Final answer:
To calculate the radius of a geosynchronous orbit, we can use Kepler's third law and the orbital period of 1 day. Plugging in the values for the gravitational constant and the mass of the Earth, we can calculate the radius of the orbit to be approximately 2.75 × 10^4 km.
Step-by-step explanation:
To calculate the radius of the geosynchronous orbit of a communication satellite, we need to use a combination of formulas. The orbital period of a satellite is given as 1 day, which is equivalent to 24 hours. Using Kepler's third law, we can relate the orbital period, T, to the radius of the orbit, R: T = 2π√(R³/(G*M)), where G is the gravitational constant and M is the mass of the Earth. Rearranging the formula, we can solve for R: R = (∛((T²*G*M)/(4π²))). Plugging in the known values, G = 6.67 × 10^-11 Nm²/kg² and M = 5.97 × 10^24 kg, we can calculate the radius of the orbit.
Plugging in the values, we have R = (∛((24² * 6.67 × 10^-11 * 5.97 × 10^24)/(4π²))) = (∛(2.28 × 10^14)) = 2.75 × 10^4 km. Therefore, the radius of the orbit is approximately 2.75 × 10^4 km.