Final answer:
The radius of the orbit of a synchronous satellite can be found using the equation vorbit = 2πr/T, where vorbit is the orbital speed, r is the radius of the orbit, and T is the period of the satellite. For a synchronous satellite with a period of 24 hours and an orbital speed of 500 km/hr, the radius of the orbit is approximately 1.40 x 10^5 km.
Step-by-step explanation:
The orbital radius of a synchronous satellite can be found using the equation vorbit = 2πr/T, where vorbit is the orbital speed, r is the radius of the orbit, and T is the period of the satellite.
To find the radius of the orbit, we rearrange the equation to get r = vorbit * T / (2π).
For a synchronous satellite, the period T is equal to 24 hours (or 86400 seconds). Let's say the orbital speed vorbit is 500 km/hr. Substituting these values into the equation, we get r = (500 km/hr) * (86400 s) / (2π).
Calculating the value using the given units and constants, we find that the radius of the orbit is approximately 1.40 x 10^5 km.