Chap 17 and 18

Question 1

What two factors determine how bright a star appears to be in the sky?

Answer 1

Luminosity of a star and it’s distance

Question 2

Explain why color is a measure of a star’s temperature.

Answer 2

The spectrum of colors, from red to blue correlate with the stars temperature. The more blue side of spectrum, the hotter, and the more red side of spectrum, the cooler.

Question 3

What elements are stars mostly made of? How do we know this?

Answer 3

Stars are primarily made up of hydrogen and helium. We know this from measuring the stars spectral lines.

Question 4

Name five characteristics of a star that can be determined by measuring its spectrum. Explain how you would use a spectrum to determine these characteristics.

Answer 4

1.) 𝑹𝒂𝒅𝒊𝒄𝒂𝒍 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚, find the Doppler shift (red-shift, blue-shift)
2.) 𝑪𝒐𝒎𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏, use spectral lines
3.) 𝑺𝒊𝒛𝒆, the smaller the star the more compact and higher pressure it is, so it has broader spectral lines, and vise versa for larger stars
4.) 𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆, use Wien’s law and color of star
5.) 𝑹𝒐𝒕𝒂𝒕𝒊𝒐𝒏, Doppler broadening of spectral lines for faster rotations

Question 5

How do objects of spectral types L, T, and Y differ from those of the other spectral types?

Answer 5

They are known as brown dwarfs because they aren’t hot enough to fuse hydrogen, but can fuse deuterium.

Question 6

The star Antares has an apparent magnitude of 1.0, whereas the star Procyon has an apparent magnitude of 0.4. Which star appears brighter in the sky?

Answer 6

Procyon, because the smaller the magnitude the more bright.

Question 7

Order the seven basic spectral types from hottest to coldest.

Answer 7

OBAFGYKM
Oh boy, another freaking giraffe kicked mom
Brown dwarfs: LTY

Question 8

How would two stars of equal luminosity—one blue and the other red—appear in an image taken through a filter that passes mainly blue light? How would their appearance change in an image taken through a filter that transmits mainly red light?

Answer 8

Blue filter: The blue star would appear brighter then red star

Red filter: The star star would appear brighter then blue star.

Question 9

Two stars have proper motions of one arcsecond per year. Star A is 20 light-years from Earth, and Star B is 10 light-years away from Earth. Which one has the faster velocity in space?

Answer 9

The further star A is moving faster as it has a larger distance to produce the same arcsecond.

Question 10

Suppose there are three stars in space, each moving at 100 km/s. Star A is moving across (i.e., perpendicular to) our line of sight, Star B is moving directly away from Earth, and Star C is moving away from Earth, but at a 30° angle to the line of sight. From which star will you observe the greatest Doppler shift? From which star will you observe the smallest Doppler shift?

Answer 10

Star B, which is moving away, will have the biggest doppler effect.
Star A, moving perpendicular, will have the smallest doppler effect.

Question 11

Star A and Star B have different apparent brightness’s but identical luminosities. If Star A is 20 light-years away from Earth and Star B is 40 light-years away from Earth, which star appears brighter and by what factor?

Answer 11

Star A is closer, and will be brighter by a factor of 1/4, so 4x times brighter

2x times away from Star A, inverse square law: 1/d ^2
1/2^2= 1/4

Question 12

As seen from Earth, the Sun has an apparent magnitude of about −26.7. What is the apparent magnitude of the Sun as seen from Saturn, about 10 AU away? (Remember that one AU is the distance from Earth to the Sun and that the brightness decreases as the inverse square of the distance.) Would the Sun still be the brightest star in the sky?

Answer 12

1/10^2 = 1/100 = 0.01
2.512^x = 0.01
log 2.512^x = log 0.01
x (log 2.512) = log 0.01

x= log 0.0/ log 2.512 = -4.99
-26.7 - (-4.99) = -21.71

Question 13

The star Sirius A has an apparent magnitude of −1.5. Sirius A has a dim companion, Sirius B, which is 10,000 times less bright than Sirius A. What is the apparent magnitude of Sirius B? Can Sirius B be seen with the naked eye?

