Astronomy test 3
The parallax angle of star A is 0.7420′′, the parallax angle of star B is 0.2860′′. How far, in lightyears, is star B?
1/.2860
The diagonal lines on the H-R diagram represent lines along which all stars would have the same radius. Label the three white lines with the correct values for the radii of stars that fall on them.
1000 solar radius (super giants & red giants) 1 solar radius (main sequence) 1 earth's radius (white dwarfs)
Look again at the orbit of the star with the highlighted orbit. By comparing the orbit to the scale bar shown on the diagram, you can estimate that this orbit has a semimajor axis of about _____.
1150 AU
How is the lifetime of a star related to its mass?
More massive stars live much shorter lives than less massive stars.
To determine the mass of the central object, we must apply Newton's version of Kepler's third law, which requires knowing the orbital period and average orbital distance (semimajor axis) for at least one star. We could consider any of the stars shown in the figure, so let's consider the star with the highlighted orbit (chosen because its dots are relatively easy to distinguish). What is the approximate orbital period of this star?
20 YEARS
The following equation, derived from Newton's version of Kepler's third law, allows us to calculate the mass (M) of a central object, in solar masses, from an orbiting object's period (p) in years and semimajor axis (a) in astronomical units: a^3 M= ______________ p^2 Using this formula with the values you found in Parts C and D, what is the approximate mass of the central object?
4 million solar masses
Galaxy
A gargantuan collection of stellar and interstellar matter- stars, gas, dust, neutron stars, black holes - isolated in space and held together by it's own gravity. Astronomers are aware of literally billions of galaxies beyond our own.
Listed following is the same set of fictitious stars given in Part A. Rank the stars based on how bright each would appear in the sky as seen from Jupiter, from brightest to dimmest.
BRIGHTEST TO DIMMEST (from Jupiter) Nismo: 100LSun, 8 ly Shelby: 100LSun, 10 ly & Ferdinand: 400LSun, 20 ly Enzo: 200LSun, 20 ly Lotus: 400LSun, 40 ly
The stars known as ________________ are the very largest and brightest of all the stars.
super giants
Which of the following statements about electron degeneracy pressure and neutron degeneracy pressure is true?
Electron degeneracy pressure is the main source of pressure in white dwarfs, while neutron degeneracy pressure is the main source of pressure in neutron stars.
The upper right region of the HR diagram
super giants
Galactic disk
Flattened region of gas and dust that bisects the galactic halo in a spiral galaxy. This is the region of active star formation.
Listed following are several astronomical objects. Rank these objects based on their density, from highest to lowest.
HIGHEST TO LOWEST DENSITY - the singularity of a black hole - a typical neutron star - one-solar-mass white dwarf - a main-sequence star
Consider the four stars shown following. Rank the stars based on their surface temperature from highest to lowest.
HIGHEST TO LOWEST TEMPERATURE A blue white dwarf star Sun An orange main-sequence star A red super giant star
What do we mean by the event horizon of a black hole?
It is the point beyond which neither light nor anything else can escape
Which of these stars has the coolest surface temperature? an A star, an F star, or a K star?
K star
What is the approximate mass of the most massive stars left on the main sequence of this star cluster? M≈0.1MSun M≈1MSun M≈10MSun M≈100MSun
M≈1MSun
Imagine that our Sun were magically and suddenly replaced by a black hole of the same mass (1 solar mass). What would happen to Earth in its orbit?
Nothing—Earth's orbit would remain the same.
From hottest to coolest, the order of the spectral types of stars is _________.
OBAFGKM
A mini-black hole with the mass of the Moon.
RSchwarzschild= 0.11mm
Galactic halo
Region of a galaxy extending far above and below the galactic disk, where globular clusters and old stars reside.
How do disk stars orbit the center of the galaxy?
They all orbit in roughly the same plane and in the same direction.
What is the common trait of all main sequence stars?
They generate energy through hydrogen fusion in their core.
Globular clusters
Tightly bound swarms of old, reddish stars. Roughly spherical collection of hundreds of thousands of stars spanning about 50 parsecs. Distributed in the halos around the Milky Way and other galaxies.
The position of a star along the main sequence tells you both its mass and its hydrogen-burning lifetime. Label the indicated blanks on the main sequence with the approximate lifetimes of stars at those positions.
