# Gravity at Earth's Center

• Teacher Resource
• Posted 08.26.08
• NOVA

In this video adapted from NOVA scienceNOW, investigate the hypothetical scenario of a person falling into a hole through the center of Earth. Astrophysicist Neil deGrasse Tyson illustrates the thought experiment; first he defines the conditions—ignore the effects of air resistance, temperature, and Earth's rotation—and then he travels through the hole. A timer and speedometer show how his speed changes as he falls toward the center of Earth, passes the center, and slows to a stop at the opposite end of the hole.

• Media Type: Video
• Running Time: 1m 46s
• Size: 5.3 MB

Source: NOVA: "Hole Through the Earth"

## Background

Gravity is a fundamental force of nature; it is an attractive force between any objects that have mass. The strength of gravity between everyday objects, such as a desk and a chair, is extremely small—too small to be noticed, in fact. However, because the strength of gravity is proportional to the masses of the objects, it is easy to observe the effects of gravity between an object that is very massive, such as Earth, and another object. For instance, objects fall toward Earth's surface because of the force of gravity between Earth and the object; a simple bathroom scale measures your weight—the force of gravity between you and Earth. Note that the force of gravity acts on both objects; Earth is attracted to you, just as you are attracted to Earth.

Depending on the location of an object relative to Earth—whether it is at Earth's surface, some distance away, or within the planet—the strength of gravity will vary. At Earth's surface, the acceleration due to gravity is about 9.8 m/s2; that is, with every second that passes, the downward speed of a falling object increases by 9.8 m/s2. However, for an object located high above Earth's surface, the acceleration due to gravity is less than 9.8 m/s2. This is because the force of gravity is related to the distance between the objects; it is inversely proportional to the square of the distance between the objects. In other words, as two objects move farther away from one another, the force of gravity between them decreases. Therefore, the farther an object is from Earth, the weaker the strength of gravity between them.

But what is gravity like within Earth? How would gravity affect an object in a hypothetical hole through the center of Earth? At the center of the planet, Earth's mass completely surrounds the object, pulling it outward in every direction. Assuming, for this thought experiment, that Earth is spherically symmetric and of uniform density, the attractive force between the object and each part of Earth would counteract a corresponding attractive force from the opposite direction. Consequently, the net gravitational force on the object would be zero.

Following this logic, the net gravitational force on an object inside a uniform spherical shell is always zero. At a given radius from Earth's center, the portion of Earth outside of that radius can be considered a shell; the net force of gravity on an object at a given radius from Earth's center is due only to the mass of Earth within that radius. As a result, as the object approaches the center of the planet and the radius decreases, the acceleration due to gravity would also decrease. Although the rate of change of velocity decreases, the object would continue to increase in velocity until it passes through the center of Earth.

To learn more about how gravity affects the motion of objects on Earth, check out Galileo: His Experiments and Projectile Motion.

## Questions for Discussion

• How would you account for the change in velocity as the person falls through Earth from one side to the other?
• Neil deGrasse Tyson says that it takes 14 minutes to reach a point halfway to the center of Earth and that it takes 21 minutes to reach the center itself. Why does it take 14 minutes to go the first half of the distance but only 7 minutes to go the second half?
• What happens as he passes the center of Earth? Why would he cycle back and forth forever?
• Why is this scenario impossible? Give several reasons.
• How do you think scientists know what would happen to a falling object, if such a hole existed?

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