You are given three locations, all a different distance from a different planet. The furthest distance (2R) is two times further than the nearest distance (R). The planets have different mass, with the biggest mass (3M) being three times the smallest mass (M). You must rank the gravitational field strength (g) for the three locations. To do so you must understand how g depends upon planet mass (Mplanet) and distance (d).
The relationship between the gravitational field strength (g) and the variables that affect it is given by the following porportionality:
![](/getmedia/6cc7bc4f-14ed-4a69-a242-02c3f220a099/gProportional?width=222&height=40)
Since both planet mass and distance vary for the three locations, you must include both variables in your ranking considerations. The proportionality states that g will be greatest for planets with the greatest mass. It also states that g will be smallest for locations with the greatest distance. That is, gravitational field strength is inversely proportional to distance squared. Combining the two effects would lead to the conclusion that a calculation of the M/d2 ratio is the only means for comparing the strength of the gravitational fields for these three locations.
So the answer demands that the following ratios be calculated and compared:
0.5•M/(R)2, 2•M/(R)2, M/(2•R)2
So organize yourself, perform the calculations, and then rank the three locations based on a comparison of the calculated results.