g}}
\][/tex]
This is the positive value for the distance [tex]\( r \)[/tex] in terms of [tex]\( F_g \)[/tex], [tex]\( G \)[/tex], [tex]\( M_1 \)[/tex], and [tex]\( M_2 \)[/tex].