Upper left hand quadrant: lifetime 10 million years Midway point: lifetime 10 billion years Lower right hand quadrant: lifetime 100 billion years
Does the following statement make sense? "Sirius looks brighter than Alpha Centauri, but we know that Alpha Centauri is closer because its apparent position in the sky shifts by a larger amount as Earth orbits the Sun."
YES
Compared to a high-luminosity main-sequence star, stars in the upper right of the H-R diagram are __________.
cooler and larger in radius
Which of these objects has the largest radius?
a 1.2MSun white dwarf
Which of these stars has the greatest surface temperature? a 30MSun main-sequence star a supergiant A star a Cepheid variable star
a 30MSun main-sequence star
Which of these stars has the largest radius? a supergiant A star a giant K star a supergiant M star
a supergiant M star
A(n) ___________ consists of hot, swirling gas captured by a white dwarf (or neutron star or black hole) from a binary companion star.
accretion disk
What do we need to measure in order to determine a star's luminosity?
apparent brightness and distance
Stars orbiting in the _______ near the galaxy's center can have orbits highly inclined to the galactic plane.
bulge
How do we know the total mass of the Milky Way Galaxy that is contained within the Sun's orbital path?
by applying Newton's version of Kepler's third law (or the equivalent orbital velocity law) to the Sun's orbit around the center of the galaxy
On an H-R diagram, stellar masses _________.
can be estimated for main sequence stars but not for other types of stars
Suppose you have a light bulb that emits 100 W of visible light. How far away would you have to put the light bulb for it to have the same apparent brightness as Alpha Centauri A in our sky? (Use 100 W as the luminosity in the inverse square law. Give the answer in km.)
d= square root of L/AB*4*pi= 100/2.7*10^-8*4*pi= 17000m = 17km = 10 miles
Near the end of Sun's life, its radius will extend nearly to the distance of Earth's orbit. Estimate the average matter density of Sun at that time. How does it compare with the density of air at sea level (density 10^{-3} g/cm^3). (Give the number of how many times denser air is compared to Sun as a red giant. The number is much larger than 1!)
density= mass/volume = 2x10^30kg/4/3xpi*r^3
The circular but relatively flat portion of the galaxy is the ________.
disk
Stars that are cooler than the Sun yet 100 to 1,000 times as luminous as the Sun is classified as ____________________
giants
The first portion of the galaxy to form was the __________.
halo
Compared to a low-luminosity main-sequence star, stars in the lower left of the H-R diagram are __________.
hotter and smaller in radius
To calculate the dashed orbits from the stellar positions, astronomers had to assume that __________.
if they observed for many more years, the dots would trace out ellipses
Compared to a main-sequence star with a short lifetime, a main-sequence star with a long lifetime is __________.
less luminous, cooler, smaller, and less massive
The total amount of power (in watts, for example) that a star radiates into space is called its _________.
luminosity
Stars are classified on the basis of their spectral type and _____________
luminosity class
The upper left and middle region of the HR diagram
main sequence
Most of the stars near the Sun are _________________
main-sequence stars
From Part E you know the mass of the central object. Now consider its size. Based on what you can see in the diagram, you can conclude that the diameter of the central mass is __________.
no more than about 70 AU
Our Milky Way galaxy is a __________.
spiral galaxy
Notice that some of the stars on the diagram are represented by a series of dots that are very close together, while others have their dots farther apart. Keeping in mind that all the stellar positions were measured at approximately one-year intervals, which stars are moving the fastest in their orbits during the time period indicated by the dots?
the dots farthest apart
We measure the mass of the black hole at the galactic center from:
the orbits of stars in the galactic center.
Estimate the maximum amount of time these very luminous stars can last as red giants from your answer to part C. t≈10^5years t≈10^7years t≈10^9years t≈10^11years
t≈10^7years
Cepheids are examples of ___________________
variable stars
A white dwarf in a close binary system will explode as a supernova if it gains enough mass to exceed the ________________________
white dwarf limit (1.4 solar masses)
A typical neutron star is more massive than our Sun and about the size (radius) of _________.
A small asteroid (10k in diameter)
Five stars are shown on the following H-R diagrams. Rank the stars based on their surface temperature from highest to lowest. If two (or more) stars have the same surface temperature, drag one star on top of the other(s).
