The distance between the sun and Earth is 1 astronaumical unit (AU). In the plot, the sun is at 0 AU, the Earth is at 1 AU, and Neptune is at 30 AU.
All sizes to scale, and the size of each moon is in scale with the distance to its host planet.
Pluto and Charon are faintly visible at this scale.
In the following figure all objects are magnified by a factor of 40 and the positions are unchanged. The planets are too large to display at this scale and so they are replaced by green dots. Pluto's moons Nix and Hydra are faintly visible at this scale.
Planet sizes are in scale with moon sizes.
Moon radius / Earth radius = .273 Jupiter radius / Earth radius = 10.9 Sun radius / Earth radius = 109 Moon orbit radius / Earth radius = 60.3 = 384399 km / 6371 km Earth orbit radius / Moon orbit radius = 389 Neptune orbit radius / Earth orbit radius = 30.1 Sets the size of the solar system Light year / Earth orbit radius = 63241 Alpha Centauri distance / Earth orbit radius = 276100 Nearest star. Distance from sun = 4.366 light years Galactic center distance / Light year = 27200 Sets the size of the Milky Way galaxy Andromeda galaxy distance/ Galactic center distance= 94 Size of local group of galaxies. Andromeda is 2.6e6 light years away Virgo cluster distance / Andromeda distance = 21 Nearest supercluster, 53.5 million light years away Edge of universe / Virgo clulster distance = 256 Define the edge of the universe to be 13.7 billion light years Mass of Earth = 5.972e24 kg Radius of Earth = 6371 km Earth-Sun distance = 1.496e11 meters
Semimajor Mass Radius Escape Orbit Parent axis (AU) (Earth=1) (Earth=1) speed speed planet (km/s) (km/s) Sun 333000 109.2 618. Mercury .387 .0553 .383 4.3 47.9 Venus .723 .8150 .950 10.46 35.0 Earth 1.000 1.0000 1.000 11.2 29.8 Mars 1.524 .1074 .532 5.03 24.1 Jupiter 5.203 317.83 10.86 59.5 13.1 Saturn 9.537 95.16 9.00 35.5 9.64 Uranus 19.19 14.50 3.97 21.3 6.81 Neptune 30.07 17.20 3.86 23.5 5.43 Pluto 39.48 .00220 .184 1.23 4.74 Moon .0123 .273 2.38 1.68 Earth Phobos 2.5e-10 .0018 .0113 2.14 Mars Deimos 1.8e-10 .0010 .0056 1.35 Mars Io .01495 .286 2.56 17.3 Jupiter Europa .00804 .245 2.02 13.7 Jupiter Ganymede .0248 .413 2.74 10.9 Jupiter Callisto .0180 .379 2.44 8.2 Jupiter Titan .0225 .404 2.64 5.6 Saturn Triton .00358 .213 1.455 4.4 Neptune Charon .000271 .093 .23 .21 Pluto Asteroids .0005 Mass of all asteroids Vesta 2.36 .0000447 .0413 .36 19.3 Asteroid Ceres 2.766 .00016 .074 .51 17.9 Asteroid Pallas 2.77 .0000359 .0427 .32 17.6 Asteroid Kuiper belt .03 Mass of all Kuiper belt objects Haumea 43.34 .00070 .0487 .84 4.48 Kuiper belt object Makemake 45.79 .0007 .11 .74 4.42 Kuiper belt object Eris 67.67 .00278 .183 1.34 3.44 Kuiper belt object"Orbit speed" refers to speed around the sun for planets and to speed around the planet for moons.
Mass of Earth = M = 5.972⋅1024 kg Radius of Earth = R = 6371 km Gravitational constant = G = 6.67⋅10-11 Newton meters2/kg2 Mass of a test object = m Force on the test object = F = -G M m / R2 = g m Gravitational acceleration = g = -G M / R2 = 9.8 meters/second2 Gravitational energy = E = -G M m / R
Mass of central object = M Gravity constant = G Distance of satellite from central object = R Velocity for a satellite on a circular orbit = Vc = (G M / R) Escape velocity for a satellite = Ve = 2 (G M / R) = 2½ VcFor a satellite on a circular orbit,
Gravity force = Centripetal force G M m / R2 = m V2c / RThe escape velocity is obtained by setting
Gravity energy = Kinetic energy G M m / R = ½ m V2e Escape Circular orbit velocity velocity (km/s) (km/s) Earth 11.2 7.9 Mars 5.0 3.6 Moon 2.4 1.7
If a cannonball is fired at a speed of 7.8 km/s then it orbits the Earth in a circle. If the speed is lower then it crashes into the Earth.
