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A satellite orbits the Earth at a speed of 1000 m⁄s. Given that the mass of the Earth is  kg and the universal gravitational constant is  N · m2 ⁄ kg2, what is the best approximation for the radius of the satellite’s orbit? |
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(A) |
 m |
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(B) |
 m |
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(C) |
 m |
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(D) |
 m |
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(E) |
 m | |
What’s the universal gravitational constant? Some people will know that this is the
G in the equation for Newton’s Law of Gravitation:
. Other people won’t know that
G is called the “universal gravitational constant,” and ETS will have successfully separated the wheat from the chaff. It’s not good enough to know some formulas: you have to know what they mean as well.
Given that we know what the universal gravitational constant is, how do we solve this problem? Well, we know the satellite is moving in a circular orbit, and we know that the force holding it in this circular orbit is the force of gravity. If we not only know our formulas, but also
understand them, we will know that the gravitational force must be equal to the formula for centripetal force,
. If we know to equate these two formulas, it’s a simple matter of plugging in numbers and solving for
r.
Knowing formulas, however, is a small part of getting the right answer. More important, you need to know how to put these two equations together and solve for r. On their own, without understanding how to use them, the equations are useless.
But there are two slightly underhanded ways of getting close to an answer without knowing any physics equations. These aren’t foolproof methods, but they might help in a
Slightly Underhanded Way #1: Elimination through Logic
By scanning the possible answer choices, you can see that the answer will begin either with a 4 or a 2.5. There are three options beginning with 4 and only two beginning with 2.5. Odds are, the correct answer begins with 4. The test makers want to give you answer choices that are close to the correct answer so that, even if you’re on the right track, you might still get caught in a miscalculation.
Second, make a rough estimate. At what sorts of distances might a satellite orbit? We can eliminate A immediately: that answer has our satellite orbiting at 4 cm from the center of the Earth! That leaves us with a choice between B and C. Those aren’t bad odds for guessing.
Slightly Underhanded Way #2: Work with the Letters
This is a method for those of you who like manipulating equations. From looking at the answer choices, you know the answer will be in meters. You’ve been given three quantities, one expressed in m/s, one expressed in kg, and one expressed in N·m2/kg2. These are the only three quantities you’ll be asked to draw upon in order to get your answer. Because F = ma, you know you can substitute kg·m/s2 for N. So a quantity expressed in N·m2/kg2 can equally be expressed in m3/kg·s2.
