The distance between earth and the moon can be determined from the time it takes for a laser beam to travel from earth to a reflector on the moon and back. If the round-trip time can be measured to an accuracy of 0.19 of a nanosecond (1 ns = 10-9 s), what is the corresponding error in the earth-moon distance?
To determine the corresponding error in the Earth-Moon distance, we need to use the speed of light as a factor since the laser beam is traveling at the speed of light.
The speed of light is approximately 299,792,458 meters per second. Since the beam makes a round trip from Earth to the Moon and back, the total distance it travels is twice the Earth-Moon distance.
Let's call the Earth-Moon distance "D." Therefore, the total distance traveled by the laser beam is 2D.
Now, we need to calculate the time it takes for the beam to travel 2D. The time is given as 0.19 nanoseconds, which is 0.19 × 10^(-9) seconds.
Using the formula:
Speed = Distance / Time
We can rearrange the formula to solve for distance:
Distance = Speed × Time
Substituting the values:
Distance = (299,792,458 m/s) × (0.19 × 10^(-9) s)
Calculating this, we find:
Distance = 56.96 m
This means that the beam travels a distance of 56.96 meters during the measured time of 0.19 nanoseconds.
To determine the corresponding error in the Earth-Moon distance, we can assume that the error in the round-trip time corresponds to twice the error in the measured time. In this case, the error is 0.19 nanoseconds.
Therefore, the error in the Earth-Moon distance is:
Error = 2 × (56.96 m × 0.19 × 10^(-9) s)
Calculating this, we find:
Error ≈ 0.216 meters
So, the corresponding error in the Earth-Moon distance is approximately 0.216 meters.
How far does light travel in .19ns?
distanceerror=c*deltatime
that will give you the distance error