Speed (km/s) Orbit type Red <7.8 Ellipse Too slow to reach orbit. Crashes into the Earth Green 7.8 Ellipse (circle) Critical speed for a circular orbit Yellow Ellipse Orbits Earth as an ellipse Cyan 11.2 Parabola Min speed to escape Earth, the "escape speed" Blue >11.2 Hyperbola More than the escape speed Elliptic orbit: Retraces its path each cycle Parabolic orbit: Departs the Earth and limits to a speed of zero Hyperbolic orbit: Departs the Earth and limits to a positive speed
In general an orbit is either an ellipse, a parabola, or a hyperbola. A circle is a special case of an ellipse with an eccentricity of 0.
The degree of elongation of an ellipse is parameterized by its "eccentricity".
Eccentricity Orbit type e = 0 Circle (a circle is a special case of an ellipse) 0 < e < 1 Ellipse (less than escape velocity) e = 1 Parabola (exactly escape velocity) e > 1 Hyperbola (more than escape velocity)In describing an ellipse we replace the radius with the "semimajor axis". For a circle they are equal.
Semimajor axis = A (equal to the radius if the ellipse is a circle) Semiminor axis = B = a (1-e2)1/2 (A=B for a circle) Periapsis = X = A (1-e) ("perigee" if the focus is the Earth) Apoapsis = Y = A (1+e) ("apogee" if the focus is the Earth) Eccentricity = e = (1-B2/A2)½ Central mass = M (mass at the focus) Gravity constant = G Orbit time = T = 2πA (GM)-½ (depends on the semimajor axis and not the eccentricity)
A planet has 5 "Lagrange points". An object orbiting at any of these points orbits in synch with the planet. L4 and L5 are the "Trojan points" and objects here are stable. If an object at one of the points is jostled it will stay in the region of the Lagrange point and stay in synch with the planet. The L1, L2, and L3 points are unstable. If an object here is jostled it will exit the region and lose synch with the planet. A spaceship can park at these points but it requires an occasional small rocket firings to maintain its position. The Webb telescope will be at L2.
If a planet orbits a star and a moon orbits a planet, and if the two orbit periods are equal, then
Star mass = M0 Planet mass = M Planet orbit time = T Moon orbit time = t = T Planet orbit radius = R Moon orbit radius = r = R ( M/M0)1/3 Hill radius = H = R (3M/M0)1/3 DerivationThe "Hill radius" characterizes the range of a planet's gravitational influence. In the limit of M << M0, the Hill radius equal to the distance from the planet to the L1 or L2 Lagrange point.
If a moon orbits too far from a planet then it gets stolen by the star. The boundary for this is around 1/3 of the planet's Hill radius. The Earth's moon is barely within this boundary.
Moon orbital radius / Earth Hill radius = .256
The moons of the gas giants are all well within their planet's Hill radius.
If two planets orbit within ~ 10 Hill radii of each other then they disrupt each other's orbits. This is a planet's "zone of gravitational dominance".
An object is defined as be a planet if it is:
*) Large enough for gravity to squash it into a round shape (Ceres is near this threshold).
*) Capable of clearing its orbit of other objects.
*) Not a satellite of something else.
Pluto doesn't make the cut because its Hill radius is small and because it orbits within Neptune's zone of gravitational influence.
