# Question on convention - R vs r using universal law of grav.

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• kjamha
In summary, the convention for representing distance in the universal law of gravitation formula is to use lowercase r for the total distance and uppercase R for the radial distance. This convention is often used to distinguish between the two types of distances in equations.
kjamha
I have a question on convention regarding the universal law of gravitation formula. Sometimes the distance is represented with the lowercase r and sometimes with the uppercase R. Why is it listed two different ways? I am thinking that r is the total distance and R is the radial distance, no? For example, the distance to a satellite might be r = R + h, where r is total distance, R is the radius of the planet and h is the distance from the surface of the planet to the satellite. I am wondering what the convention is.

kjamha said:
I have a question on convention regarding the universal law of gravitation formula. Sometimes the distance is represented with the lowercase r and sometimes with the uppercase R. Why is it listed two different ways? I am thinking that r is the total distance and R is the radial distance, no? For example, the distance to a satellite might be r = R + h, where r is total distance, R is the radius of the planet and h is the distance from the surface of the planet to the satellite. I am wondering what the convention is.

Yes, I've most often seen them used the way you suggest: r for the generic distance, R for the radius of the Earth or a specific object.

## 1. What is the difference between R and r in the universal law of gravitation?

R and r represent two different quantities in the universal law of gravitation. R represents the distance between the centers of mass of two objects, while r represents the distance between the two objects' individual masses. In other words, R is the total distance between the two objects, while r is the distance between their individual masses.

## 2. How do R and r affect the strength of gravitational force?

The strength of gravitational force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between them. This means that as R increases, the strength of gravitational force decreases, while as r decreases, the strength of gravitational force increases.

## 3. Can the universal law of gravitation be applied to objects other than planets and stars?

Yes, the universal law of gravitation can be applied to any two objects with mass. This includes objects on Earth's surface, such as people and buildings, as well as objects in space.

## 4. How does the universal law of gravitation explain the motion of planets and stars?

The universal law of gravitation states that all objects with mass are attracted to each other with a force proportional to their masses and inversely proportional to the square of the distance between them. This explains the motion of planets and stars, as they are constantly being pulled towards each other by the force of gravity.

## 5. Is the universal law of gravitation a proven theory?

Yes, the universal law of gravitation has been extensively tested and confirmed through scientific experiments and observations. It is considered a fundamental law of physics and is used to explain various phenomena in the universe.

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