# Problem on a question about the gravitation potential

• Garlic
In summary, the conversation is discussing the solution to a question involving gravitational force fields and potentials. The individual is having trouble understanding a specific step in the solution and is questioning why a certain term is not being integrated. The expert explains that the integration is split into two parts due to the difference in the force equation inside and outside the Earth, and the first integral is just the potential at the Earth's surface. The individual then thanks the expert for the clarification.
Garlic
Gold Member
Hello everyone

1. Homework Statement

In the solution of a question, regarding the gravitational force fields and gravitational potential when the mass is inside Earth (where the height of the mass is lower than the radius of earth), the step where we take the integral of the force in order to get the potential is not very clearly defined, and I have problems understanding why it looks like this:

Where does this blue marked term come from? Why isn't its integral being taken, like the term on the right?
Why can't we simply find the potential by just taking the integral of the force field (without the blue marked term)?

(Where the GN is the gravitation constant, R the radius of earth, m the mass of an object, and mE the mass of earth, r cap the unit vector of the r coordinate)

Thank you

## The Attempt at a Solution

To calculate the potential this way, you need to take the integral from ##r = \infty## to ##r = r_m##. The equation for the force is different outside the Earth than within it, so you have to split the integral into two. The first integral is then from ##r = \infty## to ##r = R## and that's the first term, which is just the potential at the Earth's surface.

Oh, now I understand it.. Thank you

## 1. What is gravitation potential?

Gravitation potential is a measure of the potential energy of an object due to its position within a gravitational field. It is a scalar quantity, meaning it has only magnitude and no direction.

## 2. How is gravitation potential different from gravitational potential energy?

Gravitational potential energy is the actual amount of energy an object possesses due to its position in a gravitational field. Gravitation potential, on the other hand, is the potential for an object to have gravitational potential energy. In other words, it is the amount of energy an object would have if it were to be placed in a certain position within a gravitational field.

## 3. What factors affect the gravitation potential of an object?

The gravitation potential of an object is affected by its mass, the mass of the object creating the gravitational field, and the distance between the two objects. The larger the mass of either object or the closer they are to each other, the higher the gravitation potential.

## 4. How is gravitation potential measured?

Gravitation potential is typically measured in units of joules per kilogram (J/kg). This unit represents the amount of energy per unit mass an object has within a gravitational field.

## 5. What is the significance of gravitation potential in physics?

Gravitation potential is crucial in understanding the behavior of objects in a gravitational field. It is used to calculate gravitational potential energy, which is essential in many physical phenomena, such as planetary orbits and satellite motion. Additionally, understanding gravitation potential is crucial in the study of general relativity and the curvature of spacetime.

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