Astronomy: Discussion Questions
Astronomy 1760-60
Fall 2010
Homework 2 Answers
Short Answer/General Questions: These should have short answers of a few sentences. 1. Explain the difference between speed and velocity and why this is important in acceleration. Give an example where an object is accelerating, but their speed is constant.
Speed: Change in position over time – distance over time Velocity: Change in position and direction over time – distance and direction over time Acceleration: Change in Velocity, so a change in speed, direction or both. Example: A change in direction but not speed would be acceleration around a curve, where speed is constant but the direction changes, which means the velocity changes, which means that acceleration occurs.
2. Why …show more content…
is light so important in astronomy? We spent a large part of our lecture talking about light and the types of light – why does this matter so much in astronomy? What is the main way astronomers get information about things outside our galaxy?
Light is important in astronomy because, outside the solar system, it is the ONLY thing that reaches us from any other place in the universe. All the information we have is from light. Light (viewed by telescopes and satellites) is the main way that astronomers gain information about the universe outside our solar system. Light tells us about the source object, the path it has taken, the things it has passed and anything it has gone through. Sometimes it’s hard to tell some of these things apart, but they are all in the light information we receive.
3. In class we talked about the three main types of energy – kinetic, potential and radiation. For each type of energy, give an example and explain why this type of energy fits in that category.
Kinetic (energy of motion) – running, throwing a ball, swatting a fly, and so many things Potential (saved energy) – energy stored in a battery, energy stored in your body (from food) Radiative energy (light energy) – light energy from the sun (feels warm when you are outside, right?)
4. What is the difference between angular resolution and magnification? Give an example from everyday life about angular resolution vs. magnification.
Astronomy 1760-60
Fall 2010
Homework 2 Answers
Angular resolution vs. Magnification – Magnification means that you are enlarging an image that you already have, but you are not adding any more detail to it. You can increase the size, but you aren’t going to see any more. Angular resolution is the smallest angle between two points that allows them to still be distinguishable, and if you increase that, you add more detail to an image. Remember, that when you blow things up on the computer (magnify) the computer screen is limiting your angular resolution, so images may seem more detailed but that’s because the screen couldn’t show you the detail that was in the image. Once the angular resolution of the screen matches the image, you can enlarge it (magnify) it all you want, you won’t see more detail. But getting a higher resolution version of the same image and magnifying it by the same amount will allow you to see more detail because that picture has more information. Which is also why those files take up so much more room on your computer.
Think about it/Experiment Questions: These questions require a little more work and slightly more time, though none of them should take too long. 1. You find a planet orbiting a star that is roughly the same mass as our sun. This planet orbits in 63 days. Using either Kepler’s 3rd Law or the Newtonian version of it (it’s up to you, just make sure to show which you used) calculate the planet’s orbital distance and compare to the Earth’s orbital distance. Remember, these two ways will have answers in different units, so make sure you know what units you are working in to compare to the Earth. Make sure to show your work for the calculations which ever way you use. Below are a few helpful pieces of information: Kepler’s 3rd Law: pg. 68 in your book, and there is an example as well. Newtonian Version: pg. 100 on the left side Earth’s distance from the Sun: 1 AU or 1.5 x 10 11 m
Keplers Law P^2 = A^3 P = 63/365 = 0.17 P^2 = 0.029 A = (0.029)^1/3 A = 0.31 AU This distance, compared to the Earth-Sun distance is 1 AU, which means that this planet is 1/3 of the distance from its sun as we are from ours.
2. In class we talked about black body spectra. Humans emit as a blackbody, not just stars. Assuming that we have a temperature of 310 K (about body temperature), use the formula on
Astronomy 1760-60
Fall 2010
Homework 2 Answers
page 123 of your book to find the wavelength where we emit most of our radiation. Compare this to our sun, which has a peak wavelength of 500 nm (visible light). What type of light do we peak in? Show your calculations to get full credit on this problem!
Lambda = 2,900,000/T = 2,900,000/310 = 9355 nm This is around 10,000 nm = 1x10^4 nm = 1x 10^-5 m = INFRARED We peak in the infrared, as do most Earth mammals. This is why night vision goggles see people at night – they are showing infrared. However, despite what movies will have you believe, they mostly don’t work well through walls. You don’t have good angular resolution through walls. And some windows now are well enough insulated that you won’t see much infrared light through them either.
3.
The atmosphere of the Earth reflects back into space a portion of the Sun’s light, so it never reaches the ground. But the atmosphere also helps keep some of the energy closer to the Earth once it does reach the ground. If we didn’t have the atmosphere, would the Earth’s surface be warmer or colder? Why do you think this? I’m not asking that you look up the answer – I want you to think about it and give me your reasoning and justify it. You can use to text book to help, but make sure to reference anything that you use from it in your …show more content…
answer.
