ASTR264 HW Chapters 4, 16
Which of the following statements about brown dwarfs is not true?
- (F) Brown dwarfs eventually collapse to become white dwarfs. - (T) All brown dwarfs have masses less than about 8% that of our Sun. - (T) Brown dwarfs form like ordinary stars but are too small to sustain nuclear fusion in their cores. - (T) Brown dwarfs are supported against gravity by degeneracy pressure, which does not depend on the object's temperature.
Which of the following statements correctly state general principles of motion? (Assume that the moving object's mass is not changing.)
- An object that is accelerating is also being acted upon by a (nonzero) net force. - An object that is accelerating is also undergoing a change in momentum. - Accelerated motion includes any motion involving a change in speed, change in direction, or both. As long as an object's mass is not changing, a net force will cause an object to undergo some type of acceleration. Because acceleration is a change in velocity, and momentum is mass times velocity, the accelerating object is also undergoing a change in momentum.
The strength of gravity:
- increases with the product of the masses of the two objects - decreases with the square of the distance between the two objects
What is the approximate range of masses that newborn main-sequence stars can have?
0.1 to 150 solar masses The lower limit is 0.08 solar masses: Below that, the core is not hot enough to sustain nuclear fusion. The upper limit of around 150 solar masses is as a result of the fact that higher-mass objects would be so luminous that they would blow themselves apart with their own radiation pressure.
This diagram shows the life tracks from protostar to the main sequence for several stars of different masses. Which track represents the star that takes the longest amount of time to reach the main sequence?
1 The lowest mass star takes the longest time.
This figure shows the life track of a 1 solar-mass star from its beginnings in a collapsing cloud fragment until it becomes a main-sequence star. At which of the numbered points is the object generating energy primarily from gravitational contraction?
1, 2, and 3 Until it reaches the main-sequence, gravitational contraction is its only source of energy.
Approximately what core temperature is required before hydrogen fusion can begin in a star?
10 million K
This figure shows the life track of a 1 solar-mass star from its beginnings in a collapsing cloud fragment until it becomes a main-sequence star. At which of the numbered points is the object generating energy primarily from hydrogen fusion?
4 only Hydrogen fusion marks the beginning of the star's main-sequence life.
Both photos show the same field of view containing a star-forming molecular cloud. One of the photos was taken in visible light and the other in infrared light. Which one is the visible-light photo, and how do you know?
A is the visible-light photo, and we can tell because dust in the molecular cloud absorbs visible light, making the cloud appear dark. Notice that we can see stars within the cloud in Photo B because infrared light can penetrate through dusty clouds.
Suppose that the Sun were to collapse from its current radius of about 700,000 km to a radius of only about 6000 km (about the radius of Earth). What would you expect to happen as a result?
A tremendous amount of gravitational potential energy would be converted into other forms of energy, and the Sun would spin much more rapidly. The dramatic shrinkage of the Sun would mean the loss of a huge amount of gravitational potential energy. Because energy is always conserved, this "lost" gravitational potential energy must reappear in other forms, such as heat (thermal energy) and light (radiative energy). Meanwhile, conservation of angular momentum would ensure that the collapsed Sun would spin much faster.
Drag each statement into the correct bin based on whether it describes motion that involves acceleration or motion at constant velocity.
Acceleration: - a car is speeding up after being stopped - a car is slowing down for a stop sign - a ball is in freefall after being dropped from a high window - a planet is orbiting the Sun in an elliptical orbit - a planet is orbiting the Sun in a circular orbit - a car is holding a steady speed around a curve Constant Velocity: - a spaceship is coasting without engine power in deep space - a car is driving 100 km/hr on a straight road - an elevator is going upward at constant speed Acceleration refers to any change in velocity. Because velocity includes both speed and direction, acceleration is occurring whenever there is any change in speed, direction, or both. Constant velocity means that both speed and direction are unchanging.
Drag each statement into the correct bin based on whether it describes motion in which the object's momentum is changing.
