Question

1 planetary motion and gravitation (continued)
summarize the relationships described by newton’s law of universal gravitation by completing the concept map below.
law of universal gravitation
relationship between $f_g$ and the distance between two objects:
relationship between $f_g$ and the masses of the two objects:

Explanation:

Step1: Recall Newton's Law of Universal Gravitation

Newton's law of universal gravitation is given by the formula $F_g = G\frac{m_1m_2}{r^2}$, where $F_g$ is the gravitational force, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between their centers.

Step2: Analyze Relationship with Distance

From the formula $F_g = G\frac{m_1m_2}{r^2}$, we can see that the gravitational force $F_g$ is inversely proportional to the square of the distance $r$ between the two objects. So the relationship between $F_g$ and the distance between two objects is: $F_g$ is inversely proportional to the square of the distance (or $F_g \propto \frac{1}{r^2}$).

Step3: Analyze Relationship with Masses

From the same formula $F_g = G\frac{m_1m_2}{r^2}$, the gravitational force $F_g$ is directly proportional to the product of the masses $m_1$ and $m_2$ of the two objects. So the relationship between $F_g$ and the masses of the two objects is: $F_g$ is directly proportional to the product of the masses (or $F_g \propto m_1m_2$).

Answer:

• Relationship between $F_g$ and the distance between two objects: $F_g$ is inversely proportional to the square of the distance ($F_g \propto \frac{1}{r^2}$)
• Relationship between $F_g$ and the masses of the two objects: $F_g$ is directly proportional to the product of the masses ($F_g \propto m_1m_2$)