Gravitational Field Strength - Questions 16 Help

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Massive objects like planets create noticeable gravitational fields in the space that surround them. Other masses, interacting with these fields, are pulled inwards towards the planet. The strength of such fields at any given location is directly proportional to the mass of the planet and inversely proportional to the square of the distance of that location to the planet's center.

There are three similar versions of this question. Here is one of those versions:

Version 1:

The value of the gravitational field strength at location X is 2.35 N/kg. Determine the gravitational field strength (in N/kg, accurate to the second decimal place) on the surface of the planet (location Y).

You are given two locations - X and Y - in the space surrounding a planet. The g value for Location X is given. You must determine the g value for Location Y. Doing so demands that you use the inverse square relationship between gravitational field strength and distance. The inverse part of inverse square means that as the distance from the planet's center gets larger the g value gets smaller. So further distances have smaller g values. The square part of inverse square means that the g value varies with the square of the distance. And so for a twice-as-far-away location, the g value is one-fourth as much. And for a three-times-as-far-away location, the g value is one-ninth as much. And for a four-times-as-far-away location, the g value is 1/16-th as much.

Applying the Inverse Square Law
Now you must apply the inverse square law discussed in the previous paragraph. In the example given above (see About This Question), Location X is two times further from the planet's center than Location Y. You can determine this distance ratio by observing the concentric circles drawn about the planet's center. Location X is on the second circle; we'd call this a distance of 2•R. Location Y is on the first circle or planet's surface; we'd call this a distance of 1•R. Being one-half as far away, the g value of Location Y is four times the g value of Location X. So multiply the g value of Location X by 4.0 to determine the g value of Location Y.

Try this link to The Physics Classroom Tutorial for more help with understanding gravitational field strength:

The Value of g