Gravity from the ground up

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Dedication......Page 7
Contents......Page 9
From the author to the reader......Page 15
From the author to his colleagues......Page 20
Ready to start......Page 23
Background: what you need to know before you start......Page 25
1 Gravity on Earth: the inescapable force......Page 29
Galileo: the beginnings of the science of gravity......Page 30
The acceleration of gravity is uniform......Page 31
Trajectories of cannonballs......Page 32
Galileo: the first relativist......Page 34
The second law: weight and mass......Page 37
The third law, and its loophole......Page 39
Preview: Newton’s gravity......Page 40
Action at a distance......Page 41
The new equivalence principle......Page 42
The gravitational redshift of light......Page 44
Summing up......Page 46
3 Satellites: what goes up doesn’t always come down......Page 47
Acceleration, and how to change your weight......Page 48
Getting into orbit......Page 50
4 The Solar System: a triumph for Newtonian gravity......Page 53
How to invent Newton’s law for the acceleration of gravity......Page 54
The orbits of the planets described by Newton’s law of gravity......Page 55
What is the value of G ?......Page 59
The Sun has a little orbit of its own......Page 60
The gravitational attraction of spherical objects......Page 61
Playing with the orbit program......Page 62
Black holes before 1800......Page 64
Light is deflected by the Sun’s gravity......Page 65
5 Tides and tidal forces: the real signature of gravity......Page 67
Ocean tides......Page 68
Spring and neap tides......Page 70
What the tidal forces do to the oceans, the Earth, and the Moon......Page 72
Tides elsewhere in astronomy......Page 74
Triumph of Newtonian gravity: the prediction of Neptune......Page 76
Tiny flaw of Newtonian gravity: Mercury’s perihelion motion......Page 77
6 Interplanetary travel: the cosmic roller-coaster......Page 79
Plain old momentum, and how rockets use it......Page 80
Energy, and how planets never lose it......Page 82
Getting to another planet......Page 84
The principle of the slingshot......Page 85
Using Jupiter to reach the outer planets......Page 87
Slinging towards the Sun......Page 88
Force and energy: how to change the energy of a body......Page 90
In the beginning . . .......Page 93
. . . was the greenhouse . . .......Page 95
The ones that get away......Page 97
The Earth’s atmosphere......Page 98
Pressure beats gravity: Archimedes buoys up balloons......Page 99
Pressure beats gravity again: Bernoulli lifts airplanes......Page 100
Helium balloons and the equivalence principle......Page 102
Absolute zero: the coldest temperature of all......Page 103
Why there is a coldest temperature: the random nature of heat......Page 104
The ideal gas......Page 105
An atmosphere at constant temperature......Page 107
The Earth’s atmosphere......Page 108
The atmospheres of other planets......Page 110
Quantum theory and absolute zero......Page 111
8 Gravity in the Sun: keeping the heat on......Page 113
A gas made of photons......Page 115
Gravity keeps the Sun round......Page 117
The Sun is one big atmosphere......Page 119
The structure of the Sun......Page 121
How photons randomly ‘walk’ through the Sun......Page 123
Rotation keeps the Sun going around......Page 126
Solar seismology: the ringing Sun......Page 127
Leaping out of the Solar System......Page 131
How far away are the stars?......Page 132
How bright are stars?......Page 133
Astronomers’ units for brightness......Page 134
Standard candles: using brightness to measure distance......Page 135
The colors of stars......Page 137
Why stars are black bodies......Page 138
The color of a black body......Page 139
Relation between color and temperature: greenhouses again......Page 141
Spectral lines: the fingerprint of a star......Page 142
How big stars are: color and distance tell us the size......Page 144
But why are stars as hot as they are, and no hotter?......Page 146
Looking ahead......Page 148
Star light, star bright . . .......Page 149
. . . first star I see tonight......Page 152
Cooking up the elements......Page 153
The solar neutrino problem......Page 155
Life came from the stars, but would you have bet on it?......Page 159
12 Birth to death: the life cycle of the stars......Page 163
The gravitational thermostat......Page 165
The main sequence......Page 166
Giants......Page 167
The Chandrasekhar mass: white dwarfs can’t get too heavy......Page 173
