Astronomy Principles and Practice Fourth Edition.pdf

Measuring distance in the Solar System 125
Figure 10.9. Measurement of the Moon’s distance by observations from two sites.
so that P may be calculated from known and measured quantities. Knowing the radius of the Earth,
the geocentric distance CM of the Moon can be found from equation (10.18).
In practice, the procedure is complicated by a number of factors. The observatories are never quite
on the same meridian of longitude so that a correction has to be made for the change in the Moon’s
declination in the time interval between its transits across the two observatories’ respective meridians.
In addition, the Moon is not a point source of light. Agreement, therefore, has to be made between
the observatories as to which crater to observe, a correction thereafter giving the distance between the
centres of Earth and Moon.
Due allowance must be made for the individual instrumental errors and the local values of
refraction. In the case of the Moon, its parallax is so large that any residual error is not great.
Since the advent of radar, laser methods and lunar probes, including lunar artificial satellites, the
Moon’s distance can be measured very accurately. The limiting accuracy is partly due to the accuracy
with which the velocity of light is known but also involves the accuracy with which the Earth observing
stations’ geodetic positions are known. Uncertainties are of the order of 0·1 ofametre, the average
distance being 384 400 kilometres. See also section 15.9.
10.6.2 The planets
It will be shown later (section 12.7) that it is relatively easy to obtain accurately the distances of
the planets from the Sun in units of the Earth’s distance from the Sun. If, therefore, the distance
of any planet from the Earth can be accurately measured in kilometres at any time, all the planetary
heliocentric distances can be found in kilometres. In particular, the astronomical unit (the mean
distance of the Earth from the Sun) can be obtained in kilometres.
All the classical parallax methods are hopelessly inaccurate where the distance of a planetary body
is concerned. The Moon’s distance is about thirty times the Earth’s diameter, which is essentially the
length of the available base-line. The distance of the asteroid Eros, at its closest approach, however, is
some 20 000 000 km, or about 1500 times the length of the base-line. Table 10.2 (p 121) shows that it
is not possible to obtain the geocentric parallax of Eros to high accuracy by this method.
Some improvement in accuracy is obtained by using one observatory, instead of two. In this
way, the factors of different instrument errors and weather conditions, which control refraction, can
be avoided. The base-line is provided by taking observations of the asteroid at different times so that
in the time interval involved, the observatory moves due to the Earth’s diurnal movement and orbital
motion. The observing programme is carried out around the time of opposition when the planet is