The temperature of the Earth without an atmosphere would be about 255 K, which is ~ 0 degrees F.
This means that the Earth may have liquid water at some times (during summer) but not most of the year and not constantly. This would also be the average temperature (meaning that the temperature would be fluctuating around this as many of you thought) but since now the average temperature is 288 K (58 F) it means the average would be almost 60 degrees colder. Many of you noted that there would be far more light and energy reaching the Earth, which is true. But much of it wouldn’t interact with the Earth that much and wouldn’t change the temperature on the surface. This is balanced by the greenhouse effect that happens with an atmosphere, which warms the surface even though it also blocks some light from reaching the surface. This balance would result in a slightly colder Earth, though like some of you guessed, it would still be livable for us today (though likely not for evolving life forms).
4. Do an experiment at home. Hang up a piece of paper at eye level with some lines on it 2 mm apart (you can make your own, or there is one posted on D2L). Walk back until you can just see them as distinct lines and could tell exactly how many there are on the page. This gives you a measure of your angular resolution. How far back did you get from the lines? Average eye sight says you should see them just resolving around 4-5 m. Were you closer or farther? Does this mean you have better than
average eyesight (better angular resolution), or worse?
Astronomy 1760-60
Fall 2010
Homework 2 Answers
Use the distance that you were away from the wall to find out the angular resolution of your eye using the formula below and the distance in meters. You can convert feet to meters by dividing the number of feet by 3.28 to get the number of meters. Angular resolution (arc minutes) = 6.8755 / Distance (m) Most people will get something along the lines of 1.5 to 1.0 angular resolution. Now you can see why Tycho Brahe’s observations were so impressive. If you wear contacts or glasses, make sure to have them in when you do this experiment. Otherwise you’re answer will be much larger than 1.5.
I stood 15.83 ft away, 15.83/3.28 which is 4.75 m. Angular resolution of my eyes (with glasses) is 6.875/4.75 = 1.45, which is pretty average. Even if you have angular resolution around 1.8 to 2, that is still pretty good vision. People who had to stand 3 ft away (angular resolution around 7) may need to get some better glasses though. The class average angular resolution = 2.43 Remember, a smaller number means that the angle between two things can be smaller when you distinguish them, meaning they can be closer. So smaller = better. In the case of angular resolution.
Fall 2010
Homework 2 Answers
Short Answer/General Questions: These should have short answers of a few sentences. 1. Explain the difference between speed and velocity and why this is important in acceleration. Give an example where an object is accelerating, but their speed is constant.
Speed: Change in position over time – distance over time Velocity: Change in position and direction over time – distance and direction over time Acceleration: Change in Velocity, so a change in speed, direction or both. Example: A change in direction but not speed would be acceleration around a curve, where speed is constant but the direction changes, which means the velocity changes, which means that acceleration occurs.
2. Why …show more content…
is light so important in astronomy? We spent a large part of our lecture talking about light and the types of light – why does this matter so much in astronomy? What is the main way astronomers get information about things outside our galaxy?
Light is important in astronomy because, outside the solar system, it is the ONLY thing that reaches us from any other place in the universe. All the information we have is from light. Light (viewed by telescopes and satellites) is the main way that astronomers gain information about the universe outside our solar system. Light tells us about the source object, the path it has taken, the things it has passed and anything it has gone through. Sometimes it’s hard to tell some of these things apart, but they are all in the light information we receive.
3. In class we talked about the three main types of energy – kinetic, potential and radiation. For each type of energy, give an example and explain why this type of energy fits in that category.
Kinetic (energy of motion) – running, throwing a ball, swatting a fly, and so many things Potential (saved energy) – energy stored in a battery, energy stored in your body (from food) Radiative energy (light energy) – light energy from the sun (feels warm when you are outside, right?)
4. What is the difference between angular resolution and magnification? Give an example from everyday life about angular resolution vs. magnification.
Astronomy 1760-60
Fall 2010
Homework 2 Answers
Angular resolution vs. Magnification – Magnification means that you are enlarging an image that you already have, but you are not adding any more detail to it. You can increase the size, but you aren’t going to see any more. Angular resolution is the smallest angle between two points that allows them to still be distinguishable, and if you increase that, you add more detail to an image. Remember, that when you blow things up on the computer (magnify) the computer screen is limiting your angular resolution, so images may seem more detailed but that’s because the screen couldn’t show you the detail that was in the image. Once the angular resolution of the screen matches the image, you can enlarge it (magnify) it all you want, you won’t see more detail. But getting a higher resolution version of the same image and magnifying it by the same amount will allow you to see more detail because that picture has more information. Which is also why those files take up so much more room on your computer.
