ASTR 310 Astrobiology 2013 Spring Semester Prof. Welsh Weighting of Questions ______________________ 10% Multiple Choice 20% Problem on "Communication with Mars" 35% Astrobiology Magazine 35% Sagan's "Hallucination" chapter Answers for Written Homework #1 Questions ========================================= Chapter 1, #17: c ~100,000 years Chapter 2, #36: C A "theory" in the scientific sense, is based on a vast amount of experiments/data and can explain a very broad set of phenomena. It is the highest level of understanding that humans have of a subject. As quoted in the Teach Yourself secion of our class webpages, "A law explains a set of observations; a theory explains a set of laws." In contrast, a hypothesis is only an educated guess. [See the explanation of the difference between "theory" and "hypothesis" at the bottom of the Class News page.] Note: Theories cannot be proved; *nothing* can be proved in science, if you use the word proof literallly. The way science works, everything is open to revision and being improved upon - ideas are never sacred and set in stone. Revision is not only possible, it is encouraged. But that does not mean a "theory" isn't correct or 100% accurate. Chapter 3, #43: c not all terrestrial planets have oceans Chapter 3, #58 "Communication with Mars" ________________________________________ The time it takes to travel to an object is the distance divided by the speed of the traveller. In formula terms, t = d/v, where t is the time, d is the distance, and v is the velocity or speed of the object. ~~~~~ ** MAKE SURE YOU SHOW ALL WORK. SHOW ALL CALCULATIONS AND FULLY EXPLAIN ALL STEPS. THE ANSWER ALONE WILL EARN NO CREDIT.** In this problem, there are two distances: (a) the distance to Mars when it is closest, and (b) the distance when Mars is furthest away. These are given as 56 million km and 400 million km, respectively. Since we are talking about radio waves, the speed is always the speed of light, c=300,000 km/s. Make *sure* you use the correct units for the distance and speed - the answer will be wrong if you use miles per hour or something like that. Part (a): t = d / c = 56 million km / c = 56,000,000 km / 300,000 km/s <---- DO NOT FORGET THE UNITS! = 186.66666667 s Now lets get the correct number of digits. It is technically incorrect to have more significant digits in your answer than you have in the question. The questions gives 2 significant digits (the "56" in 56,000,000), so the answer should have only 2 significant digits. If it has more than 2, then you are making up precision that does not exits. Thus we round the answer to: t = 190 seconds **** THIS IS THE ANSWER. Or you can say 3 min 10 seconds. Part (b): We repeat the above, except use 400 million km as the distance. Hence: t = d / c = 400 million km / c = 400,000,000 km / 300,000 km/s <---- DO NOT FORGET THE UNITS! = 1333.33333333 s Again, rounding the number of digits to have the correct precision gives us: t = 1300 seconds Now this is an awkward size. If I say you have 1300 seconds for your exam, most folks won't intuitively know what that means. So we must convert to something sensible and common to help us understand what this means. Divide 1333 seconds by 60 seconds per minute to get 22.22 minutes, or more correctly: t = 22 minutes ***** THIS IS THE ANSWER ....... *** Now comes the most important part of the homework: THINK ! *** What does this mean? Compare this with the time it takes light to get to the Moon: ~1.2 seconds (see class notes). Compare 1.2 seconds with 190 seconds. Mars is *much much* further away! How much? Do the math: 190 s / 1.2 s = 158 times further away! And this is when Mars is closest. When it is most distant, you should compare 1.2 seconds with 22 minutes. How many time further away is this? (1100 times larger!) If you were to try to remotely control a rover on Mars, there would be a time delay of twice the above times, since the signal has to get to Mars, then get back to Earth. So there would be a delay of about 6.5 minutes to 44 minutes - much, much too long to do anything in real-time. Rovers either have to move extremely slowly, cm by cm in an agonizingly long process, or or they have to have some sort of built-in software+hardware "brains" so they can drive a bit on their own. This is all for Mars. But what about Jupiter or Saturn? They are **MUCH** further away. (Do the math yourself to see if you really understand how this works. Look at the "Teach Yourself" hints.) This means the spacecraft in the outer solar system have to be very much autonomous - they need to be able to do many thing on their own, since it takes too long to communicate with them.