Astronomy 2 Exam Study Guide

Within an atomic nucleus, the strongest of the three forces is

the strong force

Across a distance of 1 millimeter, the strongest force acting between two protons is

electromagnetism

In this problem, we compare the strength of gravity to the strength of the electromagnetic (EM) force for two interacting electrons. Because both electrons are negatively charged, they will want to repel each other according to the EM force. Because electrons have mass, they will want to attract each other according to gravity. Let's see which effect will dominate. You will need the following information for this problem: 1) The force law for gravitation is: Fg=GM1M2d2(G=6.67×10−11N×m2kg2)�g=��1�2�2(�=6.67×10−11N×m2kg2) where M1�1 and M2�2 are the masses of the two objects, d� is the distance between them, and G� is the gravitational constant. ("N""N" is the abbreviation for newton, the metric unit of force.) 2) The force law for electromagnetism is: FEM=kq1q2d2(k=9.0×109N×m2Coul2)�EM=��1�2�2(�=9.0×109N×m2Coul2) where q1�1 and q2�2 are the charges of the two objects (in coulombs, the standard unit of charge), d� is the distance between them, and k� is a constant. ("Coul""Coul" is an abbreviation for coulomb.) 3) The mass of an electron is 9.10×10−31kg9.10×10−31kg. 4) The charge of an electron is −1.6×10−19Coul−1.6×10−19Coul.

Calculate the gravitational force, in newtons, that attracts the two electrons if a distance of 10−10m10−10m (about the diameter of an atom) separates them.

Express your answer in newtons to three significant figures.

5.52e-51N

Same instructions from previous:

Calculate the electromagnetic force, in newtons, that repels the two electrons at the same distance.

Express your answer in newtons to two significant figures.

2.3×e−8N

Same instructions from one above:

How many times stronger is the electromagnetic repulsion than the gravitational attraction for the two electrons?

Express your answer using two significant figures.

4.2e42

If we measure a subatomic particle's position very precisely, then

its momentum will be highly uncertain.

Which of the following is not allowed by the exclusion principle?

having two electrons in the same quantum state

Suppose you are running at a speed of about 10 km/hrkm/hr, but there is an uncertainty of 0.7 km/hrkm/hr in your precise speed. Given your mass, you can calculate your momentum and the uncertainty of that momentum.

(Hint: You'll need the first form of the uncertainty principle, uncertaintyinlocation×uncertaintyinmomentum≈Planck′sconstant.uncertaintyinlocation×uncertaintyinmomentum≈Planck′sconstant. You can use the value of Planck's constant, h=6.626×10−34kg×m2sℎ=6.626×10−34kg×m2s.)

What is the corresponding quantum limit to the measurement of your position? Assume that your mass is 65 kgkg.

Express your answer to three significant figures and include the appropriate units.

5.24e-35 m

Is this significant? Why or why not?

The uncertainty is very small compared to human size, so this effect is not significant.

In which one of the following objects does degeneracy pressure play the most important role?

a nuetron star

X-ray images of the Sun generally show the

corona

Which of these layers of the Sun is coolest?

photosphere

The total annual U.S. energy consumption is about 2×10202×1020 joules.

What is the average power requirement for the United States, in watts? (Hint: 1 wattwatt = 1 joule/sjoule/s)

Express your answer in watts to three significant figures.

6.34×e12W

The total annual U.S. energy consumption is about 2×10202×1020 joules.

With current technologies and solar collectors on the ground, the best we can hope for is that solar cells will generate an average (day and night) power of about 210 watts/m2watts/m2 . What total area would we need to cover with solar cells to supply all the power needed for the United States? Give your answer in both square meters and square kilometers.

Express your answer in meters squared to three significant figures.

3.02e10 m^2

The total annual U.S. energy consumption is about 2×10202×1020 joules.

Express your answer in kilometers squared to three significant figures.

3.02e4km^2

Use Wien's law and the Sun's average surface temperature of about 5800 K to calculate the wavelength of peak thermal emission from the Sun.

Express your answer to three significant figures and include the appropriate units.

