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Fundamentals

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:

Two locations – A and B - are shown. Each has a different set of gravitational conditions. The relative planet mass (expressed in terms of M) and the relative distance of each location from the planet's center (expressed in terms of R) are shown.


The gravitational field strength is greatest at location ________ …
… by a factor of ________.
2
4
8
 

How to Think About This Situation

You are given two locations - A and B - in the space surrounding two different planets. The two locations are the same distance (R) from the center of the planet. Yet the two planets have different masses. So the locations differ only in terms of the planet mass - with one being 2•M and the other being M. You are asked to determine which location has the greatest gravitational field strength and you are asked to determine how many times greater it is.

The relationship between the gravitational field strength (g) and the variables that affect it is given by the following porportionality:

According to the proportionality above, the location that is surrounding the more massive planet will be the location with the greatest gravitational field strength. The above proportionality shows that the g value is directly proportional to the planet mass. So the location with two times the planet mass will have a g value that is two times greater than the other location.
 

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

The Value of g
 


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