Answer: To find the radius of the satellite's circular orbit around the Earth, we can use the following formula, which relates the speed (v) of the satellite, the radius (r) of the orbit, and the gravitational constant (G) to the mass (M) of the Earth:
v = √(G * M / r)
Given:
Speed of the satellite (v) = 3 km/s = 3000 m/s (converted to meters per second)
Mass of the Earth (M) = 5.972 × 10^24 kg (approximately)
Gravitational constant (G) = 6.67430 × 10^-11 m^3 kg^-1 s^-2
Now, let's rearrange the formula to solve for the radius (r):
r = G * M / v^2
Substitute the given values into the formula:
r = (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 5.972 × 10^24 kg) / (3000 m/s)^2
r = (3.9876034 × 10^14 m^3 kg s^-2) / 9 × 10^6 m^2/s^2
r ≈ 44,294,485.888 meters
Now, let's round the final answer to three decimal places:
r ≈ 44,294,485.888 meters ≈ 44,294,486 meters
The radius of the satellite's orbit around the Earth is approximately 44,294,486 meters.