500 nm

What color does this wavelength correspond to in the visible-light spectrum?

green

Why do you think the Sun appears white or yellow to our eyes?

Because the Sun radiates in other colors, and because the atmosphere scatter the blue light stronger than the red.

How does a natural "solar thermostat" keeps the core fusion rate steady in the Sun?

If the Sun's core were a bit hotter, the fusion rate would increase. This would produce more energy, which would cause the core to expand slightly and cool. The cooling would cause the fusion rate to slow back down until the Sun was back to the original size and temperature and fusion occurred at the original rate.

How does energy generated by fusion makes its way to the Sun's surface. How long does it take?

Photons take hundreds of thousands of years to get out of the Sun because their paths zigzag repeatedly.

Because the plasma is so dense in the Sun's interior, a photon can travel a fraction of a millimeter before colliding with an electron and deflecting into a new direction.

The average power of a human body (for living and metabolism) is about 100 watts. Suppose a 80 kgkg human body could run on fusion power and could convert 0.8 %% of its mass into energy.

How much energy would be available through fusion?

Express your answer to two significant figures and include the appropriate units.

5.8e16 J

The average power of a human body (for living and metabolism) is about 100 watts. Suppose a 80 kgkg human body could run on fusion power and could convert 0.8 %% of its mass into energy.

For how long could this body then operate on fusion power?

Express your answer in years to two significant years.

1.8e7yr

What do we mean by a star's spectral type, and how is spectral type related to surface temperature and color.

Spectral types are a way of classifying stars according to their color or what spectral lines we see in their light. The spectral types run OBAFGKM, where O stars are the hottest and M are the coolest. Hotter stars look bluer to us, and cooler stars look redder.

Alpha Centauri A lies at a distance of 4.4 light-years and has an apparent brightness in our night sky of 2.7×10−8watt/m22.7×10−8watt/m2. Recall that 1ly=9.5×1012km=9.5×1015m1ly=9.5×1012km=9.5×1015m.

Use the inverse square law for light to calculate the luminosity of Alpha Centauri A.

Express your answer to two significant figures and include the appropriate units

5.9×e26W

Alpha Centauri A lies at a distance of 4.4 light-years and has an apparent brightness in our night sky of 2.7×10−8watt/m22.7×10−8watt/m2. Recall that 1ly=9.5×1012km=9.5×1015m1ly=9.5×1012km=9.5×1015m.

Suppose you have a light bulb that emits 10 watts 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? (Hint: Use 10 watts as L� in the inverse square law for light, and use the apparent brightness given above for Alpha Centauri A. Then solve for the distance.)

Express your answer to two significant figures and include the appropriate units.

5400 m

Use the parallax formula to calculate the distance to each of the following stars. Give your answers in both parsecs and light-years.

Alpha Centauri: parallax angle 0.7420''.

Express your answer in parsecs to four significant figures.

1.348 pc

Use the parallax formula to calculate the distance to each of the following stars. Give your answers in both parsecs and light-years.

Express your answer in light-years to four significant figures.

4.396, 4.396e0

light−years

Use the parallax formula to calculate the distance to each of the following stars. Give your answers in both parsecs and light-years.

Procyon: parallax angle of 0.2860''.

Express your answer in parsec to four significant figures.

3.497 pc

Use the parallax formula to calculate the distance to each of the following stars. Give your answers in both parsecs and light-years.

Procyon: parallax angle of 0.2860''.

11.40 light−years

The spectral lines of two stars in a particular eclipsing binary system shift back and forth with a period of 9 months. The lines of both stars shift by equal amounts, and their Doppler shifts indicate an orbital speed of 76,000 m/sm/s for Star 1 relative to Star 2. What are the masses of the two stars? Assume that each of the two stars traces a circular orbit around their center of mass. (Hint: See Mathematical Insight 15.4.)

Express your answers in solar masses to two significant figures separated by a comma.

6.2,6.2 MSun

Sirius A has a luminosity of 26LSun26�Sun and a surface temperature of about 9400 KK.

