1. Belen Observatory has a reflecting telescope. It has a 30” diameter circular

Question

1. Belen Observatory has a reflecting telescope. It has a 30” diameter circular primary
mirror and a 8.1875” diameter circular secondary mirror blocking the light path.
A. Given that the human pupil in low-light conditions is 6 mm in diameter, how many
times more light is collected when looking through the eyepiece than with your
unaided eye? (Don’t forget that the secondary mirror blocks some light: see the
diagram of a reflecting telescope for details.)
B. What is the telescope’s resolving power at a wavelength of 550 nm? Is it
diffraction-limited or seeing-limited?
C. Dr. Harbison wants to show off 1 Aries, a double star with a 2.8” separation. The
human eye can’t resolve stars closer than 2’. What magnification does she
need?

2. The star Betelgeuse has a temperature of 3590 K and a radius of 900 times that of
the Sun.
A. What is the peak wavelength of light from Betelgeuse?
B. How many times more luminous is Betelgeuse than the Sun (at a temperature of
5770 K)?
C. What is Betelgeuse’s absolute bolometric magnitude if the Sun’s is 4.8?
D. What kind of star is this (main sequence, giant, supergiant, white dwarf — use
the HR diagram in your textbook)? Can you calculate its mass? If you can, do
so. If you can’t, explain why not.

Explanation / Answer

1) The diameter of the 30 inches in which the 8.1875 inches is blocked so the area from which light is collected is,

= 3.14 * (15 - 4.09375)2 = 373.50 square inches

Which equals to 240967.26 square millimeters

and the eye collects from 6 mm diameter so the area of collection is,

=3.14 * 3 * 3 = 28.26 square millimeters

So the collection of light is 240967.26/28.26 = 8526.8 times light than the normal eye.

2) Resolving power = 13.8 / D in cm

13.8 / 76.2 = 0.18110 arcseconds

Theoretically it can go to 0.1811 arcseconds but due to atmospheric conditions the telescope resolution is limited to 0.4 arcseconds.

The value 0.1811 is diffraction limited and the value 0.4 is seeing limited.

3) Magnification = apparent field/True Field

Apparent Field = 2 arcminutes = 120 arcseconds

True Field = 2.9 arcseconds

Magnification = 120/2.9 = 41.38

Please ask the rest of the questions in separate questionnaire.

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