Final answer:
The distance above the surface of Venus is approximately 1.05 × 10^7 km.
Step-by-step explanation:
To determine the distance above the surface of Venus, we need to calculate the radius of the orbit of the Magellan orbiter. 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. We can rearrange the formula to solve for the semimajor axis:
a = (T^2 * G * M) / (4π^2)
Where a is the semimajor axis, T is the orbital period, G is the gravitational constant, and M is the mass of Venus.
Plugging in the values given:
a = (3.26^2 * 6.67430 × 10^-11 * 4.87 × 10^24) / (4π^2)
a = 1.05 × 10^7 km
The distance above the surface of the planet is then the semimajor axis minus the radius of Venus:
Distance = a - r
Distance = (1.05 × 10^7) - (6.05 × 10^3)
Distance = 1.05 × 10^7 km