A spacecraft in orbit around the moon measures its altitude by reflecting a pulsed 10Mz radio signal from the surface. If the spacecraft is 10km high what is the time between the emission of the pulse and the detection of the echo?
TIME= 2* DISTANCE/SPEEDLIGHT
To calculate the time between the emission of the pulse and the detection of the echo, we need to consider the round-trip time for the radio signal.
The round-trip time can be calculated by doubling the time it takes for the radio signal to travel from the spacecraft to the surface of the moon and back.
The speed of light is approximately 3 x 10^8 meters per second. To find the round-trip time, we can divide the distance traveled by the speed of light.
Given that the spacecraft is 10 km high, the total distance traveled is 2 times the altitude:
Total distance traveled = 2 x 10 km = 20 km
Converting the distance to meters, we have:
Total distance traveled = 20,000 meters
Now we can calculate the round-trip time:
Round-trip time = Total distance traveled / speed of light
Round-trip time = 20,000 m / (3 x 10^8 m/s)
Simplifying the calculation:
Round-trip time ≈ 6.67 x 10^-5 seconds
Therefore, the time between the emission of the pulse and the detection of the echo, or the round-trip time, is approximately 6.67 x 10^-5 seconds.
To determine the time between the emission of the pulse and the detection of the echo, we need to calculate the round-trip time it takes for the radio signal to travel from the spacecraft to the moon's surface and back.
First, let's calculate the distance traveled by the radio signal. The spacecraft is 10 kilometers high above the moon's surface, so the total distance traveled will be twice this value (upward plus downward journey).
The total distance traveled by the radio signal: 2 * 10 km = 20 km
Now, we can use the speed of light to calculate the time it takes for the radio signal to cover this distance. The speed of light is approximately 299,792 kilometers per second.
Time taken = Distance / Speed
Time taken = 20 km / 299,792 km/s = 0.0000668 seconds or 66.8 microseconds
Therefore, the time between the emission of the pulse and the detection of the echo is approximately 66.8 microseconds.