Answer 13

2.512^x = 10^-4
x= log 10^-4/ log 2.512 = 9.99
-1.5 -(9.99) = -11.49

Question 14

How does the mass of the Sun compare with that of other stars in our local neighborhood?

Answer 14

It’s a lot bigger, only few are more massive, majority are smaller.

Question 15

Name and describe the three types of binary systems.

Answer 15

𝑽𝒊𝒔𝒖𝒂𝒍 𝒃𝒊𝒏𝒂𝒓𝒚: two stars can be resolved by a telescope
𝑺𝒑𝒆𝒄𝒕𝒓𝒐𝒑𝒔𝒄𝒐𝒑𝒊𝒄: spectral lines are doppler shifted showing orbital motion
𝑬𝒄𝒍𝒊𝒑𝒕𝒊𝒏𝒈 𝒃𝒊𝒏𝒂𝒓𝒚: we observe a light curve as stars ecliptic one another

Question 16

Describe two ways of determining the diameter of a star.

Answer 16

Stefan Boltzmann law and lunar eclipse of the star

Question 17

You are able to take spectra of both stars in an eclipsing binary system. List all properties of the stars that can be measured from their spectra and light curves.

Answer 17

Radical velocity, size, composition, temperature, and rotation

Question 18

How do we distinguish stars from brown dwarfs? How do we distinguish brown dwarfs from planets?

Answer 18

Brown dwarfs are on the infrared spectrum, they can fuse deuterium.
They have a lot more mass then planets as they are massive.

Question 19

Describe how the mass, luminosity, surface temperature, and radius of main-sequence stars change in value going from the “bottom” to the “top” of the main sequence.

Answer 19

Radius, temperature, and luminosity all increase in top main sequence stars.

Question 20

Why do most known visual binaries have relatively long periods and most spectroscopic binaries have relatively short periods?

Answer 20

Visual binaries are further apart so they have a longer period based on kepler’s third law. Spectroscopic binaries are shorter apart so they have a shorter period.

Question 21

There are fewer eclipsing binaries than spectroscopic binaries. Explain why.

Answer 21

Our perspective on Earth can change whether or not they are eclipsing based on their angle.

Question 22

Suppose you want to search for brown dwarfs using a space telescope. Will you design your telescope to detect light in the ultraviolet or the infrared part of the spectrum? Why?

Answer 22

Infrared because brown dwarfs have lower luminosity and energy, making them only visible in infrared light

Question 23

An astronomer discovers a type-M star with a large luminosity. How is this possible? What kind of star is it?

Answer 23

This type of star is called a red giant, it’s possible because it’s large surface, an example would be Betelgeuse

Question 24

If two stars are in a binary system with a combined mass of 5.5 solar masses and an orbital period of 12 years, what is the average distance between the two stars?

Answer 24

D^3= (m1+ m2) P^2
m1+m2= 5.5 M
p= 12
D= 9.25 AU

Question 25

The lowest mass for a true star is 1/12 the mass of the Sun. What is the luminosity of such a star based upon the mass-luminosity relationship?

Answer 25

L= M ^3.5
M= 1/12
L= 1/12 ^3.5 = 1.67 x 10^-4 solar lum

Question 26

The star Betelgeuse has a temperature of 3400 K and a luminosity of 13,200 LSun. Calculate the radius of Betelgeuse relative to the Sun.

Answer 26

Lb / Ls –>
4pi (Rb^2 delta Tb^4) / 4pi (Rs^2 delta Ts^4)
13200 ls/ ls = Rb^2 (3400)^4/ Rs^2
(5800)^4
Rb^2/ Rs^2 = 13200 (5800)^4/ 3400 ^4
Rb= sqaure root(111,782) = 334
Rb= 334 Rs