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?
Find the speed of light for the laser. How much distance error does 0.19 * 10^-9 represent? Find how far the laser light travels in this time to find the error.
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To calculate the error in the earth-moon distance, we need to use the formula for the speed of light:
Speed of light = distance / time
Since the laser beam travels from Earth to the moon and back, the time it takes for the round trip is twice the measured time.
Round trip time = 2 * measured time
Now we can rearrange the formula to solve for the distance:
Distance = speed of light * round trip time
But first, let's convert the measured time accuracy from nanoseconds to seconds:
Measured time accuracy = 0.19 ns = 0.19 * 10^(-9) s = 1.9 * 10^(-10) s
Now we can substitute the values into the equation to calculate the distance:
Distance = speed of light * round trip time
Distance = speed of light * 2 * measured time
The speed of light is a constant value, approximately 299,792,458 meters per second.
So the distance = 299,792,458 m/s * 2 * measured time
Now, let's substitute the measured time accuracy into the equation:
Distance = 299,792,458 m/s * 2 * 1.9 * 10^(-10) s
Calculating the above equation will give us the corresponding error in the earth-moon distance.