What is its radius? (Hint: See Mathematical Insight Calculating Stellar Radii.)

Express your answer in meters to two significant figures.

1.3e9m

Choose the correct statement explaining what do we mean by a star's luminosity class and how we classify stars by spectral type and luminosity class.

Luminosity classes of stars are designated by Roman numerals and tell us what region of the H-R diagram the star falls in. The spectral type tells us the stars temperature while the luminosity class tells us its radius.

Which of these stars has the longest lifetime?

a main-sequence M star

Which of these stars has the largest radius?

a supergiant M star

which of these stars has the greatest surface temperature?

a 30MSun main-sequence star

What is the approximate mass of the most massive stars remain on the main sequence of this star cluster?

M≈1MSun

What is the luminosity of the most luminous stars in the cluster?

L≈1000LSun

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?

Express your answer using one significant figure.

1000

LSun/Msun

Estimate the maximum amount of time these very luminous stars can last as red giants from your answer to part C.

Express your answer in years to one significant figure.

1e7 yr

Which of these star clusters is youngest?

a cluster containing stars of all colors

Which of these star clusters is oldest?

a cluster whose brightest main-sequence stars are yellow

Which of these stars is the most massive?

A main sequence A star

Which of these stars has the coolest surface temperature?

a K star

Which of these colors of light passes most easily through interstellar clouds?

red light

Molecular clouds stay cool because their molecules emit photons. Which of these molecules produces the largest number of photons in a molecular cloud?

carbon monoxide(CO)

The amount of thermal energy inside a protostar increases with time, even though the protostar is losing radiative energy from its surface. How can we tell how much radiative energy the protostar is losing and how much thermal energy remains in the star? Which type of energy can we measure and which type do we infer from the law of conservation of energy?

We can measure radiative energy directly and infer thermal energy from models. Protostars do not lose all their gravitational potential energy via radiation, so we can derive the amount left for thermal energy

A star-forming cloud flattens into a disk that spins faster as the cloud contracts because of conservation of angular momentum. Then material from the disk gradually spirals inward toward the newly forming star at the center, accreting onto its surface and adding to its mass. What would we find if we could measure the orbital speeds of gas particles in the accretion disk? Suppose there were no friction in the disk orbiting the protostar; would this affect the orbital speeds? Overall, how would a lack of friction change the process?

Without friction, there would be almost nothing to slow the particles down. Therefore, the disk particles would continue to orbit for a very long times and formation of a star would take billions of years

Dark interstellar gas clouds contain so many dust grains that starlight cannot pass through, even though the dust grains are tiny and the spaces between them are quite large by earthly standards. A typical dust grain has a radius of about 1.00×10−71.00×10−7 meter and a mass of about 1.00×10−141.00×10−14 gram.

Estimate how many dust particles there are in a cloud containing 1300MSun of dusty gas, if 1.6 %% of the cloud's mass is in the form of dust grains.

4.2e48 dust particles

Dark interstellar gas clouds contain so many dust grains that starlight cannot pass through, even though the dust grains are tiny and the spaces between them are quite large by earthly standards. A typical dust grain has a radius of about 1.00×10−71.00×10−7 meter and a mass of about 1.00×10−141.00×10−14 gram.

Estimate the total surface area these grains would cover if you could put them side by side. You can assume that the grains are approximately spherical so that each grain covers an area πr2 where r is the grain's radius. State your answer in square light-years.

1500 ly^2

Dark interstellar gas clouds contain so many dust grains that starlight cannot pass through, even though the dust grains are tiny and the spaces between them are quite large by earthly standards. A typical dust grain has a radius of about 1.00×10−71.00×10−7 meter and a mass of about 1.00×10−141.00×10−14 gram.

Estimate the total surface area the cloud covers, assuming that its matter density is like that of a typical molecular cloud, about 10−21g/cm310−21g/cm3. (Hint: First calculate the cloud's volume from its mass and density, then determine the cloud's radius using the formula for the radius of a sphere R=(3×volume/4π)1/3�=(3×volume/4�)1/3. Then calculate the total surface area that cloud covers using the formula for the area of circle.) State your answer in square light-years.

