# Gauss law for gravitational fields

• tenchotomic
In summary: Newton's gravity gets messy when trying to apply it to irregular bodies. However, with Gauss's law, you only need to know the general idea of the law and that's it.
tenchotomic
For electrostatic fields gauss law depends on three factors viz inverse square nature ,central character and principle of linear superposition of electrostatic force.Now,within the Newton's framework of gravitation the gravitational force has all of the above properties.Then why does one does not talk about gauss law for gravitational field?

We can! That's why we can calculate the surface acceleration due to gravity by pretending all the mass is concentrated at the centre of the earth. It's also how we can easily calculate that, for instance, the force of gravity is zero anywhere inside a spherically symmetric shell.

tenchotomic said:
Then why does one does not talk about gauss law for gravitational field?

People do use gauss's law for calculating gravitational fields. We used it quite often in my Classical Mechanics course.

The reason I found for not using it much are that for a given charge configuration the flux of electrostatic fields is so very large than that of gravitational field that it becomes redundant to apply gauss's law to gravitational fields.

tenchotomic said:
The reason I found for not using it much are that for a given charge configuration the flux of electrostatic fields is so very large than that of gravitational field that it becomes redundant to apply gauss's law to gravitational fields.

I'm sorry, but that doesn't really make any sense. What do you mean it's redundant? If you mean that the procedure is extremely similar for both, then you are correct. But for a given problem you are either asked to find a gravitational field or an electric field. If you are asked to find a gravitational field for a symmetrical sphere, you would apply Gauss's law to find it, you wouldn't try to find the electric field then convert the constants to make it a gravitational field if that's what you are suggesting.

silmaril89 said:
I'm sorry, but that doesn't really make any sense. What do you mean it's redundant? If you mean that the procedure is extremely similar for both, then you are correct. But for a given problem you are either asked to find a gravitational field or an electric field. If you are asked to find a gravitational field for a symmetrical sphere, you would apply Gauss's law to find it, you wouldn't try to find the electric field then convert the constants to make it a gravitational field if that's what you are suggesting.

Sure,the methods are very similar,just replace charge by mass and adjust the constants.
But in my last thread I was not concerned about separate cases of electrostatic and gravitational field.What I meant was that,given a charge configuration (which obviously has some mass),if you compare the gravitational flux with electric flux you wll practically get a negligible gravitational flux all the time.This is due to large charge/mass ratio of the configuration you are working with.That's why I used the term redundant.Its same as ,for example, when you are talking about interaction between two electrons,its redundant to talk about gravitational interaction between them.

The gauss's law equivalent for gravitational field is used. I've even seen it being used in a graduate qualifying exam (or at least, if you know how to use it, you could have solved a problem with the last amount of effort). The magnitude of the "flux" is irrelevant in choosing a technique. After all, the gravitational force is similarly exceedingly weak as well when compared to an electrostatic force. Yet, that doesn't stop us from calculating its force!

Zz.

I'm told that Gauss' law can't be used in 3+1 space-time so Newton's gravity yes, Einstein's gravity no.

The use of gauss is especially useful when you are inside a body and Newton's laws starts getting a little bit messy you need to invoke sheel theorem (http://en.wikipedia.org/wiki/Shell_theorem)

Gauss's law is much easier in these situations especially with irregular bodies ... IMO.

## What is Gauss law for gravitational fields?

Gauss law for gravitational fields is a fundamental law in physics that relates the distribution of mass to the gravitational field it produces. It states that the flux of the gravitational field through any closed surface is proportional to the enclosed mass.

## How is Gauss law for gravitational fields different from Gauss law for electric fields?

While both laws are named after mathematician Carl Friedrich Gauss, they apply to different physical phenomena. Gauss law for electric fields relates the distribution of electric charge to the electric field it produces, while Gauss law for gravitational fields relates the distribution of mass to the gravitational field it produces. The equations also differ in the constant used to relate the two quantities.

## What is the mathematical equation for Gauss law for gravitational fields?

The mathematical equation for Gauss law for gravitational fields is ∮g · dA = -4πGM, where g is the gravitational field, dA is the differential area element, and M is the enclosed mass. This equation is a special case of Gauss's law of gravitation, which relates the gravitational field to the source mass.

## What is the significance of Gauss law for gravitational fields?

Gauss law for gravitational fields is significant because it allows us to calculate the gravitational field at any point in space by knowing the mass distribution in the surrounding space. This makes it a powerful tool for understanding and predicting the behavior of objects under the influence of gravity.

## How is Gauss law for gravitational fields used in practical applications?

Gauss law for gravitational fields is used in a variety of practical applications, including predicting the motions of celestial bodies, calculating the gravitational force between objects, and designing spacecraft trajectories. It is also used in gravitational mapping techniques, such as measuring the Earth's gravitational field to map its internal structure.

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