Final answer:
To calculate the orbital period and velocity for a satellite orbiting Planet Alpha Omega, convert its diameter to radius, add the altitude for the total orbital radius, use the gravitational constant and the mass of the planet to calculate the velocity, and finally determine the period using the orbital radius and velocity.
Step-by-step explanation:
To calculate the orbital period and velocity for a satellite orbiting Planet Alpha Omega, we need to consider the given mass of the planet, its diameter, and the altitude at which the satellite is orbiting. First, we convert the diameter to radius by dividing it by two, then we add the altitude to that radius to get the orbital radius. Using orbital mechanics formulas, we then calculate the velocity and period using the gravitational constant.
Step 1: Convert diameter to radius
Radius of Alpha Omega = Diameter / 2
Radius of Alpha Omega = 20,300 km / 2 = 10,150 km
Orbital radius including altitude = Radius of Alpha Omega + Altitude
Orbital radius = 10,150 km + 720 km
Orbital radius = 10,870 km
Orbital radius in meters = 10,870 × 1,000 = 10,870,000 m
Step 2: Calculate velocity
Orbital velocity (v) = √((G × M) / r)
Where G is the gravitational constant (6.674 × 10^-11 N m^2/kg^2), M is the mass of Alpha Omega, and r is the orbital radius.
Step 3: Calculate orbital period (T)
T = 2πr / v
Without doing the actual math, the steps above are what's necessary to calculate both the orbital period and velocity for the satellite. However, without a calculator or computation in the response, the actual values for the period and velocity are not provided.