Acceleration: - a car is speeding up after being stopped - a car is slowing down for a stop sign - a ball is in freefall after being dropped from a high window - a planet is orbiting the Sun in an elliptical orbit - a planet is orbiting the Sun in a circular orbit - a car is holding a steady speed around a curve Constant Velocity: - a spaceship is coasting without engine power in deep space - a car is driving 100 km/hr on a straight road - an elevator is going upward at constant speed Momentum is defined as mass times velocity, so if an object's velocity is changing (that is, if it is accelerating), then its momentum must also be changing.
Drag each statement into the correct bin based on whether the motion requires the action of a net force.
Acceleration: - a car is speeding up after being stopped - a car is slowing down for a stop sign - a ball is in freefall after being dropped from a high window - a planet is orbiting the Sun in an elliptical orbit - a planet is orbiting the Sun in a circular orbit - a car is holding a steady speed around a curve Constant Velocity: - a spaceship is coasting without engine power in deep space - a car is driving 100 km/hr on a straight road - an elevator is going upward at constant speed The only way to change an object's momentum is to apply a net force to it, so if an object's momentum is changing, then a net force must be acting upon it. For example, in the case of the planets orbiting the Sun, the net force is from gravity. In the case of the accelerating cars, the net force is from the engine.
The following diagrams are the same as those from Part A. This time, rank the pairs from left to right based on the size of the acceleration the asteroid on the left would have due to the gravitational force exerted on it by the object on the right, from largest to smallest.
According to Newton's second law, the asteroid with the largest acceleration will be the one that has the strongest gravitational force exerted on it by the object on the right. That is why the ranking here is the same as the ranking for Part A.
If you actually performed and compared the two trials chosen in Part C, you would find that, while the basketball and marble would hit the ground at almost the same time, it would not quite be exact: The basketball would take slightly longer to fall to the ground than the marble. Why?
Because air resistance has a greater effect on the larger ball. The larger size and lower density of the basketball means it will encounter more air resistance than the marble, so it will take slightly longer to reach the ground.
The following five diagrams show pairs of astronomical objects that are all separated by the same distance
Because the distance is the same for all five cases, the gravitational force depends only on the product of the masses. And because the same asteroid is on the left in all five cases, the relative strength of gravitational force depends on the mass of the object on the right. Continue to Part B to explore what happens if we instead ask about the gravitational force acting on the object on the right.
Assume you have completed the two trials chosen in Part A. Which of the following possible outcomes from the trials would support Newton's theory of gravity? Neglect effects of air resistance.
Both balls fall to the ground in the same amount of time. Newton's theory of gravity predicts that, in the absence of air resistance, all objects on Earth should fall with the same acceleration of gravity, regardless of mass. This means that balls dropped from the same height should take the same amount of time to reach the ground.
Newton's theory of gravity has been tested extensively, and while it passed many tests, it did not pass all of them. For example, its prediction for how Mercury's orbit changes with time disagrees slightly with observations.
Einstein's general theory of relativity improves on Newton's theory: In most cases the two theories of gravity predict the same results, but in the situations where they differ, Einstein's theory works better than Newton's.
Each of the following items states a temperature, but does not tell you whether the temperature is measured on the Fahrenheit, Celsius, or Kelvin scale. Match the items to the appropriate temperature scale.
F: Hot day 100 degrees, ice cream 26 degrees. C: Water freezes 0 degrees. Room temperature 24. Water boils at 100. K: Coldest possible temperature 0 degrees, water boils at 373.15
Jupiter is a failed star. T/F?
False
Each of the following diagrams shows a spaceship somewhere along the way between Earth and the Moon (not to scale); the midpoint of the distance is marked to make it easier to see how the locations compare. Rank the five positions of the spaceship from left to right based on the strength of the gravitational force that Earth exerts on the spaceship, from strongest to weakest. (Assume the spaceship has the same mass throughout the trip; that is, it is not burning any fuel.)
Gravity follows an inverse square law with distance, which means the force of gravity between Earth and the spaceship weakens as the spaceship gets farther from Earth.
The following diagrams are the same as those from Part A. This time, rank the five positions of the spaceship from left to right based on the strength of the gravitational force that the Moon exerts on the spaceship, from strongest to weakest.
