F = g(m1*m2)/r^2

Definition

The equation $$f = g\frac{m_1 m_2}{r^2}$$ represents Newton's law of universal gravitation, which describes the gravitational force between two masses. In this formula, $$f$$ 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 the centers of the two masses. This relationship shows that the force of gravity is directly proportional to the product of the two masses and inversely proportional to the square of the distance separating them.

5 Must Know Facts For Your Next Test

1. The gravitational force is always attractive, meaning it pulls objects toward each other rather than pushing them apart.
2. The value of $$g$$ is constant, but its effects can be observed differently depending on mass and distance; for example, gravity on Earth is approximately 9.81 m/s².
3. If either mass $$m_1$$ or $$m_2$$ increases, the gravitational force $$f$$ increases proportionally.
4. As the distance $$r$$ increases between the two masses, the gravitational force $$f$$ decreases rapidly due to the inverse-square relationship.
5. This law applies universally, meaning it holds true for all objects with mass, from small objects on Earth to large celestial bodies in space.

Review Questions

• How does changing the distance between two masses affect the gravitational force acting between them according to this formula?
  • According to the formula $$f = g\frac{m_1 m_2}{r^2}$$, increasing the distance $$r$$ between two masses results in a decrease in gravitational force. Specifically, since the force is inversely proportional to the square of the distance, doubling the distance would result in a reduction of gravitational force to one-fourth its original value. This shows how sensitive gravitational attraction is to changes in distance.
• What implications does Newton's law of universal gravitation have on our understanding of planetary motion and orbits?
  • Newton's law of universal gravitation explains how celestial bodies interact through gravitational forces, allowing us to understand their orbits. For example, a planet's orbit around a star can be predicted by applying this formula, where each body exerts a gravitational pull on one another. This understanding led to significant advances in astronomy and physics by enabling predictions about planetary positions and motions based on their masses and distances.
• Critically evaluate how Newton's law of universal gravitation can be applied to modern physics scenarios beyond just simple two-body problems.
  • Newton's law of universal gravitation has broad applications that extend beyond simple two-body problems to complex systems involving multiple bodies, such as galaxies and star clusters. This law helps physicists understand phenomena like gravitational waves and black holes within general relativity's framework. Additionally, while it provides accurate predictions for many scenarios, its limitations are highlighted in extreme conditions where general relativity becomes essential. This evaluation showcases how foundational concepts can evolve and integrate into advanced theories in modern physics.

Related terms

Gravitational Constant: A fundamental physical constant denoted by $$g$$, approximately equal to 6.674 × 10^-11 N(m/kg)^2, used in the equation for gravitational force.

Mass: A measure of the amount of matter in an object, typically measured in kilograms (kg), that influences its gravitational attraction.

Distance: The separation between two objects, measured from center to center, which affects the strength of the gravitational force according to the inverse-square law.