Neutron stars......Page 174
Fire or ice: supernova or white dwarf......Page 175
Death by disintegration......Page 178
What is left behind: cinders and seeds......Page 179
Looking at binaries......Page 181
The orbit of a binary......Page 182
Planetary perturbations......Page 183
Tidal forces in binary systems......Page 185
Accretion disks in binaries......Page 187
Fun with the three-body problem......Page 188
14 Galaxies: atoms in the Universe......Page 191
Globular clusters: minigalaxies within galaxies......Page 192
Galaxies are speeding apart......Page 195
Measuring the Universe: the distances between galaxies......Page 196
Most of the Universe is missing!......Page 197
Gangs of galaxies......Page 198
The missing mass......Page 200
Radio galaxies: the monster is a giant black hole......Page 202
Quasars: feeding the monster......Page 203
Galaxy formation: how did it all start? Did it all start?......Page 205
Fast motion means relativity......Page 207
General relativity is Einstein’s relativistic theory of gravity.......Page 208
Relativity is special......Page 209
The Michelson-Morley experiment: light presents a puzzle......Page 212
Michelson’s interferometer: the relativity instrument......Page 214
Special relativity: general consequences......Page 215
The extra inertia of pressure......Page 220
Conclusions......Page 221
Nothing can travel faster than light......Page 223
Light cannot be made to stand still......Page 224
Clocks run slower when they move......Page 225
The length of an object contracts along its motion......Page 227
Loss of simultaneity......Page 228
The mass of an object increases with its speed......Page 232
Energy is equivalent to mass......Page 233
Photons have zero rest-mass......Page 234
Consistency of relativity: the twin paradox saves the world......Page 235
Relativity and the real world......Page 238
Gravity in general relativity is . . .......Page 239
. . . geometry......Page 241
Spacetime: time and space are inseparable......Page 242
Relativity of time in the spacetime diagram......Page 243
Time dethroned . . .......Page 244
. . . and the metric reigns supreme!......Page 245
The geometry of relativity......Page 247
Proper measures of time and distance......Page 248
Equivalence principle: the road to curvature......Page 249
The equivalence principle: spacetime is smooth......Page 251
Driving from Atlanta to Alaska, or from Cape Town to Cairo......Page 253
Dimpled and wiggly: describing any surface......Page 255
Newtonian gravity as the curvature of time......Page 257
Do the planets follow the geodesics of this time-curvature?......Page 259
How to define the conserved energy of a particle......Page 260
The deflection of light: space has to be curved, too......Page 262
Space curvature is a critical test of general relativity......Page 264
How Einstein knew he was right: Mercury’s orbital precession......Page 265
Weak gravity, strong gravity......Page 266
19 Einstein’s recipe: fashioning the geometry of gravity......Page 267
Einstein’s kitchen: the ingredients......Page 268
Einstein’s kitchen: the active gravitational mass comes first......Page 269
Einstein’s kitchen: the recipe for curving time......Page 270
Einstein’s kitchen: the recipe for curving space......Page 272
Einstein’s kitchen: the recipe for gravitomagnetism......Page 273
The geometry of gravitomagnetism......Page 277
Gyroscopes, Lense, Thirring, and Mach......Page 279
The cosmological constant: making use of negative pressure......Page 281
The big picture: all the field equations......Page 284
The search for simplicity......Page 286
General relativity......Page 287
Looking ahead......Page 288
Nuclear pudding: the density of a neutron star......Page 289
It takes a whole star to do the work of 100 neutrons......Page 291
What would a neutron star look like?......Page 294
Where should astronomers look for neutron stars?......Page 296
Pulsars: neutron stars that advertise themselves......Page 299
The mystery of the way pulsars emit radiation......Page 300
The rotation rate of pulsars and how it changes......Page 301
Puzzles about the rotation of pulsars......Page 303
Pulsars in binary systems......Page 304
X-ray binary neutron stars......Page 305
Gamma-ray bursts: deaths of neutron stars?......Page 306
The relativistic structure of a neutron star......Page 309
The relation of mass to radius for neutron stars......Page 310
Neutron stars as physics labs......Page 311
The first black hole......Page 313