260 ly^2

Dark interstellar gas clouds contain so many dust grains that starlight cannot pass through, even though the dust grains are tiny and the spaces between them are quite large by earthly standards. A typical dust grain has a radius of about 1.00×10−71.00×10−7 meter and a mass of about 1.00×10−141.00×10−14 gram.

Based on your answers to parts B and C, what do you think the chances are that a photon passing through the cloud will hit a dust grain?

Photon entering the cloud will probably collide with at least one grain.

What happens to a cloud's thermal pressure if its temperature falls while its density rises?

More information is needed to determine what thermal pressure does.

What happens within a contracting cloud in which gravity is stronger than pressure and temperature remains constant?

it breaks into smaller fragments

Why are the very first stars thought to have been much more massive than the Sun?

The temperatures of the clouds that made them were higher because they consisted entirely of hydrogen and helium.

What slows down the contraction of a star-forming cloud when it makes a protostar?

trapping of thermal energy inside the protostar

What effects are jets and magnetic fields thought to have on a protostar?

They carry away angular momentum, helping the protostar grow in mass

Which kinds of stars are most common in a newly formed star cluster?

M stars

Models of the first star-forming clouds indicate that they had a temperature of roughly 180 KK and a particle density of roughly 270,000 particles per cubic centimeter at the time they started trapping their internal thermal energy.

Estimate the mass at which thermal pressure balances gravity for these values of pressure and temperature.

Express your answer in kilograms.

1.7e32 kg

Models of the first star-forming clouds indicate that they had a temperature of roughly 180 KK and a particle density of roughly 270,000 particles per cubic centimeter at the time they started trapping their internal thermal energy.

How does that mass compare with the Sun's mass?

Express your answer in solar masses.

84 MSun

What is the estimated lifetime of a star with that mass?

less than 10 million years

Suppose a new star cluster is born with one O star, 10 A stars, 100 G stars, and 1000 M stars. Which stellar type dominates the light output from the cluster?

class O

What would the color of this star cluster appear to be if you observed it from a distance so great that you could not make out the individual stars?

Violet

Suppose you observe a binary system containing a main-sequence star and a brown dwarf. The orbital period of the system is 1 year, and the average separation of the system is 1 AUAU . You then measure the Doppler shifts of the spectral lines from the main-sequence star and the brown dwarf, finding that the orbital speed of the brown dwarf in the system is 21 times greater than that of the main-sequence star.

How massive is the brown dwarf?

Express your answer in kilograms to three significant figures.

9.06e28kg

The fundamental particles of matter are

quarks and leptons

Which of the following is not allowed by the exclusion principle?

having two electrons in the same quantum state

Within an atomic nucleus, the strongest of the four forces is

the strong force

At the center of the Sun, fusion converts hydrogen into

helium, energy, and neutrinos.

Which of the groups of particles has the greatest mass?

four individual protons

Which of these layers of the Sun is coolest?

photosphere

Two stars that have the same apparent brigntness in the sky must have the same luminosity.

False

If the star Alpha Centauri were moved to a distance 10 times as far from Earth as it is now, its parallax angle would:

get smaller

What do we need to measure in order to determine a star's luminosity?

apparent brightness and distance

What two pieces of information would you need in order to measure the masses of stars in an eclipsing binary system?

What two pieces of information would you need in order to measure the masses of stars in an eclipsing binary system?

Some of the stars on the main sequence of the H-R diagram are not converting hydrogen to helium.

false

What two pieces of information would you need in order to measure the masses of stars in an eclipsing binary system?

the time between eclipses and the average distance between the stars

Some of the stars on the main sequence of the H-R diagram are not converting hydrogen to helium.

false

What is the approximate composition of the interstellar medium (by mass) in our region of the Milky Way?

70% hydrogen, 28% helium, 2% heavy elements

The buildup of thermal energy in a collapsing gas cloud leads to thermal pressure that can halt the gravitational collapse. What must happen for the gravitational collapse to continue?