Think about it/Experiment Questions: These questions require a little more work and slightly more time, though none of them should take too long. 1. You find a planet orbiting a star that is roughly the same mass as our sun. This planet orbits in 63 days. Using either Kepler’s 3rd Law or the Newtonian version of it (it’s up to you, just make sure to show which you used) calculate the planet’s orbital distance and compare to the Earth’s orbital distance. Remember, these two ways will have answers in different units, so make sure you know what units you are working in to compare to the Earth. Make sure to show your work for the calculations which ever way you use. Below are a few helpful pieces of information: Kepler’s 3rd Law: pg. 68 in your book, and there is an example as well. Newtonian Version: pg. 100 on the left side Earth’s distance from the Sun: 1 AU or 1.5 x 10 11 m
Keplers Law P^2 = A^3 P = 63/365 = 0.17 P^2 = 0.029 A = (0.029)^1/3 A = 0.31 AU This distance, compared to the Earth-Sun distance is 1 AU, which means that this planet is 1/3 of the distance from its sun as we are from ours.
2. In class we talked about black body spectra. Humans emit as a blackbody, not just stars. Assuming that we have a temperature of 310 K (about body temperature), use the formula on
Astronomy 1760-60
Fall 2010
Homework 2 Answers
page 123 of your book to find the wavelength where we emit most of our radiation. Compare this to our sun, which has a peak wavelength of 500 nm (visible light). What type of light do we peak in? Show your calculations to get full credit on this problem!
Lambda = 2,900,000/T = 2,900,000/310 = 9355 nm This is around 10,000 nm = 1x10^4 nm = 1x 10^-5 m = INFRARED We peak in the infrared, as do most Earth mammals. This is why night vision goggles see people at night – they are showing infrared. However, despite what movies will have you believe, they mostly don’t work well through walls. You don’t have good angular resolution through walls. And some windows now are well enough insulated that you won’t see much infrared light through them either.
3.
The atmosphere of the Earth reflects back into space a portion of the Sun’s light, so it never reaches the ground. But the atmosphere also helps keep some of the energy closer to the Earth once it does reach the ground. If we didn’t have the atmosphere, would the Earth’s surface be warmer or colder? Why do you think this? I’m not asking that you look up the answer – I want you to think about it and give me your reasoning and justify it. You can use to text book to help, but make sure to reference anything that you use from it in your …show more content…
answer.
The temperature of the Earth without an atmosphere would be about 255 K, which is ~ 0 degrees F.
This means that the Earth may have liquid water at some times (during summer) but not most of the year and not constantly. This would also be the average temperature (meaning that the temperature would be fluctuating around this as many of you thought) but since now the average temperature is 288 K (58 F) it means the average would be almost 60 degrees colder. Many of you noted that there would be far more light and energy reaching the Earth, which is true. But much of it wouldn’t interact with the Earth that much and wouldn’t change the temperature on the surface. This is balanced by the greenhouse effect that happens with an atmosphere, which warms the surface even though it also blocks some light from reaching the surface. This balance would result in a slightly colder Earth, though like some of you guessed, it would still be livable for us today (though likely not for evolving life forms).
4. Do an experiment at home. Hang up a piece of paper at eye level with some lines on it 2 mm apart (you can make your own, or there is one posted on D2L). Walk back until you can just see them as distinct lines and could tell exactly how many there are on the page. This gives you a measure of your angular resolution. How far back did you get from the lines? Average eye sight says you should see them just resolving around 4-5 m. Were you closer or farther? Does this mean you have better than
average eyesight (better angular resolution), or worse?
Astronomy 1760-60
Fall 2010
Homework 2 Answers
Use the distance that you were away from the wall to find out the angular resolution of your eye using the formula below and the distance in meters. You can convert feet to meters by dividing the number of feet by 3.28 to get the number of meters. Angular resolution (arc minutes) = 6.8755 / Distance (m) Most people will get something along the lines of 1.5 to 1.0 angular resolution. Now you can see why Tycho Brahe’s observations were so impressive. If you wear contacts or glasses, make sure to have them in when you do this experiment. Otherwise you’re answer will be much larger than 1.5.
I stood 15.83 ft away, 15.83/3.28 which is 4.75 m. Angular resolution of my eyes (with glasses) is 6.875/4.75 = 1.45, which is pretty average. Even if you have angular resolution around 1.8 to 2, that is still pretty good vision. People who had to stand 3 ft away (angular resolution around 7) may need to get some better glasses though. The class average angular resolution = 2.43 Remember, a smaller number means that the angle between two things can be smaller when you distinguish them, meaning they can be closer. So smaller = better. In the case of angular resolution.