Final answer:
To find the orbital radius, use Kepler's third law. To find the orbital speed, use the equation for calculating the speed of an object in circular orbit.
Step-by-step explanation:
To find the orbital radius of the Enterprise, we can use Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semimajor axis of the orbit. For a circular orbit, the orbital period is equal to the time it takes for the spaceship to complete one full revolution. Therefore, we can set up the equation as follows: (2.0 hours)2 = 4.0 hours2 = (orbital radius)3. Solving for the orbital radius, we find that it must be approximately 1.59 times the radius of Venus.
To find the orbital speed of the Enterprise, we can use the equation for calculating the speed of an object in circular orbit: V = 2πR/T, where V is the orbital speed, R is the orbital radius, and T is the orbital period. Substituting the given values, we get V = 2π(orbital radius)/(2.0 hours). Simplifying the expression, we find that the orbital speed must be approximately π times the radius of Venus per hour.