Name: Lab Time: PH04 Lab 2 Measuring Distances Pre-Lab 2. Goals This is the second lab. Like the first lab this lab does not seem to be part of a complete sequence of the study of astronomy, but it will make since as we see that our guiding themes in this course are science, gravity, and the size of the universe. We could ask at this time how big is the universe, or how do we go about learning about the universe, or how does gravity affect the life of the universe? All good questions, and we will answer them. The first thing to consider is the size of the Solar System. 2.2 Introduction Just like with light, there are some standard units that we will use for the sizes of the objects we are measuring. We are not going to be talking about small things, but very large things now. Question#: Fill in the lists below with the standard units needed. Plus give the definitions for the units given in the second list. For definitions you can use the text or the internet. Make sure when using the internet to be careful of your source. Fill in the standard unit that you would think that we would use in for the following items The standard unit of length on the Earth. The standard unit for distances between the planets. The standard unit for distances between the stars. The standard unit of time. From previously, the standard unit that we use to measure the wavelength of light. Give the definition and value in km of the following distance units. The Astronomical Unit (AU) The Light Year (ly)
2 PH04 LAB 2. MEASURING DISTANCES PRE-LAB The Parsec (pc) Give the definition without values for the following units. Degree Arcminute Arcsecond 2.3 Observations The Solar System is something that we can find a lot about without a telescope. There are many things that you will see when you look at the night sky, and some of them will be very important. So the observations we are going to make are going to depend on your ability to look at the sky on some night before this is due. You are going to need to go outside and look at the sky to answer some of these questions. Other questions will be developed by giving you some observations to think about. I will walk you through questions, hypothesis, predictions and model. Question#2: When you look at the sky what do you see? Describe in a couple of sentences what the sky looks like. Remember that you are just looking at the sky. There is no book answer just your observations. Now we will make some other observations. Lets think about light, specifically the light from the Sun reflecting off of the planets. When we see Mars in the sky, the light has gone from the Sun reflected off of Mars and arrived back on Earth. We collect that light so that we may study Mars. Or we send a probe to Mars and it sends us back radio light that we can analyze as well. So light can tell us what objects are made from, but it is also the thing that we use to gather any information. The following table gives some information about the Solar System. We have used this table in the previous lab. Now we want to think about it again.
2.3. OBSERVATIONS 3 Planet Distance from Amount of Light Travel Name the Sun (AU) Sunlight (Earth) Time from the Sun(min.) Mercury 0.4 6.25 3.8 Venus 0.7 2 5.8 Earth 8.3 Mars.5 2 2.45 Jupiter 5 25 4.5 Saturn 0 00 83 Uranus 20 400 66 Neptune 30 900 249 Pluto 40 600 332
4 PH04 LAB 2. MEASURING DISTANCES PRE-LAB Question#3: What observations can you make about this table? See if you can connect the discussion that we are beginning to have with your observations. Don t try to come up with the answers to the physics questions try to look at what you are seeing. Now one more set of observations. This is one that will probably be the hardest, but it will be one of the more important observations. Task#: This is a serious task, so try it and really think about what you are observing. Find an object a small distance away (about 20 feet away is the best for this process). Now close your right eye, and hold your thumb up until it covers the object in your view. Now close your left eye and open your right eye. What do you see? Describe it in the best possible way you can. Now this last task may seem silly, but there is an astronomical phenomenon that mimics what you just observed. Question#4: Find the definition of stellar parallax in the text and then write how that is similar to the previous task. 2.4 Questions Task#2: I am going to give you a list of hypotheses that come out of the previous observations. I want you to write whether you agree or disagree with these hypotheses. If you disagree, then tell me why.. Stellar Parallax is useful to find the distance to nearby stars.
2.5. MODEL 5 2. We can use radar measurements to find the size of the Solar System. 3. We can use radar measurements to find the distances to the nearest stars. These are the hypotheses that I came up with from my observations. Question#5: Can you come up with one other hypothesis that I didn t mention? 2.5 Model We can make a couple of models from all of this material. I will always help you to build the model, but we will do it by you answering questions for me. Question#6: You made some observations from the Solar System table. One of those observations was probably that light takes longer to get from the Sun to a planet the further that planet is from the Sun. Now, you are going to send a radar signal to some planets and wait for that signal to get back to Earth. Assume that the planet is at it s closest to Earth.Using this idea complete the following list. Approximate the time you think you would need to wait to get receive your signal if you sent it to Mars. (Remember that you are sending the signal and waiting for it to get back) Approximate the time for your signal if your target was Pluto. I claim that we can write a rule for the travel time of a radar signal based on those two approximations. This rule is t = 2 ld (2.) t is the travel time, and ld is the light distance to the object. In the case of Mars ld = 4.2min. Do you agree? It turns out that we can figure out the distance to an object by knowing how long it takes for a radar (or any light) signal to go to and come back from an object.
6 PH04 LAB 2. MEASURING DISTANCES PRE-LAB Remember that the speed is distance per time: s = d T (2.2) s is speed d is distance and T is time A car traveling 60 km sec will travel 60 km every second. Radar light traveling at 300,000 km sec will travel 300,000 km every second. If we want to know how far away our car is, we need to know how fast it was traveling and how long it was traveling. If we take the above equation and reorganize it, we see that: d = s T (2.3) So for our radar signal, if we know how long it was traveling across space from the object we sent it to, we can tell how far away that object is. But the time it traveled to from the object is just half of the entire travel time for the signal from our Earth source to our Earth detector or T = t 2 So our model for finding the distance to an object using radar (or any other light signal) is d = c t 2 d is the distance in km c is the speed of light 300,000 km sec and t is the travel time from source to receiver in seconds. (2.4) We can do the same thing for parallax, but the geometry and math can become more difficult. So I will give you the model for the distance using parallax: D = b 2 tan( P 2 ) (2.5) D is the distance in the units you choose to measure in b is the baseline (distance between the two measurements) P is the parallactic angle It is understood that these do not make much sense yet. You will be using this model in the lab, and it will become more clear then. The astronomical version of distance using parallax is: d = p (2.6)
2.6. PREDICTIONS 7 d is the distance in parsecs p is the parallactic angle in arcseconds. So we can get the distance as long as we can measure the angle. 2.6 Predictions One last thing with this lab. We want to make some predictions about what we would expect to measure. There will be two last questions to answer. Question#7: What can you predict about your measurements of distance using radar signals from Earth? Think about the limitations and the usefulness. Question#8: What can you predict about your measurements of distance using stellar parallax? Think about what you can and can t use this for.