key term - $F = G \frac{m_1 m_2}{r^2}$

Definition

$F = G \frac{m_1 m_2}{r^2}$ is the mathematical expression that represents Newton's Universal Law of Gravitation, which describes the gravitational force between two objects. This equation shows that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

5 Must Know Facts For Your Next Test

1. The gravitational force between two objects is always attractive, meaning it pulls the objects towards each other.
2. The gravitational force is a long-range force, meaning it can act over large distances without any physical contact between the objects.
3. The gravitational force is proportional to the product of the masses of the two objects, indicating that more massive objects exert a stronger gravitational pull.
4. The gravitational force is inversely proportional to the square of the distance between the objects, meaning that as the distance increases, the force decreases rapidly.
5. The gravitational constant, $G$, is a universal constant that has the same value throughout the universe and does not depend on the properties of the objects involved.

Review Questions

• Explain the relationship between the masses of the two objects and the gravitational force acting between them.
  • According to the equation $F = G \frac{m_1 m_2}{r^2}$, the gravitational force between two objects is directly proportional to the product of their masses. This means that as the masses of the two objects increase, the gravitational force between them also increases. For example, if the mass of one object doubles, the gravitational force between the two objects will also double, assuming all other factors remain constant.
• Describe how the distance between the two objects affects the gravitational force acting between them.
  • The equation $F = G \frac{m_1 m_2}{r^2}$ shows that the gravitational force is inversely proportional to the square of the distance between the two objects. This means that as the distance between the objects increases, the gravitational force between them decreases rapidly. For instance, if the distance between the two objects is doubled, the gravitational force between them will be reduced by a factor of four (i.e., it will be one-quarter of the original value).
• Analyze the role of the gravitational constant, $G$, in the equation and explain its significance in the context of Newton's Universal Law of Gravitation.
  • The gravitational constant, $G$, is a fundamental physical constant that represents the strength of the gravitational force between two objects. It is a universal constant, meaning that it has the same value throughout the universe and does not depend on the properties of the objects involved. The value of $G$ is approximately $6.67 \times 10^{-11} \, N \cdot m^2/kg^2$. The inclusion of $G$ in the equation $F = G \frac{m_1 m_2}{r^2}$ is crucial, as it allows us to quantify the gravitational force between any two objects with known masses and separation distance, and is a key component of Newton's Universal Law of Gravitation.

Related terms

Gravitational Constant (G): The gravitational constant, denoted as $G$, is a fundamental physical constant that represents the strength of the gravitational force between two objects. Its value is approximately $6.67 \times 10^{-11} \, N \cdot m^2/kg^2$.

Mass (m): Mass is a measure of the amount of matter in an object. It is represented by the variables $m_1$ and $m_2$ in the equation, which refer to the masses of the two objects experiencing the gravitational force.

Distance (r): The distance between the centers of the two objects, represented by the variable $r$ in the equation, is a crucial factor in determining the strength of the gravitational force between them.