Question

Gravity causes objects to be attracted to one another. This attraction keeps our feet firmly planted on the ground and causes the moon to orbit the earth. The force of gravitational attraction is represented by the equation F=Gm1m2r2, where F is the magnitude of the gravitational attraction on either body, m1 and m2 are the masses of the bodies, r is the distance between them, and G is the gravitational constant. In SI units, the units of force are kg⋅m/s2, the units of mass are kg, and the units of distance are m.

Answer 1

So the problem are asking to find the value of G base on the formula of the said equation of the magnitude of gravitational attraction on either body. Base on that, the possible answer or the derived formula of the said function is G = Fr^2/m1m2. I hope you are satisfied with my answer and feel free to ask for more 

Answer 2

The unit of the gravitational constant is $\boxed{{{{{\text{m}}^{\text{3}}}} \mathord{\left/{\vphantom {{{{\text{m}}^{\text{3}}}} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}} \right.\kern-\nulldelimiterspace} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}}$.

Further Explanation:

According to the Newton’s Law of gravitation, the gravitational force of attraction between two bodies kept at a distance $r$ is directly proportional to the product of their masses and inversely proportional to the square of the distance between the bodies.

The mathematical expression for the Newton’s law of gravitation is as shown below.

$F = \dfrac{{G{m_1}{m_2}}}{{{r^2}}}$  

Here, $G$ is the gravitational constant, ${m_1}\& {m_2}$ are the masses of the bodies and $r$ is the distance between two bodies.

Rearrange the above expression fir the gravitational constant $G$.

$G = \dfrac{{F{r^2}}}{{{m_1}{m_2}}}$  

Substitute the SI units of force, distance and mass in the above expression.

$\begin{aligned}G&=\dfrac{(\text{kg}\cdot\text{m/s}^2)(\text{m})^2}{(\text{kg})(\text{kg})}\\&=\dfrac{\text{m}^3}{\text{kg}\cdot\text{s}^2}\\&=\text{m}^3/\text{kg}\cdot\text{s}^2\end{aligned}$  

Thus, the unit of the gravitational constant is $\boxed{{{{{\text{m}}^{\text{3}}}} \mathord{\left/{\vphantom {{{{\text{m}}^{\text{3}}}} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}} \right.\kern-\nulldelimiterspace} {{\text{kg}} \cdot {{\text{s}}^{\text{2}}}}}}$.

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Answer Details:

Grade: High School

Chapter: Gravitation

Subject: Physics

Keywords:  Gravity, attracts, two bodies, one another, gravitational constant, force, masses of the body, magnitude of force, distance, units, SI units.