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.
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Gravitational Field Strength - help12
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 ________.
4/3
3/2
2
3
4
9/2
12
You are given two locations - A and B - in the space surrounding two different planets. The g value for the two locations differ for two reasons - the planet mass creating the gravitational field is different for the two locations and the distance from the location to the center of the planet is different. 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. You will have to consider both of these factors.
The relationship between the gravitational field strength (g) and the variables that affect it is given by the following porportionality:
For two locations in the example problem above (see About This Question), Location B has three times the planet mass. This factor tends to make the g value greatest for Location B. However Location A is closer to the planet's center. Since the g value and distance (squared) are inversely proportional, Location A's smaller distance makes the g value greatest for Location A. So the two factors - the planet mass factor and the distance factor - are in competition with each other. Because of this, the only way to determine which location has the greatest g value is to compare the Mplanet/d2 ratio for each. That is, compare the size of M/(R)2 for Location A (in the example) to 3M/(2R)2 for Location B. Whichever evaluates to the largest value has the largest g value.
You must also determine how many times greater the g value is for one location compared to the other location. This quantitative comparison involves finding the ratio of the larger g value to the smaller g value. Simply take the ratio of the two expressions M/(R)2 and 3M/(2R)2. If you are divinding the larger value by the smaller, then you will get a number greater than 1.
Try this link to The Physics Classroom Tutorial for more help with understanding gravitational field strength:
The Value of g