Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 10912 result(s) returned

1 Introducing cosmology

General relativity has a very different conceptual basis from that of Newtonian mechanics. Its success in accounting for the precession of Mercury's orbit, and the bending of light by massive objects like the Sun, gives us confidence that our picture of space and time should be Einstein's rather than Newton's. In this and the following units, we turn our attention to the study of the large-scale structure of spacetime. We see how spacetime as a whole is curved by the gross distribution of mas
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Learning outcomes

By the end of this unit you should be able to:

  • describe the characteristics of light emitted by stars, and hence the information of cosmological interest that can be deduced from it;

  • distinguish between true and false statements relevant to the distribution and motion of stars within galaxies, and of galaxies within clusters and superclusters;

  • outline the methods used for estimating the distances to stars and to galaxies;

  • explain and
    Author(s): The Open University

    License information
    Related content

    Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Introduction

In this unit, we present the three main lines of experimental evidence pointing to the big bang origin of the Universe: (i) the recession of the galaxies; (ii) the microwave remnant of the early fireball; and (iii) the comparison between the calculated primordial nuclear abundances and the present-day composition of matter in the Universe.

A data sheet of useful information is provided as a pdf for your use. You may wish to print out a copy to keep handy as you progress through the unit
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Acknowledgements

The material acknowledged below is Proprietary and used under licence (not subject to Creative Commons licence). See Terms and Conditions.

Grateful acknowledgement is made to the following for permission to reproduce:

Figure 1a: Neil Borden/Science Photo Library; Figure: 1b NOAA/Science Photo Library; Figure 1c: Max-Planck-Institute for Radio Astronomy/Science Photo Library; Figure 11: Science Photo Library; Figure 14: Science Museum.


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

6 Appendix: a note on displacement current density

This appendix is optional reading. It is included for the sake of comparison with other texts.

The Ampère–Maxwell law,

is sometimes expressed in the form


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.2 The energy of electromagnetic waves

The energy density of an electric field E is

Although we will not prove it in this unit, a very similar result applies to magnetic fields. The energy density of a magnetic field B is

Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.1.6 Pulling it all together

The electric and magnetic fields given by Equations 7.21 and 7.23 can satisfy all four of Maxwell's equations in empty space. Gauss's law and the no-monopole law are immediately satisfied because the fields are transverse. Faraday's law and the Ampère–Maxwell law will also be satisfied if we can find electric and magnetic fields that obey Equations 7.24 and 7.26.

We are looking for wave-like solutions, so it is sensible to try

Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.1.5 Getting agreement with the Ampère–Maxwell law

Finally, our electric and magnetic fields must satisfy the Ampère–Maxwell law in empty space. Using Equations 7.21 and 7.23, we obtain

which requires that

Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.1.4 Getting agreement with the no-monopole law

Substituting Equation 7.23 into the no-monopole law gives immediate agreement because

The no-monopole law is analogous to Gauss's law in empty space, and it leads to a similar conclusion: the magnetic wave must be transverse. This has already been established using Farada
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.1.3 Getting agreement with Faraday's law

Substituting Equation 7.21 into Faraday's law gives

This shows that a propagating electric wave is automatically accompanied by a transverse magnetic wave. The magnetic field oscillates in the y-direction, which is perpendicular to the direction of propagation and
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

5.1.2 Getting agreement with Gauss's law

Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain


Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

2.7 The ‘salt’ in seawater

The difficulty with having so much of the Earth's water locked up in the oceans is summed up poetically by Coleridge's ‘Ancient Mariner’, becalmed on board ship in the doldrums, beneath a blazing Sun.

Water, water, everywhere,

And all the boards did shrink;

Water, water, everywhere,

Nor any drop to drink.

(Samuel Taylor Coleridge, The Rime of the Ancient Mariner, 179
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

2.1 Where water occurs and how we measure it

When astronauts first ventured to the Moon in the late 1960s, they were captivated by a vision of the Earth in colour as it had never been seen before (Figure 2). It is not surprising that, after pictures like this were published, the Earth became known as the ‘blue planet’.

Figure 2
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

1 Overview

As you walk down the street one day, you hear a voice from somewhere behind you that seems to be discussing this unit. It says:

‘My dad's tutor's no joker, and he told me the TMA's going to hit home with a bang.’

You turn to find the face behind the voice, which is a gravelly Glaswegian baritone, but the man has gone, leaving you to ponder what he has said. Let us call his sentence exam
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.7 Vitamin C (ascorbic acid)

Activity 14

What is the condition that results from vitamin C deficiency and what are its symptoms?

Answer

You will probably remember from the start of this
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.6.6 Vitamin B12 (cobalamin)

Vitamin B12 is yet another group of compounds, this time with an atom of the metal called cobalt (present in only trace quantities in the body) in their structure, hence the alternative name ‘cobalamin’. Vitamin B12 works alongside folate and if levels of it are low, folate deficiency symptoms occur too. It is stored in the liver and in general the body does not appear to need a regular intake. Many people have enough B12 stored in their liver to last for
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.6.4 Vitamin B6 (pyridoxine)

Vitamin B6 is composed of pyridoxine and two closely related compounds. It is found in small quantities in many foods, though it can be destroyed in the cooking process. No clear deficiency disease has been recognised in humans as being directly caused by lack of this vitamin, since it is often found in conjunction with other B vitamins and their absence has greater effects. Its main role is in the conversion of some amino acids into other ones, depending on the requirements of the
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.6.3 Niacin (vitamin B3)

Niacin, which comprises two compounds, nicotinic acid and nicotinamide, also occurs widely in food and is added to many breakfast cereals. It is easily absorbed into the blood from the digestive system and plays a vital role in energy production in cells. It appears to reduce the levels of low density lipoproteins or LDLs in the blood and increase high density lipoproteins or HDLs, perhaps by affecting the proteins that carry the fats. This is important because LDLs are a way of transporting
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.6 Vitamin B

Vitamin B, often called the vitamin B complex, consists of a whole range of different compounds, some of which have similar functions and work together. However, unlike the families of compounds forming vitamins E and K, the B vitamins are sufficiently different from one another to be given individual names or numbers, and to be listed separately on many food labels. Except for vitamin B12, the body can only store limited amounts of B vitamins and because they are all water-soluble
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

3.5 Vitamin K

Like vitamin E, vitamin K is fat-soluble and composed of a series of related compounds. Vitamin K is widely distributed in the diet (see Table 1) and it is absorbed from the small intestine with the assistance of bile acids. Vitamin K is also manufactured by the bacteria that inhabit the human large intestine and appears to be absorbed there too. The main role of vitamin K is in blood clotting. This process requires the presence of a number of different chemicals, called clotting factors, in
Author(s): The Open University

License information
Related content

Except for third party materials and/or otherwise stated (see terms and conditions) the content in OpenLearn is released for use under the terms of the Creative Commons Attribution-NonCommercial-Share

Pages 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546