Copyright

Gravitational Field: Definition & Formula

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Magnetic Poles: Definition & Shifts

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 What is a Gravitational Field?
  • 1:20 Formula
  • 4:55 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Log in or Sign up

Timeline
Autoplay
Autoplay
Speed

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Thomas Zesiger

Thomas has taught electronics and communications engineering, math, and physics and has a master's degree in electrical engineering.

This lesson defines what a gravitational field is and some practical examples encountered in the real world. We also develop the equations governing the gravitational field and explain what the units of measurement mean.

What Is a Gravitational Field?

A gravitational field is the force field that exists in the space around every mass or group of masses. This field extends out in all directions, but the magnitude of the gravitational force decreases as the distance from the object increases. It is measured in units of force per mass, usually newtons per kilogram (N/kg). A gravitational field is a type of force field and is analogous to electric and magnetic fields for electrically charged particles and magnets, respectively.

There are two ways of showing the gravitational field around an object: with arrows and with field lines. Both of these are shown in the picture below. Arrows show the magnitude and direction of the force at different points in space. The longer the arrow, the greater the magnitude. Field lines show the direction the force would act on an object placed at that point in space. The magnitude of the field is represented by the spacing of the lines. The closer the lines are to each other, the higher the magnitude.

Arrows and field lines that represent gravitational field
Illustrations of gravitational field about an object using arrows and field lines

The gravitational field varies slightly at the earth's surface. For example, the field is slightly stronger than average over subterranean lead deposits. Large caverns that may be filled with natural gas have a slightly weaker gravitational field. Geologists and prospectors of oil and minerals make precise measurements of the earth's gravitational field to predict what may be beneath the surface.

Formula

The earth and moon exert a force, or pull, on each other even though they are not in contact. In other words, the two bodies interact with one another's gravitational field. Another example is the interaction of the earth and a satellite in orbit around it.

From these examples, Newton developed the law of universal gravitation. The law of universal gravitation says that every object exerts a gravitational pull on every other object. The force is proportional to the masses of both objects and inversely proportional to the square of the distance between them (or the distance between their centers of mass if they are spherical objects). Using variables, we write F is proportional to mM/d^2, where F is the force, m is the mass of the smaller object, M is the mass of the larger object, and d is the distance between the two objects.

In 1798, English physicist Henry Cavendish performed precise measurements of the actual gravitational forces acting between masses using a torsion balance. The outcome of his experiment resulted in the constant of proportionality in the law of universal gravitation called the universal gravitational constant. Inserting this into the proportionality results in the equation F = G(mM/d^2). The value for G is 6.67 x 10^-11 newton-meters squared per square kilogram (N-m^2/kg^2).

The following is a diagram of the torsion balance set up used by Cavendish to determine the universal gravitational constant.

Diagram of torsion balance set up
Diagram of torsion balance set up used by Cavendish to determine universal gravitational constant

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support