Astronomy Principles and Practice Fourth Edition.pdf

126 The reduction of positional observations: I
near the observer’s meridian at midnight. Observations are made a few hours before midnight and
a few hours after midnight. Before the development of radar, many observatories carried out such
observing programmes, notably between 1900 and 1901 and between 1930 and 1931, when Eros was
in opposition. The value of the solar parallax (see section 10.4) derived from these programmes was
probably not any more accurate than one part in a thousand.
Nowadays, the use of powerful radio telescopes as radar telescopes has enabled the accuracy to
be increased by a factor of at least one hundred. The geocentric distance of the planet Venus has been
measured repeatedly by this method. It consists essentially of timing the interval between transmission
of a radar pulse and the reception of its echo from Venus. This interval, with a knowledge of the velocity
of electromagnetic radiation (the speed of light) enables the Earth–Venus distance to be found. Thus,
if EV, c and t are the Earth–Venus distance, velocity of radio waves and time interval respectively,
EV = 1 2 ct.
Various corrections have to be made to derive the distance Venus-centre to Earth-centre. For
example, the distance actually measured is the distance from the telescope to the surface of Venus. The
effect of the change of speed of the radar pulse when passing through the ionosphere also has to be
taken into account.
An even more accurate value of the solar parallax has been obtained by tracking Martian artificial
satellites such as Mariner 9 over extended periods of time. Range and range rate measurements (i.e.
line of sight distance and speed by radio tracking) allow the distance Earth-centre to Mars-centre to be
found.
10.7 Stellar parallax
10.7.1 Stellar parallactic movements
The direction of a star as seen from the Earth is not the same as the direction when viewed by a
hypothetical observer at the Sun’s centre. As the Earth moves in its yearly orbit round the Sun, the
geocentric direction (the star’s position on a geocentric celestial sphere) changes and traces out what is
termed the parallactic ellipse. Thus, in figure 10.10, the star X at a distance d kilometres is seen from
the Earth at E 1 to lie in the direction E 1 X 1 relative to the heliocentric direction SX ′ . Six months later,
the Earth is now at the point E 2 in its orbit and the geocentric direction of the star is E 2 X 2 .
The concepts used in stellar parallax are analogous to those used in geocentric parallax. Thus, if
we looked upon the Earth’s orbital radius a as the base-line, we can define the star’s parallax as P,
given by
sin P = a d . (10.30)
Because stellar distances are so great compared with the Earth’s orbital radius, we can assume
that the Earth’s orbit to be circular. Angle P is small so that we can write equation (10.30) as
P = 206 265 a d
where P is in seconds of arc.
Again, if we draw E 1 Y parallel to SX in figure 10.10 and let YE 1 X = E 1 XS = p, wehave,
from △E 1 XS,
sin p
= sin XE 1S
a d
or
sin p = a d sin XE 1S.