Astronomy Principles and Practice Fourth Edition.pdf

Problems—Chapter 15 237
2. One star is three times brighter than another. What is the difference in magnitude between the two stars.
3. Two stars differ in magnitude by three. What is the ratio of their brightnesses
4. The energy received per unit time from two stars is in the ratio 2:1. The brighter star has a magnitude of
+2·50. What is the magnitude of the fainter star
5. The apparent magnitude of Jupiter on a particular night is −1·3. Its brightness is compared with a star whose
magnitude is +1·0. What is the ratio of the brightnesses of Jupiter and the star
6. Two stars have magnitudes +4·1 and+5·6. The brighter star provides 5 × 10 −8 W for collection by a
particular telescope. How much energy would be collected from the fainter star
7. Two stars are close together on the celestial sphere and measurements show that they have the same
brightness. It is also known that one star has a magnitude of +8·5. What would be the magnitude of
the pair of stars if they were seen as a single object
8. The surface of a star is radiating as a black body with a temperature of 6000 K. If the temperature were to
increase by 250 K, by what fraction would the energy liberated per unit area increase
9. The constant in Wien’s displacement law is 2·90 × 10 −3 m K. What is the wavelength corresponding to the
maximum radiation output of a star whose surface temperature is 5000 K
10. The wavelength associated with the hydrogen spectrum may be expressed in the form:
λ mn =
R
(1/n 2 − 1/m 2 ) .
For the lines in the visible part of the spectrum (Balmer series), n = 2 and the first line of the series, Hα is
at 6562 Å. Show why observations of the lines of the Lyman series (n = 1) may only be made from rockets
or satellites.
11. A spectrometer is just able to detect a wavelength shift of 0·01 Å. What would be the minimum strength of
magnetic field that might be detected in a star if the spectral region around 4500 Åweretobeused
12. From the spectrum taken of a star, the Hβ line (4861 Å) exhibits a blue wavelength displacement of 0·69 Å.
What is the relative velocity of approach of the star
13. The equatorial radius of Saturn is 60 400 km and its rotation period is 10 h 14 m . What is the maximum
Doppler displacement of a spectral line at 5000 Å obtained from the light reflected by a selected area of the
planet’s disc