Hello! I was just wondering if someone could help me with a question in a OCR Cosmology paper (Feb 2002) about special relativity. (It's question 8c, if you're interested!)
"The star alpha Centauri is 4.2 light years from Earth. A spaceship travels at 0.98c from Earth to apha Centauri.
(i) Calculate the time taken for the journey, according to observers on Earth.
(ii) Show that the distance between Earth and alpha Centauri, according to the astronauts, is about 0.8 light years.
(iii) Calculate the time taken for the journey, as measured by the astronauts."
I always dread the relativity questions; they always make my head spin.
I've come up with some answers, but I don't think they're correct.
t=4.29 years (3s.f.)
(ii) Length = Rest length * (1 - (v^2)/(c^2) )^(1/2)
Length = 4.2 * (1 - 0.98^2 )^(1/2)
Lenth = 0.836 LY (3s.f.)
(iii) Time = (Time measured by observers)/(1 - (v^2)/(c^2))^(1/2)
Time = (4.29...)/(1 - 0.98^2)^(1/2)
Time = 21.5 years (3s.f.)
Any chance of some help to put my mind at rest? Thanks!!!
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Spaceships and Special Relativity watch
- Thread Starter
- 15-04-2006 16:47
- 15-04-2006 17:19
(i) and (ii) are fine. (iii) is the wrong way round!
You show in (ii) that the distance according to the astronauts is shorter due to length-contraction. At the same time, in their frame, they observe the planet coming towards them at 0.98c! If the observed distance is shorter but the speed is the same, then in the astronauts frame, it takes them less time to reach the planet than observed from Earth.
So for (iii), there are two approaches.
1) Use time dilation since you've already worked out the time, t0, observed from Earth...
t = t0*(1-(v2/c2))1/2
OR 2) Because you've already used the Lorentz transformation in part (ii), you can just do time = distance/speed for astronauts:
time = 0.836LY / 0.98c = 0.853 years = 44 weeksLast edited by Morbo; 15-04-2006 at 17:22.
- 15-04-2006 17:30
Arghh. Original poster. How long is this module? I was looking forward to spending loads of time studying it, but now considering we haven't even started it yet, I'm panicking a bit.
- Thread Starter
- 17-04-2006 02:22
Hey - it's hard to define actually how long the module is. I guess that you're doing the OCR syllabus to ask the question; the textbook is pretty good but the content is pretty unusual. It doesn't really follow the same style as the rest of the physics course: the first couple of chapters are basically history (you have to learn about funny crystalline spheres, Plato, Copernicus, Galileo, Newton) and there's very little 'pure physics' involved and thus very little original mathematics (when you talk about Newton it's mostly a discussion about gravitational attraction - already covered in the Unifying Concepts paper), which is disappointing for those who do Further Maths (me included), because it seems that it's those type of exam questions that get most of the marks! The questions on these first few chapters are often very wordy but tend to link in with the topics that come later (e.g. how Newton was wrong about his ideas of absolute space in the light of Einstein's relativity).
After the history lesson, the style changes and becomes a bit more like the physics we've studied previously. Firstly, you study how astronomers find the distances of stars away from Earth - there's a tiny bit of maths defining two new distance units (the parsec and the light year); there's a funny little formula involving a log that you have to learn that allows you to judge the 'true' brightness of a star negating its distance from the Earth. The derivation is pretty dodgy and you have to learn that too.
However, you're soon back to wooly discussion about the formation of stars, which is related to a graph describing their temperature and 'true brightness' which you have to learn and explain. There's really not much to learn - our GCSE Science seemed to cover the basics - but it's surprising how little you take in after the first read through.
You start asking those fundamental questions, like why the sky is dark at night and this leads onto the rejection of the ideas of a static universe; a little more history and wooly discussion leads you onto another formula (of the type a=bc so there's very little they can question you on in the exam) describing how this expansion varies with the distance from Earth. Things start to get a little more interesting with talk of the red-shift and the Doppler effect (another easy equation to learn) until you start talking about the Big Bang, which is really just a load more parrot-like regurgitation of facts (things are mentioned that you'll never really need to talk about in the exam, e.g. W and Z bosons etc., that just over-load your brain).
When you think your mind has received sufficient beating, in comes the final two chapters on relativity, my favourite topic (!). In my opinion, the textbook does this really badly; I'm sure there's really not much to it - but the sheer lack of understanding by the whole class is really astounding. It's the kind of thing you'll read over and over again and think that you understand for five minutes, and then it's gone. I've had to buy an American book off eBay for a decent source of information ("Relativity Visualized" by Lewis C. Epstein - I strongly recomended - the diagrams in this book are fantastic - vastly better than those in the textbook which aren't annotated in the most part and just look like random coloured shapes strewn across the page) : I've given up on the Internet - just try searching relativity and you'll see what I mean: it's either far too complicated or doesn't explain it at all. All the syllabus really requires is for you to regurgitate a few thought experiments and learn a formula; maybe I'm completely thick but the thought experiments in textbook about time dilation and general relativity don't make any sense at all to me. I really don't like writing things in exams that I don't feel comfortable with and thus I think I consciously block relativity out of my mind when reading it! My physics teacher gave me a book entitled 'Relativity' written by Einstein himself but that just scared me even more! From what I've read, most of the understanding of general relativity comes from studying the equations, but these are far too complex for A-Level so the comprehension is mostly qualitative in the cosmology part of the syllabus.
To be honest, studying cosmology at A-Level has sucked all the life out of the topic; the reason I took A-Level physics was largely because of my love of space - I really enjoyed studying the basics at GCSE. I'll probably feel a lot happier once I've learnt the material (along with my peers) so that we can all have a proper discussion about it. I think it'll largely depend on who's teaching you; our physics teacher seems to feel that the Cosmology syllabus is something that we can do on our own for the most part - I've learnt most of the Cosmology in the last week. We had little to no structure to our lessons when started the Cosmology at the beginning of year 13; it seemed that we picked and chose which topics sounded interesting and our teacher talked about them in vastly too much depth for our first introductory lessons, assuming that we all had a good background in the subject and the physics behind it (we hadn't even studied Newton's law of Gravitation at that time). Thus, I think whether you'll enjoy it or not will largely depend on your teacher; as to the length of the course, I think all the class will have to work very hard to comprehend the subject so that we're able to answer exam questions on it. However, I'm sure you'll be able to complete it in time; as I've said, it's a hard slog but you'll get it in the end.
Don't panic - get a textbook as soon as you come back after Easter and start reading through (if you're like me and the textbook doesn't make itself crystal clear in the relativity section, I'd strongly recommed you get that book - I think amazon uk stock it if you can't find it on eBay). Good luck!
(Many thanks to Worzo for putting me on the straight-and-narrow on that relativity question; I knew something smelled fishy. Your explanation was very clear and non-condescending. Thank you!)