Gravity follows an inverse square law with distance, which means the force of gravity between the Moon and the spaceship increases as the spaceship approaches the Moon. Now continue to Part C for activities that look at the effects of both distance and mass on gravity.
Which of the following types of molecule is the most abundant in an interstellar molecular cloud?
H2 Hydrogen is the most abundant element, and molecular hydrogen is the most abundant molecule.
Suppose that two asteroids are orbiting the Sun on nearly identical orbits, and they happen to pass close enough to each other to have their orbits altered by this gravitational encounter. If one of the asteroids ends up moving to an orbit that is closer to the Sun, what happens to the other asteroid?
It will end up on an orbit that is farther from the Sun. Total energy must be conserved, so if one asteroid loses energy and moves to a closer orbit, the other must gain energy and move to a more distant orbit.
The following diagrams are the same as those from Part A. Again considering only the two objects shown in each pair, this time rank the strength, from strongest to weakest, of the gravitational force acting on the object on the right.
Newton's third law tells us that the gravitational force exerted on the asteroid on the left by the object on the right will be equal in magnitude, but opposite in direction to the gravitational force exerted on the object on the right by the asteroid on the left. That is why the ranking here is the same as the ranking for Part A.
Einstein's theory, like Newton's, predicts that, in the absence of air resistance, all objects should fall at the same rate regardless of their masses. Consider the following hypothetical experimental results. Which one would indicate a failure of Einstein's theory?
Scientists dropping balls on the Moon find that balls of different mass fall at slightly different rates. Dropping the balls on the Moon removes any potential effects due to air resistance, so a result in which mass affects the rate of fall would directly contradict the prediction of Einstein's (as well as Newton's) theory.
This figure shows frames from a computer simulation of star formation, starting at the left with a large molecular cloud measuring more than a light-year across. What is happening as time passes (from left to right)?
The cloud is fragmenting into smaller pieces that will form stars. This type of fragmentation is why most clouds give birth to many stars.
In Part A, you found that your weight will be greater than normal when the elevator is moving upward with increasing speed. For which of the following other motions would your weight also be greater than your normal weight?
The elevator moves downward while slowing in speed. In a downward-moving elevator, the elevator can be slowing only if it has an upward acceleration. As you know from Part A, an upward acceleration will give you an increased weight. Therefore, in an elevator that moves downward while slowing in speed, the acceleration is upward and your weight is greater than normal.
The main photo and the smaller inset both show the same field of view containing a star-forming molecular cloud. One of the photos was taken in visible light and the other in infrared light. Which one is the infrared photo, and how do you know?
The main (larger) photo is the infrared because molecular clouds emit much more infrared light than visible light. Molecular clouds are too cool to emit visible light. Notice that the bright region in the large, infrared image is the dark region in the smaller, visible inset.
This famous image from the Hubble Space Telescope shows what is sometimes called the "pillars of creation." Which of the following best describes what it shows?
The pillars are clouds of gas and dust in which many new stars are forming; the edges of the pillars are sculpted by ultraviolet radiation from stars outside the pillars. The ultraviolet radiation heats and erodes the dark gas, giving the star-forming clouds of the pillars their distinctive shape.
Each diagram shows a single experimental trial in which you will drop a ball from some height. In each case, the ball's size, mass, and height are labeled. Note that two diagrams show a basketball, one diagram shows a bowling ball of the same size but larger mass, and one diagram shows a much smaller marble with the same mass as the basketball. You have a timer that allows you to measure how long it takes the ball to fall to the ground. Which pair of trials will allow you to test the prediction that an object's mass does not affect its rate of fall?
The simplest way to test the effects of mass is to compare the results of two trials that are identical except for the mass of the balls. In the language of experimental design, we say that the mass is the "variable of interest" for this experiment, and we therefore hold the other variables (size and height) constant so that they cannot affect the results.
Consider again the experimental trials from Part A. This time, you wish to test how the size of an object affects the rate of its fall. Which pair of trials should you compare?
The variable of interest is now size, so appropriate trials to compare are those in which size differs but other variables are constant.
How are magnetic fields thought to affect star formation in molecular clouds?
