The gravitational force formula, also known as Newton’s law of universal gravitation, is a fundamental concept in physics that describes the attractive force between two objects with mass. This formula, F = G * (m1 * m2) / d^2, allows us to calculate the gravitational force between any two objects, given their masses and the distance between them.
Theorem: Newton’s Law of Universal Gravitation
Newton’s law of universal gravitation states that every point mass attracts every other point mass by a force acting along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.
Physics Formula
The gravitational force formula is expressed as:
F = G * (m1 * m2) / d^2
Where:
– F is the force of gravitational attraction between the two objects (in Newtons, N)
– G is the universal gravitational constant, approximately equal to 6.67 x 10^-11 N(m/kg)^2
– m1 and m2 are the masses of the two objects (in kilograms, kg)
– d is the distance between the centers of the two objects (in meters, m)
Physics Example
Let’s consider a simple example to illustrate the concept of gravitational force. Imagine two objects with masses m1 = 10 kg and m2 = 5 kg, separated by a distance d = 2 meters. According to Newton’s law of universal gravitation, these two objects will attract each other with a force F given by the formula:
F = (6.67 x 10^-11 N(m/kg)^2) * ((10 kg) * (5 kg)) / (2 m)^2
F = 8.3375 x 10^-10 N
Therefore, the force of attraction between the two objects is 8.3375 x 10^-10 Newtons.
Physics Numerical Problem
Let’s consider a more complex example to illustrate the concept of gravitational force. Imagine a spaceship with a mass of 10,000 kg, orbiting a planet with a mass of 5 x 10^24 kg and a radius of 6 x 10^6 m. The spaceship is initially at a distance of 10^7 m from the center of the planet. Calculate the gravitational force acting on the spaceship and the acceleration due to gravity at the spaceship’s location.
First, we need to calculate the gravitational constant G using the formula G = F * (d^2) / (m1 * m2). We know that the force of gravity between two objects is given by F = G * (m1 * m2) / d^2, so we can rearrange this formula to solve for G. Substituting the given values, we get:
G = (9.81 m/s^2) * (6 x 10^6 m)^2 / (10,000 kg * 5 x 10^24 kg)
G = 6.67 x 10^-11 N(m/kg)^2
Next, we need to calculate the gravitational force acting on the spaceship using the formula F = G * (m1 * m2) / d^2. Substituting the given values, we get:
F = (6.67 x 10^-11 N(m/kg)^2) * (10,000 kg * 5 x 10^24 kg) / (10^7 m)^2
F = 3.335 x 10^7 N
Therefore, the gravitational force acting on the spaceship is 3.335 x 10^7 Newtons.
Finally, we need to calculate the acceleration due to gravity at the spaceship’s location using the formula g = G * m / r^2. Substituting the given values, we get:
g = (6.67 x 10^-11 N(m/kg)^2) * (5 x 10^24 kg) / (6 x 10^6 m + 10^7 m)^2
g = 0.25 m/s^2
Therefore, the acceleration due to gravity at the spaceship’s location is 0.25 m/s^2.
Figure
The following figure illustrates the concept of gravitational force between two objects:
[Insert Figure Here]
Data Points, Values, and Measurements
The following table summarizes the key data points, values, and measurements related to gravitational force:
| Symbol | Description | Value | Unit |
|---|---|---|---|
| G | Gravitational constant | 6.67 x 10^-11 | N(m/kg)^2 |
| m1 | Mass of first object | Variable | kg |
| m2 | Mass of second object | Variable | kg |
| d | Distance between objects | Variable | m |
| F | Force of gravitational attraction | Variable | N |
| g | Acceleration due to gravity | 9.81 | m/s^2 |
References
- Gravity Equation | Formula, Calculation & Example – Lesson. (n.d.). Study.com. Retrieved June 19, 2024, from https://study.com/academy/lesson/isaac-newtons-formula-for-the-force-of-gravity-definition-example.html
- How did Newton come up with his formula for gravitational force? – History of Science and Mathematics Stack Exchange. (2017, January 8). Retrieved June 19, 2024, from https://hsm.stackexchange.com/questions/5558/how-did-newton-come-up-with-his-formula-for-gravitational-force
- Exploring the “G” in Newton’s Law of Universal Gravitation. (2023, November 7). HowStuffWorks. Retrieved June 19, 2024, from https://science.howstuffworks.com/math-concepts/gravitational-constant.htm
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