# II.6 Measuring the Earth - Moon Distance with a Laser

## 1. Principle of this measurement

From the Earth, a flash of light is sent towards the Moon. This light is reflected back to the Earth with a reflector which was placed on the Moon ground by members of an Apollo mission. The duration of the travel of the light there and back dt is measured, and as the velocity of light is well known, the Earth-Moon distance can then be computed.

### Suggestion:

Find the average distance Earth-Moon from the the books you have, or among the data on the server, or the minimum and maximum distances between these two celestial bodies, and find out the exact value of the velocity of light. Then, infer the duration of the light travel time (to the Moon and back) in those cases.

## 2. How is this experiment performed in reality?

### Suggestion:

Look for real results of an experiment made by CERGA in the "Côte d'Azur Observatory" in France: P>

1. Duration: dt
2. Value of the velocity of light they use: c
3. Duration of the flash
4. Energy of the flash
5. Instruments used to measure durations
6. Energy collected back
7. Wavelength L of the Laser ray
8. Structure of the reflector on the Moon
Otherwise, you can use the following results (coming from F. Mignard at CERGA):
1. Duration:
dt: it depends on the Earth-Moon distance when the measurement is performed.
Average dt = 2.55 seconds
2. c = 299 792 458 m/s
3. Duration of the impulse: 130 ps
4. Impulse energy: 0.25 J
5. Time measurements:
• Detection-emission by InAsGa diod
• Return detection by avalanche Si diod
• Duration by Dassault electronic and Cesium Clock
6. Returned energy: 7 * 10-20 J i.e. 1 photon for 50 shootings
7. L: 532 nm
8. Receptor on the Moon: retroreflectors net on a cube corner, with a 5x5 cm entrance pupil on aone square meter board.

### Using real values:

Compute the Earth-Moon distance with these values.

How accurate is the measurement? Is it the distance between Earth and Moon, or between the the CERGA laboratory telescope and the reflector on the Moon?

## 3. The reason for using a Laser

### Calculate:

What would be the energy received by the reflector on the Moon (surface: s), at the distance D, if all the energy coming from the source was sent out in all directions?

If we assume that the reflector is a source sending the light in half a sphere, compute what would then be the energy received on Earth by the receiver (surface: s' ).

### Suggestion:

At the CERGA site, look for the "aperture" of the light beam sent to the Moon, and the aperture of the reflected beam.

Otherwise, use the following data:

Aperture of the emitted beam out of the atmosphere: 5 seconds of arc, i.e. 10 km on the Moon.

Aperture of the returned beam: 3 seconds of arc i.e. 6 km on the Earth.

Make the previous calculations with this values.

If you can get a plan of the reflector, see the trajectory of the light rays. Show it was conceived to send the reflected light back in the same direction as the incident light whatever it may be.

### Try to answer this:

Why is a Laser used instead of ordinary light?

## 4. Conclusions

### Suggestion:

Ask astronomers what use are these measurements and which new knowledge they have brought.

Author: Frederic DAHRINGER, CLEA.