What black holes can do – to photons......Page 314
Danger: horizon!......Page 316
Singularities, naked or otherwise......Page 317
What black holes can do . . . to orbits......Page 318
Making a black hole: the bigger, the easier......Page 320
Disturbed black holes......Page 321
Limits on the possible......Page 322
Spinning black holes drag everything with them......Page 324
The naked truth about fast black holes......Page 325
Mining the energy reservoir of a spinning black hole......Page 326
Wormholes: space and time tubes......Page 330
Hawking radiation: black holes are truly black bodies......Page 332
Black hole entropy: a link to nineteenth century physics......Page 334
Black hole entropy: a link to twenty-first century physics......Page 335
Gravitational waves are inevitable......Page 337
Transverse waves of tidal acceleration......Page 338
How gravitational waves act on matter......Page 339
How gravitational waves are created......Page 341
Strength of gravitational waves......Page 342
Gravitational waves carry energy, lots of energy......Page 344
The Binary Pulsar: a Nobel-Prize laboratory......Page 345
Gravitational waves from binary systems......Page 347
Listening to black holes......Page 350
Gravitational collapse and pulsars......Page 352
Gravitational waves from the Big Bang: the Big Prize......Page 353
Catching the waves......Page 354
Michelson returns: the relativity instrument searches for waves......Page 355
LISA: catching gravitational waves in space......Page 357
Pretty obvious, really, . . .......Page 359
. . . but not always easy......Page 360
How a gravitational lens works......Page 361
Why images get brighter......Page 362
Making multiple images: getting caustic about light......Page 363
The Einstein ring......Page 364
MACHOs grab the light......Page 366
The third image: the ghost in a mirror......Page 367
Lensing shows us the true size of quasars......Page 370
Weak lensing reveals strong gravity......Page 371
24 Cosmology: the study of everything......Page 373
What is ‘‘everything’’?......Page 374
Copernican principle: ‘‘everything’’ is the same ‘‘everywhere’’......Page 375
The Hubble expansion and the Big Bang......Page 377
The accelerating Universe......Page 378
Was there a Big Bang?......Page 379
Looking back nearly to the beginning......Page 381
Cosmic microwave background: echo of the Big Bang......Page 382
The rest frame of the Universe......Page 383
Big Crunch or Big Freeze: what happens next?......Page 385
Cosmology according to Newton......Page 386
Cosmology according to Einstein......Page 387
Evolving the Universe......Page 388
The cosmological scale-factor......Page 391
What is the cosmological expansion: does space itself expand?......Page 393
The age of the Universe......Page 394
Physical cosmology: everything but the first nanosecond......Page 395
The laws of physics prefer matter over anti-matter......Page 396
The Universe becomes ordinary......Page 397
Making helium: first steps toward life......Page 398
Does it correspond to reality?......Page 400
Three and only three neutrinos: a triumph for Big Bang physics......Page 401
From nuclei to atoms: the Universe goes transparent......Page 403
The evolution of structure......Page 404
Ghosts of the dark matter......Page 407
What is the dark matter?......Page 409
Cosmology could be complicated . . .......Page 411
Gravity is geometry: what is the geometry of the Universe?......Page 412
Friedmann’s model universes......Page 415
What the Universe looks like......Page 418
27 Ask the Universe: cosmic questions at the frontiers of gravity......Page 419
The puzzle of the slightly lumpy Universe......Page 421
Einstein’s ‘‘big blunder’’......Page 422
The cosmological constant in particle physics......Page 423
Inflation: a concept waiting for a theory......Page 425
Inflation power: the active vacuum......Page 426
Inflating the Universe......Page 428
Inflation put to the test......Page 429
Is inflation still going on?......Page 430
Is Einstein’s law of gravity simply wrong?......Page 432
Cosmic defects......Page 433
Cosmic rays......Page 434
Quantum gravity: the end of general relativity......Page 435
A Universe for life: the Anthropic Principle......Page 438
Causality in quantum gravity: we are all quantized......Page 442
The quantization of time?......Page 443
Time for the twenty-first century......Page 444
Appendix: values of useful constants......Page 447
Glossary......Page 449
Index......Page 471