Final answer:
To find the radius of the satellite's orbit, we can use the formula for centripetal acceleration: a = v^2/r. Given that the satellite's speed is 3 km/s and the gravitational acceleration is 9.8 m/s^2, the radius of the orbit is approximately 915,306.1225 meters.
Step-by-step explanation:
To find the radius of the satellite's orbit, we can use the formula for centripetal acceleration: a = v^2/r. Rearranging this equation, we have r = v^2/a. Given that the satellite's speed is 3 km/s, we plug in this value for v. We also need to know the gravitational acceleration, which is the same as the acceleration due to Earth's gravity, approximately 9.8 m/s^2. However, we need to convert 3 km/s and 9.8 m/s^2 to the same units, so multiplying 3 km/s by 1000 m/km, we get 3000 m/s.
r = (3000 m/s)^2 / (9.8 m/s^2)
r = 915306.1225 m.
Therefore, the radius of the satellite's orbit is approximately 915,306.1225 meters.