Newton's Law of Universal Gravitation

Definition

Newton's Law of Universal Gravitation is a fundamental principle that describes the attractive force between any two objects with mass. It states that the force of gravity between two objects 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 directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
2. The gravitational constant, 'G', has a value of approximately 6.67 × 10^-11 N⋅m^2/kg^2, and is a universal constant that does not depend on the nature of the objects or the force.
3. The gravitational force is always attractive, meaning that it pulls objects towards each other, and it acts along the line connecting the centers of the two objects.
4. Newton's Law of Universal Gravitation applies to all objects in the universe, from the smallest particles to the largest celestial bodies.
5. The inverse square law of gravity means that as the distance between two objects increases, the gravitational force between them decreases dramatically.

Review Questions

• Explain how the gravitational force between two objects is calculated according to Newton's Law of Universal Gravitation.
  • The gravitational force between two objects is calculated using the formula: $F = G \frac{m_1 m_2}{r^2}$, where $F$ 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 them. The force is directly proportional to the product of the masses and inversely proportional to the square of the distance, which is known as the inverse square law of gravity.
• Describe how the gravitational force between two objects changes as the distance between them increases.
  • According to the inverse square law, as the distance between two objects increases, the gravitational force between them decreases dramatically. Specifically, if the distance between the objects is doubled, the gravitational force between them decreases by a factor of four (1/2^2). This means that the gravitational force falls off very quickly with increasing distance, and objects that are farther apart experience a much weaker gravitational attraction than those that are closer together.
• Analyze how the gravitational force between the Earth and an object near its surface, as described by Newton's Law of Universal Gravitation, is related to the acceleration due to gravity at that location.
  • The gravitational force between the Earth and an object near its surface is directly related to the acceleration due to gravity at that location, as described by Newton's Law of Universal Gravitation. Specifically, the acceleration due to gravity, $g$, is equal to the gravitational force per unit mass of the object, which can be expressed as $g = G \frac{M_E}{r^2}$, where $M_E$ is the mass of the Earth and $r$ is the distance from the center of the Earth to the object. This relationship allows us to use the principles of Newton's Law of Universal Gravitation to understand and predict the behavior of objects near the Earth's surface, such as the motion of falling objects and the orbits of satellites.

Related terms

Gravitational Force: The attractive force that exists between any two objects with mass, as described by Newton's Law of Universal Gravitation.

Gravitational Constant: A universal constant, denoted as 'G', that represents the strength of the gravitational force between two objects.

Inverse Square Law: The principle that the strength of a force (such as gravity) decreases with the square of the distance from the source of the force.