The Apollo 11 astronauts set up a panel of efficient...

The Apollo 11 astronauts set up a panel of efficient corner-cube retroreflectors on the Moon's surface (Fig. 35.8 $\mathrm{a}$ ). The speed of light can be found by measuring the time interval required for a laser beam to travel from the Earth, reflect from the panel, and return to the Earth. Assume this interval is measured to be 2.51 $\mathrm{s}$ at a station where the Moon is at the zenith. What is the measured speed of light? Take the center-to-center distance from the Earth to the Moon to be $3.84 \times 10^{8} \mathrm{m}$ . Explain whether it is necessary to consider the sizes of the Earth and the Moon in your calculation.

The Apollo 11 astronauts set up a panel of efficient corner-cube retroreflectors on the Moon's surface (Fig.
35.8 $\mathrm{a}$ ). The speed of light can be found by measuring the time interval required for a laser beam to travel from the Earth, reflect from the panel, and return to the Earth. Assume this interval is measured to be 2.51 $\mathrm{s}$ at a station where the Moon is at the zenith. What is the measured speed of light? Take the center-to-center distance from the Earth to the Moon to be $3.84 \times 10^{8} \mathrm{m}$ . Explain whether it is necessary to consider the sizes of the Earth and the Moon in your calculation.

Key Concepts

Time-of-Flight Measurement

This key concept involves determining the speed of light by measuring the time it takes for a light pulse to travel to a distant target and return. In practice, a laser beam is sent from Earth to a reflector and the round-trip time is recorded. The speed of light is then calculated by dividing the total distance traveled (which is twice the one-way distance) by the measured time, exemplifying the application of the formula v = (2d)/t in physical measurements.

Round-Trip Distance Calculation

This concept emphasizes that when a light signal is sent from a source and reflected back, the total distance covered by the light is twice the one-way distance to the target. Understanding and applying this factor is crucial when computing the speed of light from the time-of-flight data, ensuring that the calculation correctly accounts for the light's journey to the target and back.

Negligibility of Finite Object Sizes in Astronomical Measurements

In many astronomical measurements, such as determining the speed of light between Earth and the Moon, the sizes of the objects (like the Earth and Moon) are small compared to the center-to-center distances used. This concept highlights that, for the purpose of these calculations, the physical dimensions of the bodies can be ignored unless they introduce significant error. The error induced by not accounting for their finite sizes is negligible relative to the overall separation distance in space.

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