They can help resist gravity, so that more total mass is needed before the cloud can collapse to form stars. The magnetic fields that thread clouds inhibit the movement of gas, thereby adding to the resistance to gravity provided by thermal pressure (and turbulent gas motions).
Which of the following statements is probably true about the first stars in the universe?
They were made only from hydrogen and helium. Most of the heavier elements were created in stars and thus did not exist when the first stars formed.
This photo shows gas associated with a protostar. What is this gas doing?
This photo shows gas associated with a protostar. What is this gas doing? The long, mostly straight paths shows that these are jets flowing outward from the protostar.
Suppose you are in an elevator car when the elevator cable breaks. Which of the following correctly describes what happens and why.
You float weightlessly within the elevator car because you and the elevator both begin to accelerate downward at the same rate. Once the cable breaks, you and the elevator car both fall with the acceleration of gravity. This means you are no longer pressing against the scale or the elevator floor, so you float weightlessly within the car -- though only until you and the car hit the ground!
Which star spends the longest time in the protostellar phase of life?
a 1 solar-mass star Lower mass stars take longer in all phases of life.
What kind of gas cloud is most likely to give birth to stars?
a cold, dense gas cloud This type of cloud has lower thermal pressure (because of the low temperature) and stronger gravity (because of the high density), giving gravity the upper hand.
What is a protostar?
a star that is still in the process of forming It generates energy by gravitational contraction, as it is not yet hot enough for nuclear fusion it its core.
The dark area stretching from the center of this picture to the upper right is about 50 light-years long and lies in the plane of the Milky Way Galaxy. What is it?
a star-forming cloud It is dark because it contains cool, molecular gas, which is the type of gas cloud in which stars can form.
A forming star spins more rapidly as it collapses because of conservation of ____.
angular momentum
If a protostar has a mass too small for it to sustain nuclear fusion, it becomes the type of object known as a ____.
brown dwarf
An apple contains ______ energy that your body can convert into other forms energy.
chemical potential
What law explains why a collapsing cloud usually forms a protostellar disk around a protostar?
conservation of angular momentum A protostellar disk forms as a consequence of conservation of angular momentum, which makes the cloud rotate faster as it shrinks in size.
The collapse of a protostar with less than 0.08 times the mass of the Sun is halted by ____.
degeneracy pressure
Suppose you look at a star that can be seen through the edge of a dusty interstellar cloud. The star will look _______ than it would if it were outside the cloud.
dimmer and redder It is dimmer because the dust absorbs some of the star's light, and redder because dust scatters blue light more effectively than red light.
A star is born when it comes into ____, in which the energy released by fusion matches the energy it radiates into space.
energy balance
A gas cloud in which gravity is perfectly balanced against pressure is said to be in ____.
gravitational equilibrium
An asteroid that is moving farther from the Sun is gaining ______ energy.
gravitational potential
The basic requirement for a cloud to collapse to form a star is that __________.
gravity must be strong enough to overpower the cloud's internal pressure The cloud will continue to collapse, ultimately forming a star, as long as gravity is strong enough to overcome the cloud's internal pressure.
Suppose you are in an elevator. As the elevator starts upward, its speed will increase. During this time when the elevator is moving upward with increasing speed, your weight will be __________.
greater than your normal weight at rest Increasing speed means acceleration, and when the elevator is accelerating upward you will feel a force pressing you to the floor, making your weight greater than your normal (at rest) weight.
As the cloud shrinks in size, its central temperature __________ as a result of its __________.
increases; gravitational potential energy being converted to thermal energy As the cloud shrinks in size, its gravitational potential energy decreases. Because energy cannot simply disappear, the "lost" gravitational potential energy must be converted into some other form. Some of it is converted into thermal energy, which raises the temperature of the gas cloud. The rest is mostly converted into radiative energy, which is released into space as light.
Which part of the electromagnetic spectrum generally gives us our best views of stars forming in dusty clouds?
infrared Infrared light can pass through dusty clouds, unlike visible light.
Which of the following phenomena is not commonly associated with the star-formation process?
intense ultraviolet radiation coming from a protostar Protostars are too cool to emit much ultraviolet light.
