# Is there such a thing as Gm/r?

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• concernedhuman
In summary, the conversation discusses the similarities between various formulas, including Fg = Gmm/r2, Fe = kQq/r2, E = kQ/r2, and g = Gm/r2. The question arises if there is a corresponding formula for kQ/r, which is found to be -GM/r and is known as Gravitational Potential. It is always negative and approaches zero towards an infinitely remote distance, decreasing even further towards the center of mass M. It is usually denoted as M instead of m. This information is helpful and clarifies any confusion about the use of m in the formulas.
concernedhuman
Since Fg = Gmm/r2and Coulomb's law being similar to that: Fe = kQq/r2,
and we also have E = kQ/r2 and g = Gm/r2 being alike,
I was wondering if there's anything that corresponds to the potential equation kQ/r. I converted it myself and figured that it's going to be Gm/r, and I'm not sure if a formula for that exists.

If m stands for the mass of the body whose gravitational field we are considering then there is, except that it is standard to use M rather than m. The quantity is -GM/r and is called Gravitational Potential. It is always negative, asymptotically approaches zero as we go towards an infinitely remote distance and it decreases ever deeper into negative territory as we approach the centre of the mass M.

berkeman and concernedhuman
andrewkirk said:
If m stands for the mass of the body whose gravitational field we are considering then there is, except that it is standard to use M rather than m. The quantity is -GM/r and is called Gravitational Potential. It is always negative, asymptotically approaches zero as we go towards an infinitely remote distance and it decreases ever deeper into negative territory as we approach the centre of the mass M.
Thank you so much! This is helpful and yes I apparently didn't use the right m

## 1. Is Gm/r a real concept in science?

Yes, Gm/r is a real concept in science. It refers to the gravitational constant (G) multiplied by the mass (m) and divided by the distance (r) between two objects. This concept is commonly used in physics and astronomy to calculate the force of gravity between two objects.

## 2. How is Gm/r related to Newton's Law of Universal Gravitation?

Gm/r is directly related to Newton's Law of Universal Gravitation, which 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. Gm/r is used to represent this relationship mathematically.

## 3. Can Gm/r be used to calculate the force of gravity on Earth?

Yes, Gm/r can be used to calculate the force of gravity on Earth. The value of Gm/r for Earth is approximately 3.986 x 10^14 m^3/s^2, which is commonly used in formulas to calculate the acceleration due to gravity on the surface of Earth.

## 4. Are there any real-world applications for Gm/r?

Yes, there are many real-world applications for Gm/r. It is used in various fields such as astronomy, geology, and engineering to calculate the gravitational forces between objects, such as planets, stars, and satellites. It is also used in space missions to accurately predict and plan trajectories.

## 5. How was Gm/r first discovered?

Gm/r was first discovered by Sir Isaac Newton in the late 17th century. He developed the concept as part of his Law of Universal Gravitation, which revolutionized our understanding of gravity and its effects on celestial bodies. It has since been refined and used in various scientific fields to make accurate calculations and predictions.

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