# Gravitational equipotential multiple choice problem

• Grizzly_1
In summary, the person does not understand how to answer the question, as they do not know the direction of the field lines.
Grizzly_1
Homework Statement
The diagram shows gravitational equipotential. Adjacent equipotential are separated by an equal gravitational potential difference V.

Which point has the greatest gravitational field strength?
Relevant Equations
E=-GM/(r^2)
Hello everyone, thank you for taking your time to read this. I was assigned a homework task of multiple choice questions to do with gravitational fields. This is one of the last questions and I have been pondering over it for some time now. I don't understand how any sort of answer is achievable.

To the best of my knowledge, gravitational field strength is directly proportional to the mass of the object that is causing the field, and inversely proportional to the square of the distance between the mass causing the field and the point at which you are determining field strength. In this case, as we do not know the location of the mass we cannot determine the direction of the field lines, and by extension we cannot tell if the potential differences are decreasing from D to A, or A to D.

If you knew which way the potential gradient was increasing, I think you could work out which point had the greatest gravitational field strength as it is the point at which potential is the least (most negative), as this implies it is closest to the mass or masses that are causing the field.

As you do not know this, I do not know how you could answer such a question, they are just arbitrarily placed about the square and I do not know the relevance of equipotentials, as these are just indications about lines that have an equal potential difference along its length, this doesn't tell us anything relevant to finding at which point the gravitational field is greatest.

So this is my reasoning so far, I am truly stumped. I hope someone can help out in solving this tricky question (or perhaps not tricky and I am just being silly).

Last edited by a moderator:
On a topographical map of terrain on the Earth, how can you tell the steepest parts from those that are flatter?

Does this help?

kuruman said:
Does this help?
View attachment 325485
berkeman said:
On a topographical map of terrain on the Earth, how can you tell the steepest parts from those that are flatter?
Hello, thank you for responding. I understand both of your comments (I think), you are saying that, in the area were the equipotential lines are closest together, there must be a greater potential difference gradient, and therefore a greater field strength. I now understand, you have both helped me greatly. Thank you again!

berkeman and kuruman
Grizzly_1 said:
Hello, thank you for responding. I understand both of your comments (I think), you are saying that, in the area were the equipotential lines are closest together, there must be a greater potential difference gradient, and therefore a greater field strength. I now understand, you have both helped me greatly. Thank you again!
You got it!

## What is a gravitational equipotential surface?

A gravitational equipotential surface is a surface on which all points have the same gravitational potential energy. This means that no work is required to move an object along this surface because the gravitational force does not change along it.

## How do gravitational equipotential surfaces relate to gravitational fields?

Gravitational equipotential surfaces are always perpendicular to the gravitational field lines. This is because the gravitational force acts in the direction of the steepest decrease in potential, and no work is done when moving perpendicular to this force.

## Why is understanding gravitational equipotential surfaces important?

Understanding gravitational equipotential surfaces is important because they help in visualizing and analyzing the gravitational field in a region. This can be useful in various applications, such as satellite navigation, astrophysics, and geophysics.

## How do you determine the shape of gravitational equipotential surfaces around a massive object?

The shape of gravitational equipotential surfaces around a massive object is determined by the distribution of mass. For a spherically symmetric mass, like a planet, these surfaces are concentric spheres. For irregularly shaped masses, the surfaces can be more complex and are determined through mathematical modeling.

## Can gravitational equipotential surfaces intersect each other?

No, gravitational equipotential surfaces cannot intersect each other. If they did, it would imply that a point in space has two different gravitational potential values at the same time, which is impossible.

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