Star-forming clouds appear dark in visible-light photos because the light of stars behind them is absorbed by __________.
interstellar dust Although dust makes up only a small fraction of a star-forming cloud's mass, it is responsible for absorbing the visible light of stars behind the cloud.
Rapidly moving comets have more ______ energy than slowly moving ones.
kinetic
The vast majority of stars in a newly formed star cluster are ______.
less massive than the Sun In general, the lower the mass, the more common the star.
Suppose you are in an elevator that is moving upward. As the elevator nears the floor at which you will get off, its speed slows down. During this time when the elevator is moving upward with decreasing speed, your weight will be __________.
less than your normal weight at rest Even though the elevator is still moving upward, the fact that its speed is slowing means that the acceleration is downward. The situation is rather like that of a ball that is still on its way up after you throw it: the ball slows as it goes upward because of the downward acceleration of gravity. Because the acceleration of the elevator is downward, your weight is lower than normal.
Nuclear fusion in stars converts some of the ______ energy of hydrogen nuclei into light and heat.
mass
Interstellar dust consists mostly of _____.
microscopic particles of carbon and silicon These tiny, solid particles are important, even though their total mass makes up less than 1% of the interstellar medium.
A star that has not yet finished forming is called a ____.
protostar
The light from Polaris travels through space in the form of ______ energy.
radiative
As a star forming cloud shrinks in size, its rate of rotation ________ because ____________.
speeds up; its total angular momentum is conserved The law of conservation of angular momentum states that, in the absence of external influences (torques), the angular momentum of an object or a system of objects stays constant. Since the angular momentum of an object depends on both its size and rate of rotation, the cloud's rate of rotation will increase as its size (or radius) decreases in order to conserve angular momentum.
The video shows a collapsing cloud of interstellar gas, which is held together by the mutual gravitational attraction of all the atoms and molecules that make up the cloud. As the cloud collapses, the overall force of gravity that draws the cloud inward gradually becomes ____ because __________.
stronger; the strength of gravity follows an inverse square law with distance The force of gravity between any two particles increases as the particles come closer together. Therefore, as the cloud shrinks and particles move closer together, the force of gravity strengthens. This will tend to accelerate the collapse as long as no other force resists it. This is the case during the early stages of the collapse before the internal gas pressure builds up. (Once the gas pressure builds up, the outward push of the pressure can counteract the inward pull of gravity, which is why the cloud eventually stops contracting.)
Consider Earth and the Moon. As you should now realize, the gravitational force that Earth exerts on the Moon is equal and opposite to that which the Moon exerts on Earth. Therefore, according to Newton's second law of motion __________.
the Moon has a larger acceleration than Earth, because it has a smaller mass Newton's second law of motion, F=ma, means that for a particular force F, the product mass x acceleration must always be the same. Therefore if mass is larger, acceleration must be smaller, and vice versa.
The interstellar clouds called molecular clouds are _______.
the cool clouds in which stars form They are called molecular clouds because they are cold enough to allow their hydrogen atoms to pair up into hydrogen molecules (H2).
When you are standing on a scale in an elevator, what exactly does the scale measure?
the force you exert on the scale Your presence in an elevator cannot change either your mass or the gravitational force exerted on you by Earth. The scale measures the force that is exerted on it, which in an elevator is a combination of the force due to gravity and a force due to the elevator's acceleration.
What do we mean by the interstellar medium?
the gas and dust that lies in between the stars in the Milky Way galaxy In other words, it's the stuff that occupies the spaces between stars.
What can we learn about a star from a life track on an H-R diagram?
the surface temperature and luminosity the star will have at each stage of its life A star's particular life track depends only on its mass.
Due to its much higher density, water heated to 80 degrees (Celsius) contains more ______ energy than air at the same temperature.
thermal
As a protostar shrinks in size, its central temperature rises along with its ____.
thermal pressure
Most interstellar clouds remain stable in size because the force of gravity is opposed by _______ within the cloud.
thermal pressure Thermal pressure is the pressure resulting from the thermal motions of the particles in the cloud.
When does a protostar become a main-sequence star?
when the rate of hydrogen fusion becomes high enough to balance the rate at which the star radiates energy into space This event marks what we consider to be the birth of the star.
