3. Astronomers observe a new comet approaching the sun. They obtain the

location of the comet relative to the sun, and the velocity of the comet. But they don't have

long-term data to directly tell whether the trajectory of the comet is an ellipse or a hyperbola.

Still, astronomers can figure it out. After all, an elliptical orbit means that the comet is

gravitationally bound to the sun: it can never escape to an infinite distance. But a hyperbolic

trajectory extends to infinity: the comet is unbound and must escape the Sun's gravity.

Chose, from the following options, the test that astronomers can apply, using their position

and velocity observations, that distinguishes between a bound and an unbound comet. If an

option is incorrect, briefly explain why. If it is correct, give the exact inequality they will

apply, using the velocity and distance to the sun of the comet, and if needed, data about other

objects in the solar system. State whether the inequality indicates a bound or unbound comet.

(a) Lcomet > LEarth. (Compare angular momenta.)

(b) Ecomet > 0. (The total orbital energy of the comet is positive.)

(c) Icomet > ISun (Compare moments of inertia.)

(d) Apcomet > Fcomet. (Compare the momentum change to the gravity on the comet.)

(e) Tcomet > 0. (The total torque on the comet is positive.)