All five stars appear at the same place along the horizontal axis showing spectral type. Because spectral type is related to surface temperature, all five stars must have the same surface temperature. Now proceed to Part C to determine how these stars vary in luminosity.
Galactic disk
An immense, circular, flattened region containing most of our Galaxy's luminous stars and interstellar matter.
Listed following are several fictitious stars with their luminosities given in terms of the Sun's luminosity (LSun) and their distances from Earth given in light-years (ly). Rank the stars based on how bright each would appear in the sky as seen from Earth, from brightest to dimmest. If two (or more) stars have the same brightness in the sky, show this equality by dragging one star on top of the other(s).
BRIGHTEST TO DIMMEST: Nismo: 100LSun, 8 ly Shelby: 100LSun, 10 ly & Ferdinand: 400LSun, 20 ly Enzo: 200LSun, 20 ly Lotus: 400LSun, 40 ly
The following figure shows how four identical stars appear in the night sky seen from Earth. The shading is used to indicate how bright (white) or dim (dark gray) the star would appear in the sky from Earth. Rank the stars based on their distance from Earth, from farthest to closest.
FARTHEST TO CLOSEST Dark charcoal grey Dark grey Light grey White grey
The _______________ is greater for low-mass stars than it is for high-mass stars.
main-sequence lifetime
A 2×10^8 MSun black hole in the center of a quasar.
RSchwarzschild= 6.0×10^8km
Estimate the Schwarzschild radius (in kilometers) for a mini-black hole formed when a superadvanced civilization decides to punish you (unfairly) by squeezing you until you become so small that you disappear inside your own event horizon. (Assume that the your weight is 50 kg)
RSchwarzschild= 7×10−29 km
The parallax angle of star A is 0.7420′′, the parallax angle of star B is 0.2860′′. What star is closer to Earth?
Star A Whichever star is closest... the bigger number
A(n) ____________ occurs when fusion creates iron in the core of a star.
massive star supernova
A(n) ______ occurs when hydrogen fusion ignites on the surface of a white dwarf in a binary system.
nova
The Schwarzschild radius of a black hole depends on ________.
only the mass of the black hole
Describe how this result help account for the fact that red giants have strong stellar winds?
The sun gives off particles increasing stellar winds
You've now found that the central object has a mass of about 4 million solar masses but is no more than about 70 AU in diameter—which means it cannot be much larger than the size of our planetary system. Why do these facts lead astronomers to conclude that the central object is a black hole?
There is no known way to pack so much mass into such a small volume without it collapsing into a black hole.
Galactic bulge
Thick distribution of warm gas and stars around the center of a galaxy.
What is the escape velocity from a red giant of 1 solar mass and a radius of 100 solar radii? (Solar radius = 7×10^5 km). Give the answer in km/s, round to the nearest 10.
Vesc= square root 2GM/r = 2*6.67*10^-11 m^3/kgs^2*10^30kg ------------------------------------- 7*10610
The Sun's location in the Milky Way Galaxy is _________.
in the galactic disk, roughly halfway between the center and the outer edge of the disk
On an H-R diagram, stellar radii _________.
increase diagonally from the lower left to the upper right
Compute the ratio between the luminosity from part B to the mass from part A. How does that ratio compare with the Sun's ratio of luminosity to mass?
L/M = 1000 LSun/MSun
Alpha Centauri A lies at a distance of 4.4 light years and has an apparent brightness in our night sky of 2.7×10^{-8} W/m^2. Use the inverse square law for light to calculate the luminosity of Alpha Centauri A. [Answer: 5.9×10^{??} W; give the exponent only]
L= AB/4pi*d^2 2.7*10^-8*4pi*d^2 d=4.4ly*9.5*10^15m/ly 5.9*10^26W
Listed following are several astronomical objects. Rank these objects based on their diameter, from largest to smallest. (Note that the neutron star and black hole in this example have the same mass to make your comparison easier, but we generally expect black holes to have greater masses than neutron stars.)
LARGEST TO SMALLEST DIAMETER - main-sequence star of a spectral type A - Jupiter - a one-solar-mass white dwarfs - the moon - a two-solar-mass neutron star - the event horizon of a two-solar-mass black hole
Listed following are several astronomical objects. Rank these objects based on their mass, from largest to smallest. (Be sure to notice that the main-sequence star here has a different spectral type from the one in Part A.)
