Final answer:
The required altitude of the orbit is approximately 881.7 km.
Step-by-step explanation:
To determine the required altitude of the orbit, we can use Kepler's third law. The period of an orbit is related to the radius of the orbit. The formula is given by: T^2 = 4π^2(a+r)^3/GM, where T is the period, a is the semi-major axis (radius of the orbit), r is the radius of the Earth, G is the gravitational constant, and M is the mass of the Earth. In this case, the period is given as 103.8 minutes. We can rearrange the formula to solve for the altitude:
a = (T^2 * GM / 4π^2)^(1/3) - r
Plugging in the values and solving:
a = ((103.8*60)^2 * 6.67x10^-11 * 5.98x10^24 / (4π^2))^(1/3) - 6.38x10^6
a ≈ 881.7 km
Therefore, the required altitude of the orbit is approximately 881.7 km.