Download PHYS 1470 3.0 W16/17 Highlights of Astronomy Assignment #1

PHYS 1470 3.0 W16/17 Highlights of Astronomy
Assignment #1
Deadline: 11:30 am February 9, 2017
The solutions must be typed or a penalty will be incurred.
Each student must hand in his/her own assignment. While you may confer with
someone else on how to approach a problem, your solutions must be your own.
Also, students are discouraged from providing answers that are strictly numerical,
but rather should include a brief description in words (and even a sketch where
warranted).
1. Assume that you are an observer located at a latitude of 40 degrees north (on
Earth). Draw a fully labeled diagram showing from your vantage point:
a) the horizon, the zenith, the celestial equator and Polaris (the north star).
b) What is the altitude (elevation) of Polaris?
c) What is the altitude (elevation) of the celestial equator at its highest point?
2. The right ascension, RA, of the star Betelgeuze a supergiant in the constellation
Orion, is 05h 55m 10s.
a) If Betelgeuze’s Hour Angle, HA, is +3h 11m 00s what is the Local Sidereal
Time, LST?
b) If the Local Sidereal Time is 4h 10m 00s what is the Hour Angle of
Betelgeuze?
c) From which direction did Betelgeuze rise? In which direction will Betelgeuze
set?
d) Search the web to find Betelgeuze’s declination, decl.
e) Give the name of the coordinate system for which “declination” is defined.
3. You have a friend, 40 Earth years old, who comes from a (fictitious) planet that
orbits the Sun (in a circle) exactly half way between Jupiter and Venus. Call this
planet Yorkus. Yorkus has a radius 4/5 times the Earth's radius and a mass 1.5
times the Earth's mass. Using the information provided in the Appendices of our
book, in the slides or in your notes from class, answer the following questions.
a) What is the escape velocity in km/s from the surface of Yorkus?
b) What is the orbital speed in km/s of Yorkus as it revolves about the Sun?
c) If the Canadian Space Agency launched a space probe into a minimum
energy orbit between Earth and Yorkus, how long (yr) would it take the probe
to reach Yorkus? (Note: a minimum energy orbit would use the velocity of the
earth. The orbit is an ellipse with the sun at one focus, the perihelion at the
earth and the aphelion at Yorkus. Sketch and label the orbits of Earth, Yorku
and the space probe.)
4. Doppler Shift: The Hb (hydrogen beta) line, which is strong in the spectra of
moderately hot stars, has a wavelength of 486.133 nm in the laboratory (i.e., at
rest with respect to the observer). What wavelength (nm) would we observe the
Hb line on Earth if it were emitted by a star:
a) moving at a speed of 200 km/s toward Earth?
b) moving at a speed of 300 km/s away from Earth?
5. Calculate the blackbody temperatures (K) from the peak wavelengths given in a)
through b), and the peak wavelengths (m) from the temperature given in c)
a) 180 nm (surface of hot star)
b) 3.5 µm (surface of cold star)
c) 50 K (interstellar cloud)
6. The star Sirius has a surface temperature of 9750 K and a radius 2.4 times larger
than the Sun's.
a) What is the ratio of the flux (energy per square meter per second) emitted
from the surface of Sirius to the flux emitted from the surface of the Sun?
b) What is the ratio of the luminosity of Sirius to the luminosity of the Sun?
7. The York Observatory 40 cm telescope has a focal ratio of f/10.
a) What is the light-gathering power of this telescope relative to that of a single
human eye? Use a pupil diameter of 7 mm.
b) What is the diffraction-limited angular resolution (in arc-seconds) of this
telescope for a wavelength of 480 nm?
c) What would be the focal length (in mm) of the eyepiece necessary to achieve
a magnification of 200 with this telescope?
Total marks Q1 = 4 marks
Q2 = 7 marks
Q3 = 8 marks
Q4 = 2 marks
Q5 = 3 marks
Q6 = 4 marks
Q7 = 7 marks
TOTAL – 35 marks