Enter any 3 of the following: the mass of object 1, the mass of object 2, the distance between their centers, and the gravitational force. This calculator will compute the missing value using Newton’s law of universal gravitation.
- All Physics Calculators
- All Force Calculators
- Acceleration Calculator
- Mass to Weight Calculator
- GBE (Gravitational Binding Energy) Calculator
- Weight to Force Calculator
- Attraction Force Calculator
Gravitational Force Formula
The gravitational force between two objects is calculated with the following formula:
F = G * M * m / R^2
- Where F is the gravitational force.
- M and m are the masses of the two objects.
- R is the distance between the centers of the objects.
- G is the gravitational constant, which is equal to 6.67430×10^-11 N·m^2/kg^2.
To calculate the gravitational force, multiply the two masses by the gravitational constant (G), then divide by the square of the center-to-center distance between them.
Gravitational Force Definition
Gravitational force is the force of attraction that arises between objects with mass. This force is a fundamental force of nature. For a given separation distance, the larger the masses, the larger the gravitational force.
How to calculate gravitational force?
The following example shows how someone might calculate the gravitational force between two circular objects that have their centers of mass exactly in the center of their body.
How to calculate the gravitational force
- First, determine the mass of the larger object
In many cases, the larger object is a body like a planet or celestial body. In this case, the mass will need to be calculated using the known physics of gravity. For the most part, you can just look up the mass of any planet in the solar system. For this example, we will assume the object is the Earth, which has a mass of 5.972 × 10^24 kg.
- Next, weigh or measure the mass of the smaller object
For this example, we are going to use a bowling ball as our smaller object. We will say that we put the ball on a scale and find the mass to be 10 kg.
- Next, measure the center-to-center distance between objects
Since we are using the Earth as the larger object, we can take the radius of the Earth, add the height the bowling ball is placed at, and then add the radius of the bowling ball. Near Earth’s surface, this total is approximately 6,371 km (≈ 6.371 × 10^6 m).
- Finally, enter all of the known information into the formula
We now have all of the information needed to perform our calculation. We enter all of the information and find the force due to gravity to be approximately 98 N.
- Analyze the results
Check the answer to make sure it makes logical sense and apply what you learned to other problems.
FAQ
How does the distance between two objects affect the gravitational force between them?
The gravitational force between two objects decreases as the square of the distance between them increases. This means that if the distance between two objects is doubled, the gravitational force between them becomes one-fourth of its original value.
Why is the gravitational constant (G) important in calculating gravitational force?
The gravitational constant (G) is a key factor in the calculation of gravitational force because it quantifies the strength of gravity in the universe. Without this constant, it would be impossible to calculate the precise force of attraction between two masses.
Can the gravitational force between two objects ever be zero?
For two objects with nonzero mass at any finite separation distance, the gravitational force is not zero (it is always attractive). However, the force can become extremely small and approaches zero as the distance between the objects becomes very large.