LARGEST TO SMALLEST MASS - a typical black hole (formed in a supernova) - a typical neutron star - main-sequence star of spectral type M - Jupiter - the Moon
What is the luminosity of the most luminous stars in the cluster? L≈1LSun L≈10LSun L≈100LSun L≈1000LSun
L≈1000LSun
The Large Magellanic Cloud is a small galaxy that orbits the Milky Way. It is currently orbiting the Milky Way at a distance of roughly 160000 light-years from the galactic center at a velocity of about 300 km/s. Use these values in the orbital velocity law to get an estimate of the Milky Way's mass within 160000 light-years from the center. (The value you obtain is a fairly rough estimate because the orbit of the Large Magellanic Cloud is not circular.)
MMilkyWay= 1×10^12MSun
The figure shows a standard Hertzsprung-Russell (H-R) diagram. Label the horizontal and vertical axes using the two blanks nearest the center of each axis, and label the extremes on the two axes using the blanks on the ends of the axes.
On the vertical axis it shows the luminosity and brightness upwards and dimness which is downwards. On the horizontal axis it shows surface temperature to the left how hot to the left how cold.
Sirius A has a luminosity of 26LSun and a surface temperature of about 9400 K. What is its radius? (Hint: See Mathematical Insight Calculating Stellar Radii.)
R = 1.3×10^9m
Listed following is a set of statements describing individual stars or characteristics of stars. Match these to the appropriate object category.
RED GIANT AND SUPER GIANT: -found in the upper right of the H-R diagram -very cool but very luminous MAIN-SEQUENCE: -the majority of stars in our galaxy -the sun, for example -the hottest and most luminous stars WHITE DWARFS: -very hot very dim -not much larger in radius than Earth
A 6 MSun black hole that formed in the supernova of a massive star.
RSchwarzschild= 18km
Listed following are distinguishing characteristics of different end states of stars. Match these to the appropriate consequence of stellar death.
WHITE DWARF: -in a binary system, it can explode as a supernova -has a mass no greater than 1.4 MSun -supported by electron degeneracy pressure -typically about the size (diameter) of Earth NEUTRON STAR: -sometimes appears as a pulsar -usually has a very strong magnetic field BLACK HOLE -viewed from afar, time stops at its event horizon -size defined by its Schwarzschild radius
If star A is closer to us than star B, then Star A's parallax angle is _________.
larger than that of Star B
Assuming that we can measure the apparent brightness of a star, what does the inverse square law for light allow us to do?
calculate the star's luminosity if we know its distance, or calculate its distance if we know its luminosity
The parallax angle of star A is 0.7420′′, the parallax angle of star B is 0.2860′′. How far, in a parsec, is star A?
distance= 1/Parallax angle 1/0.7420 = 1.33
The radius of a white dwarf is determined by a balance between the inward force of gravity and the outward push of _____________________
electron degeneracy pressure
A tightly packed group of a few hundred thousand very old stars is a _________________.
globular cluster
Pulsars are thought to be _________.
rapidly rotating neutron stars
The right middle region above the main sequence in the HR diagram
red giants
A _________ stands out in a photo of a galaxy because it shines brightly with light from massive young stars and glowing clouds of gas and dust
spiral arm
A(n) _________________ can occur only in a binary system, and all such events are thought to have the same luminosity.
white dwarf supernova
The bottom left region of the HR diagram
white dwarfs
__________________ are no longer generating energy through nuclear fusion
white dwarfs
In a massive star supernova explosion, a stellar core collapses to form a neutron star roughly 10 kilometers in radius. The gravitational potential energy released in such a collapse is approximately equal to GM2/r where M is the mass of the neutron star, r is its radius, and G=6.67×10−11m3/kg×s2 is the gravitational constant. Using this formula, estimate the amount of gravitational potential energy released in a massive star supernova explosion. How does it compare with the amount of energy released by the Sun during its entire main-sequence lifetime?
~10^46 joules Esupernova explosion -------------------------- ~ 10^2 ESun total
A typical white dwarf has a mass of about 1.0MSun and the radius of Earth (about 6400 kilometers). Calculate the average density of a white dwarf, in kilograms per cubic centimeter. How does this compare to the mass of familiar objects?
ρ = 1800kg/cm3 This is about the mass of a small pickup truck.
