Astronomy Principles and Practice Fourth Edition.pdf

282 Visual use of telescopes
For small telescopes, coated mylar disks may be fitted over the telescope aperture and these are
commercially available. An alternative and convenient way of viewing the solar image produced by a
small telescope, using a conventional eyepiece, is that of projection—see section 24.5.2.
Problems—Chapter 17
1. An f/10 telescope with a focal length of 3000 mm is used with an eyepiece of 2 mm focal length. What is
the magnifying power of the system Would the magnification allow all the collected light to enter the pupil
of the eye
2. The star with the largest apparent diameter subtends an angle of the order of 10 −7 radians. What size of
telescope would be required to resolve the star as a disc (Assume an effective wavelength of 5500 Å.)
3. An f/10 telescope has a diameter of 500 mm. What is the resolving power of the telescope and what is the
size of the Airy disc in the focal plane (Assume an effective wavelength of 5500 Å.)
4. An f/10 achromatic telescope has a diameter of 500 mm. The images of a star corresponding to the blue
and red ends of the spectrum are separated by 0·05 mm along the telescope’s axis. How does the size of the
circle of least confusion compare with the theoretical size of the Airy disc (Take the effective wavelength
as being 5500 Å for the Airy disc calculation.)
5. An f/12 reflecting telescope with a diameter of 300 mm suffers from spherical aberration. The longitudinal
spread of the image is given by F/F = 0·001. How does the size of the circle of least confusion compare
with the theoretical size of the Airy disc (Assume an effective wavelength of 5500 Å.)
6. Given two refracting telescopes A and B, the diameter of the objective of A being 1000 mm, calculate the
diameter of the objective of B if the limiting magnitudes of A and B are +16·m40 and +15·m40 respectively.
Neglect any light losses. Calculate the limiting magnitudes of A if one-fifth of the incident light is lost.
7. Calculate the diameter of a telescope in which the star ζ CMi (5·m11) would appear as bright as Sirius
−1·m58 to the unaided eye. (Assume that the diameter of the pupil of the eye is 8 mm and that 30% of the
light incident on the telescope collecting area is lost.)
8. Tycho’s supernova of 1572 attained its greatest brilliance at magnitude −4 on approximately October 1st and
thereafter began to fade, finally becoming invisible to the unaided eye on approximately March 1st 1574. If
the apparent brightness b at a time t after October 1st 1572 is related to the apparent brightness b 0 on that
date by the equation
b = b 0 10 −t/τ
where τ is a constant to be determined, find the last date (to the nearest month) on which observers could
have seen the nova if they had had a 150 mm telescope available.
9. A telescope with a focal length of 6000 mm is used to make double star observations. A turn of the
micrometer screw causes the cross-wires to alter their separation by 0·1 mm. When a particular double
star is observed, the setting of the cross-wires corresponds to 3·72 turns of the micrometer. What is the
angular separation of the two stars