a factor of
- A Since the centripetal force on each satellite is equal to the gravitational
force it feels due to the earth, the question is equivalent to, “How does FA, the
gravitational force on satellite A, compare to FB, the gravitational force on
satellite B?” Because both satellites have the same mass, Newton’s law of
gravitation tells us that the gravitational force is inversely proportional to r^2.
Since satellite B is 3 times farther from the center of the earth than satellite A,
the gravitational force that satellite B feels is the gravitational
force felt by satellite A. (Be careful if you tried to apply the formula
for centripetal force and concluded that the answer was (B). This is wrong
because even though both satellites orbit at a constant speed, they don’t orbit
at the same speed, so the formula for centripetal force cannot be used
directly.)
- C Since the centripetal force always points along a radius toward the center of
the circle, and the velocity of the object is always tangent to the circle (and
thus perpendicular to the radius), the work done by the centripetal force is
zero. Alternatively, since the object’s speed remains constant, the work–
energy theorem tells us that no work is being performed.
