# What is the Potential Function and Gravitational Field of Earth?

• frogger832
In summary, the conversation discusses finding the potential function and gravitational field of the earth and using those equations to determine the work required to get a satellite into orbit. The speaker also suggests referring to the textbook for a definition of potential function and the equation for gravitational force.
frogger832
I'm sorry if this sounds confusing. But I'm writing this question exactly how it is written in my textbook. I am stumped on this problem: Find the potential function and gravitational field of the earth. Then use those equations to determine the work that must be done to get a 100kg satellite into orbit. Ignore other planetary objects and relativity

Welcome to PF;
To ask that question, your text-book must have given you a definition of "potential function" - probably in relation to a force or a potential energy - and also the equation for the gravitational force between two masses. Go look for them and the way forward will become clearer.

## 1. What is the potential function of Earth's gravitational field?

The potential function of Earth's gravitational field is a measure of the work that would be required to move a unit mass from an infinite distance away to a specific point in the field. In other words, it is a measure of the potential energy of a mass at a particular point in space due to Earth's gravity.

## 2. How is the potential function of Earth's gravitational field calculated?

The potential function of Earth's gravitational field is calculated using the equation V = -GM/r, where G is the gravitational constant, M is the mass of Earth, and r is the distance from the center of Earth to the object. This is known as the inverse square law, which means that the potential function decreases as the distance from Earth's center increases.

## 3. What is the relationship between potential function and gravitational field strength?

The gravitational field strength at a point in Earth's gravitational field is equal to the negative gradient of the potential function at that point. This means that the strength of the gravitational field is directly proportional to the rate of change of the potential function at that point.

## 4. How does the potential function and gravitational field vary on different parts of Earth's surface?

The potential function and gravitational field on Earth's surface vary depending on the distance from the center of Earth, the distribution of mass within Earth, and the shape of Earth. This leads to slight variations in the strength of the gravitational field and potential function at different points on Earth's surface.

## 5. How does Earth's potential function and gravitational field affect objects on its surface?

Earth's potential function and gravitational field affect objects on its surface by exerting a force on them, causing them to accelerate towards the center of Earth. This force is what we experience as weight. The strength of this force depends on the mass of the object and the strength of Earth's gravitational field at that point.

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