F = G(m1m2)/r^2

Definition

F = G(m1m2)/r^2 is the mathematical expression that represents Newton's Law of Universal Gravitation. It describes the force of gravitational attraction between two objects with masses m1 and m2, separated by a distance r, and governed by the universal gravitational constant G.

5 Must Know Facts For Your Next Test

1. The force of gravitational attraction between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
2. The gravitational constant (G) is a universal physical constant that has a value of approximately 6.67 × 10^-11 N⋅m^2/kg^2.
3. The inverse square law, as represented by the r^2 term in the equation, means that as the distance between the objects doubles, the gravitational force decreases by a factor of four.
4. The gravitational force acts along the line connecting the centers of the two objects and is always attractive, never repulsive.
5. The gravitational force is a conservative force, meaning that the work done in moving an object between two points is independent of the path taken.

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(m1m2)/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 proportionally. For example, if the mass of one object doubles, the gravitational force between the two objects will also double, all other factors being equal.
• Describe how the distance between the two objects affects the gravitational force.
  • The gravitational force between two objects is inversely proportional to the square of the distance between them, as represented by the r^2 term in the equation. This means that as the distance between the objects increases, the gravitational force decreases rapidly. For instance, if the distance between the objects doubles, the gravitational force will decrease by a factor of four. This inverse square relationship is known as the inverse square law and is a fundamental principle of gravitational interactions.
• Analyze the role of the gravitational constant (G) in the equation F = G(m1m2)/r^2 and explain its significance.
  • The gravitational constant (G) is a fundamental physical constant that quantifies the strength of the gravitational force between two objects. It has a value of approximately 6.67 × 10^-11 N⋅m^2/kg^2. The presence of the gravitational constant in the equation F = G(m1m2)/r^2 indicates that the gravitational force is a universal phenomenon, governed by a fixed, universal parameter. The value of G determines the overall magnitude of the gravitational force and allows for the comparison and prediction of gravitational interactions across different scales, from the smallest particles to the largest celestial bodies in the universe.

Related terms

Gravitational Force: The attractive force between two objects with mass, acting along the line connecting their centers.

Gravitational Constant (G): A fundamental physical constant that quantifies the strength of the gravitational force between two objects.

Inverse Square Law: A physical law stating that the strength of a force decreases with the square of the distance from the source of that force.