SCN3797-ABED_1: 9.2 Review of Gravitational Fields

A vector equation emphasizes that the gravitational field and the gravitational force act in the same direction.

This equation provides a way to calculate the strength of the gravitational field in newtons per kilogram. Gravitational field strength can also be calculated in another way. Substituting Newton's law of universal gravitation into the previous equation leads to an alternative equation that describes gravitational field strength.

Both equations for calculating the magnitude of the gravitational field for a point in space contain a mass variable, but these masses refer to different things.

Did you know

In Physics 20 you normally used m/s 2 as the units for gravitational fields, which works very well for kinematics. In Physics 30 you will see N/kg, which is similar to the units for electric field strength of N/C.

\frac{N}{k g} = \frac{\frac{k g \cdot m}{s^{2}}}{k g} = \frac{m}{s^{2}}

Self-Check 1

Use the data from "Table 4.1" on page 218 of your textbook to calculate the gravitational field strength on the surfaces of Mars and Jupiter.

Given

Required

The gravitational field strength at the surface of Mars.

The gravitational field strength at the surface of Jupiter.

Analysis

Paraphrase

The gravitational field strength on the surface of Mars is 3.70 N/kg.

The gravitational field strength on the surface of Jupiter is 24.8 N/kg. The new gravitational force is 16 times larger than the original force.

Self-Check 2

An astronaut in her space suit has a mass of 105.5 kg. Use your answers from the previous question to determine the force of gravity that would act on this astronaut on the surface of each planet.

Suggested Answer

Given

Required

The magnitude of the gravitational force acting on the astronaut on Mars and on Jupiter.

Paraphrase

The magnitude of the gravitational force acting on the astronaut on Mars is 390 N.

The magnitude of the gravitational force acting on the astronaut on Jupiter is 2.62 × 10 ³ N.

Self-Check 3

Suppose a space probe moves from an initial position orbiting a planet to a final position that is only ¼ the distance away. Use the ratio method to determine how the value of gravitational field in the final position compares to the value of gravitational field in the initial position.