MATH PRETEST

These are the types of formulae you will be working with this semester. Take a few minutes to practice your algebra skills.

2) L = (R)² (T)⁴ R = 10, T = 2, L = ?

4) angular diameter = 206,000 linear diameter
                                                distance

angular diameter = 0.76", linear diameter = 150 X 10⁶ km, distance = ?

6) (m₁ + m₂) P² = (a₁ + a₂)³ , a₁ + a₂ = 15, P = 100, m₁ = 2m₂, find m₁ and m₂

1. GENERAL MATH SKILLS

1) Write the following in scientific notation:

a) 0.0003

b) 0.002

c) 130,000,000

d) 27 billion

2) Convert the following:

a) 3 cm to angstroms

b) 207 angstroms to meters

c) 27 kpc to pc

d) 23 seconds to years

e) 14 pc to au

3) A light year is defined to be the distance light travels in one years. Given that light travels at 300,000 km/sec, calculate the length of a light year in km. (Hint- take the speed of light and multiply it by the number of seconds in one year. Make sure all the units cancel, leaving you with km/yr. Then multiply by 1 year to cancel the years.)

2. LIGHT

1) Calculate the frequency of light of wavelength

a) 1 m

b) 1 cm

c) 1915 angstroms

2) calculate the wavelength of light of frequency

a) 10 M Hz

b) 100 K Hz

3) Compare the energy of light of

a) 4700 angstroms to 6000 angstroms

b) 14 M Hz to 28 M Hz

4) Calculate the surface temperature of a body with peak wavelength

a) 0.3 cm

b) 7000 A

c) 412 A

5) Calculate the peak wavelength for a body of surface temperature

a) 6000 K

b) 1000 K

c) 15,000 K

6) A 6000 A wavelength is seen in the spectrum of a neighboring star to be at 6005 A. What is the star's radial velocity? Is it redshifted or blueshifted? Is it receding or approaching?

7) Repeat for a star where the line is seen at 5998 A.

1) Compare the light gathering power of

a) a 10 inch to a 4 inch

b) a 7 inch to a 6 inch

2) An 8 inch scope of focal length 4000 mm is used with an eyepiece of focal length 25 mm.

a) Calculate the resolving power

b) Calculate the magnification

3) A 0.3m scope of focal length 3500 mm is used with an eyepiece of focal length 30 mm.

a) Calculate the resolving power at a wavelength of 5000 A.

b) Calculate the magnification

4. THE SUN

1) Show that the angular size of the sun as seen from earth is about 1/2 degree. (diameter of the sun = 1.4 X 10⁶ km, distance = 1.496 X 10⁸ km)

2) What is the angular size of the sun as seen from Pluto (in seconds of arc)? Distance = 5.914 X 10⁹ km.

3) What is the angular size of the sun as seen from Alpha Centauri (distance = 4.3 ly - convert to km). Given the limiting resolution of telescopes, do you think we actually see the true size of a star when we look at it through a telescope?

1) Calculate the distance in pc and ly for stars of parallax angle

a) 0.7"

b) 0.2"

c) 0.056"

2) A star has a parallax of 0.03" and a proper motion of 0.2"/yr. Calculate its distance and V_t.

3) If the previous star has a V_r of +30 km/sec, calculate its space velocity.

4) A star has a parallax of 0.12" and a proper motion of 1.7"/year. Calculate its distance in pc and ly and V_t.

5) If the previous star has V_r = -170 km/sec, calculate its space velocity.

6. MAGNITUDES

1) How much brighter is a

a) 2 mag. star than a 6 mag. star?

b) 7 versus 17

c) 5 versus 12

2) A star has an apparent magnitude of +2 and an absolute magnitude of -7. What is its distance?

3) A star has an apparent magnitude of -1 and a distance of 100 pc. What is its absolute magnitude?

4) A star has an absolute magnitude of +3 and a distance of 10,000 pc. What is its apparent magnitude?

7. LUMINOSITY AND LIFETIME

1) What is the relative luminosity of a star

a) 2X the size of sun and 3X hotter

b) 1/3 the size of sun and 1/4 as hot

c) 4X the size of sun and the same temperature.

2) What is the relative size of a star

a) 2X the temperature of sun and 2X the luminosity

b) 1/2 the temperature and 3X as luminous

c) 3X as hot and 1/2 the luminosity.

3) What is the luminosity and lifetime (in years) of a main sequence star

a) twice the mass of sun

b) 4X the mass of sun

c) 1/3 the mass of sun

1) Two equal mass stars orbit each other at an average distance of 50 au in 300 years. Find the mass of each star.

2) Two stars orbit each other at an average distance of 27 au in 110 years. If one star is twice the mass of the other, calculate the individual masses.

3) Two stars orbit each other at an average distance of 42 au in 150 years. If one star is 3X more massive than the other, calculate the individual masses.

9. STELLAR CORPSES

1) Calculate the Schwarzschild radius of a black hole of mass

a) 5 solar masses (a typical stellar black hole)

b) 100,000 solar masses (in nucleus of our galaxy)

c) 10 kg (a Hawking primordial black hole)

1) Calculate the mass of the Milky Way interior to a region with distance and orbital period

a) 5 kpc, 153 million years

b) 17 kpc, 463 million years

2) The Large Magellanic Cloud is about 50 kpc from the center of the Milky Way and orbits it once every 2 billion years. Assuming that we can neglect the mass of the LMC, what is the mass of the Milky Way? How does this compare with your answer in 1b?

3) Two identical dwarf elliptical galaxies orbit each other at a distance of 60 kpc every 97 billion years. Calculate the individual mass of the galaxies.

4) In the spectrum of a galaxy, a 4400 A line appears at 7200. Calculate the recessional velocity.

5) In the spectrum of a quasar, a 3100 A line is shifted BY 340 A. What is its recessional velocity? Assuming H = 50 km/s/Mpc, what is its distance?

6) A quasar is discovered at Z = 0.7. What is its distance if

a) H = 50 km/s/Mpc

b) H = 75 km/s/Mpc

c) H = 100 km/s/Mpc

1) For the following values of H, calculate the maximum age of the universe:

a) 120 km/s/Mpc

b) 82 km/s/Mpc

c) 47 km/s/Mpc

Are any of these ruled out by observation?