Astronomy Principles and Practice Fourth Edition.pdf

432 Practical projects
24.5.4 The eccentricity of the Earth’s orbit
Inspection of the AA shows that the apparent solar diameter changes from
a maximum of 16 ′ 15·′′ 9onJanuary4thto
a minimum of 15 ′ 43·′′ 1onJuly4th
this being caused by the variation in the distance of the Earth from the Sun according to the eccentricity
of its orbit.
If care is taken in making solar drawings with the same equipment throughout the year, with the
image board holding the paper kept at a constant distance from the telescope, the variation in the size of
the solar disc can be recorded and a value obtained for the eccentricity of the Earth’s orbit. Investigation
of the figures just given shows that the variation in the apparent size of the solar disc is about 3·5%. In
order to detect this and measure it reasonably well over the year, the diameter of the projected image
must be of the order of 100 mm giving a variation of about 3·5 mm.
24.5.5 Use of a pinhole camera
The simplest means of taking photographs of the Sun is with a pinhole camera. In this system, a
tiny hole acts as a lens and the image that it produces can be recorded on film. A very convenient
arrangement has the pinhole at one end of a long tube, blackened on its inside, with the body of a
single lens reflex camera, without its lens, at the other end.
For the pinhole camera to give reasonable images, the focal ratio must be f/1000 or higher. Thus,
a 1 mm hole attached to a 1 m tube is sufficient. Since the Sun subtends about 1/2 ◦ , its image with a
1 m tube is equal to
1000
× π mm = 8·7 mm.
2 180
Even with such a focal ratio, the illumination of the Sun’s image is high and a typical exposure
of 1/1000th of a second is required using Pan X film. The demand for an extremely high shutter speed
may be relaxed by using either a higher focal ratio, filters over the pinhole or a slower film or even a
photosensitive photographic paper rather than celluloid film.
A pinhole camera under good conditions is capable of allowing pictures of sunspots to be taken
and is useful for recording the shape of the Sun, say at the time of a partial eclipse or when the Sun is
just rising or setting.
When a celestial object is on the horizon, refraction alters its true altitude by over half a degree
(see section 10.2). For an extended object such as the Sun, refraction has a differential effect so that
the lower limb is more refracted than the upper limb. Thus, when the Sun is close to the horizon, it has
an elliptical shape with the lower and upper limbs closer together than the east and west limbs. The
distortion is easily seen with the unaided eye at a location where there is an uninterrupted view of the
horizon. It may be photographed using a pinhole camera. (An ordinary camera is generally insufficient
because of its short focal length.) From measurements of the images, a value for the differential
refraction may be determined.
24.5.6 Atmospheric extinction
A pinhole camera arrangement is also a suitable means for measuring the apparent solar brightness. If,
at the bottom of the light-type tube as described earlier, a solid state photodiode is placed with means
of measuring the ensuing current, the response to solar radiation may be recorded as the zenith distance
changes.
The size of the photosensitive area with respect to the solar image is not too important. When
making a measurement, the tube should be directed towards the Sun and the maximum reading taken