The cloud must radiate away some of its thermal energy.

Which of these colors of light passes most easily through interstellar clouds?

red light

What is the key distinction between protostars and true main-sequence stars?

Protostrars generate most of their energy from gravitational contraction, and main-sequence stars generate their energy from nuclear fusion.

Which kind of pressure prevents the formation of stars with mass greater than 150 MSun?

radiation pressure

What can we learn about a star from a life track on an H-R diagram?

what surface temperature and luminosity it will have at each stage of its life

After the helium flash in a low-mass star, the star's luminosity

goes down

What happens to the core of a star after a planetary nebula ocurs?

it becomes a white dwarf

estimate how long the sun would last if it were merely a huge fire that was releasing chemical energy. assume that the sun begins with roughly 10^8 joules per kilogram, a chemical energy content typical of atomic matter.

1.7e4 years

choose the correct description, where on this diagram do we find stars that are: cool and dim; cool and luminous; hot and dim; hot and luminous

Stars that are cool and dim are located in the lower right of the plot. cool and luminous stars are in the upper right, hot and dim stars are in the lower left, and hot and luminous stars are in the upper left.

How would that life story be different if the protostar formed in a cloud without any angular momentum?

there would be no protostar disk or jets, and probably no protostellar winds. if a binary is to be formed in such a cloud, it would be a close binary.

Carbon fusion occurs in high-mass stars but not in low-mass stars because

the cores of low-mass stars never get hot enough for carbon fusion.

After a high-mass star explodes in a supernova, what is left behind?

almost always either a neutron star or a black hole

Why are main-sequence lifetimes shorter for more massive stars?

Higher core temperatures allow fusion to proceed much more rapidly.

Choose the correct explanation of how do red giants manufacture carbon-rich dust grains, and why are these important to life.

The convection in a low-mass star in its final stages of life dredges up carbon from the core and brings it to the surface. Because the carbon can then be lost via the stellar winds, these stars seed the interstellar medium with carbon, including the carbon that is used for life on Earth.

Choose the correct statement about what happens to a low-mass star after helium flash.

Its luminosity goes down

What would you be most likely to find if you returned to the solar system in 10.0 billion years?

a white dwarf

During its final days as a red giant, the Sun will reach a peak luminosity of about 3000LSun3000�Sun. Earth will therefore absorb about 3,000 times as much solar energy as it does now, and it will need to radiate 3,000 times as much thermal energy to keep its surface temperature in balance.

Estimate the temperature Earth's surface will need to attain in order to radiate that much thermal energy. You will need to use the formula for emitted power per unit area. (Assume that Earth's temperature today is around 300 KK.)

2200K

I just discovered a 3.5 MSunMSun main-sequence star orbiting a 2.5 MSunMSun red giant. I'll bet that red giant was more massive than 2.5 MSunMSun when it was a main-sequence star.

Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false) and choose the correct explanation.

This statement is sensible. The 2.5MSunMSun red giant had to be more massive than its companion at some point in the past in order for it to be more advanced in its evolutionary state than its companion.

If the Sun had been born as a high-mass star 412412 billion years ago rather than as a low-mass star, the planet Jupiter would probably have Earth-like conditions today, while Earth would be hot like Venus.

Choose the correct explanation of whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false).

This statement is not sensible. If the Sun had been born as a high-mass star 4.5 billion years ago, it would have exploded as a supernova a long time ago.

Decide whether the statement makes sense (or is clearly true) or does not make sense (or is clearly false) and choose the correct explanation.

The oxygen in my lungs comes from supernova explosions.

This statement makes sense. Low-mass stars do not produce elements heavier than carbon. Oxygen was mostly generated in high-mass stars and released through galaxy by supernovae explosions.

Which of these stars has the hottest core?

a white main-sequence star

What would stars be like if hydrogen had the smallest mass per nuclear particle?

Nuclear fusion would not occur in stars of any mass.

Which of these stars has the shortest life expectancy?

a 1 MSun star in a close binary with a 2 MSun star