Earth Earth Solar radii masses masses Neutron star 3.0 Maximum mass before a neutron star becomes a black hole White dwarf 1.4 Maximum mass before a white dwarf becomes a neutron star Sun 109 333000 1.0 Red dwarf 9 25000 .075 Minimum mass to fuse hydrogen and be a star Brown dwarf 10 4130 .0124 Minimum mass to fuse deuterium & max planet mass Jupiter 10.9 318 .00095 Largest gas giant in the solar system Uranus 4.0 14.5 Smallest gas giant in the solar system Earth 1.0 1.0 Venus .95 .82 Mars .53 .11 Mercury .38 .0553 Smallest object capable of clearing its orbital zone Ganymede .41 .025 Titan .40 .022 Smallest object with an atmosphere Callisto .38 .018 Io .29 .015 Moon .27 .012 Europa .24 .0080 Triton .21 .0036 Eris .18 .0028 Pluto .18 .0022 Ceres .074 .00016 Round asteroid. Min mass to be round Vesta .041 .000045 Largest object that is not roundThe minimum mass to be a gas is somewhere between the mass of Earth and Uranus.
The minimum mass to have an atmosphere is in the range of .02 Earth masses. If we base the definition of a planet on this mass, then Ganymede, Titan, and Callisto potentially qualify, and Pluto doesn't.
If the definition of a planet is based on gravitational roundness, and if orbital state is ignored, then a deluge of objects quality.
History of the discovery of solar system objects:
Year Object Semi major Earth Discoverer axis (AU) masses 1781 Uranus 19.19 14.50 Herschel 1801 Ceres 2.77 .00016 Piazzi 1802 Pallas 2.77 .0000359 Olbers 1804 Juno 2.67 .0000045 Harding 1807 Vesta 2.36 .0000447 Olbers 1845 Astraea 2.57 .00000049 Hencke 1846 Neptune 30.07 17.20 Galle, using calculations by Verrier 1930 Pluto 39.48 .00220 Tombaugh 2002 Quaoar 43.37 .00023 Trujillo, Brown 2003 Sedna 506.2 .0002 Brown, Trujillo, Rabinowitzs 2004 Orcus 39.47 .000108 Brown, Trujillo, Rabinowitzs 2005 Haumea 43.22 .00070 Brown 2005 Makemake 45.79 .0007 Brown 2005 Eris 67.67 .00278 Brown 2007 OR10 66.99 .0005 Schwamb, Brown, Rabinowitz 1851 15 asteroids are known and they are grouped into their own category. 2000 The American Museum of Natural History builds a planet exhibit designed by Neil Tyson 2001 A New York Times article points out that Pluto is not present in the AMNH planet exhibit. 2006 Soter publishes a paper defining planethood in terms of "clearing the orbit". 2006 The International Astronomical Union redefines planethood, drawing from the Soter definition. Pluto is expelled from the planet club. Ceres, Pluto, Eris, Haumea, Makemake, Quaoar, Sedna, and Orcus are deemed to be "dwarf plaents".
The Earth's spin angular momentum is conserved and the north pole always points toward the north star. The Earth's tilt is more important than the distance from the sun for determining warmth.
Earth maximum orbital distance (apocenter) = 1.017 AU Earth minimum orbital distance (pericenter) = .983 AU Solar intensity at 1 AU = 1 (scaled units) Solar intensity at apocenter = .967 (scaled units) Solar intensity at pericenter = 1.035 (scaled units) Apocenter intensity / Pericenter intensity = 1.070 Sun intensity in space = 1366 Watts/meter2 Earth surface, sun at zenith, clear day = 1050 Watts/meter2 Earth surface, average over day and night = 250 Watts/meter2 Earth tilt angle = 23 degrees Projected intensity at 0 degrees = cos( 0) = 1 Projected intensity at 23 degrees = cos(23) = .921 Projected intensity at 46 degrees = cos(46) = .695The change from projecting at 23 degrees exceeds the change from orbital ellipticity.
Abundances in parts per thousand.
Sun Earth Earth Human crust core Hydrogen 706 1.5 100 Helium 275 - - Oxygen 5.92 460 650 Carbon 3.03 1.8 180 Neon 1.76 - - Iron 1.17 63 1000 .060 Nitrogen 1.10 41 30 Silicon .65 270 20 Magnesium .60 29 .50 Sulfur .40 .42 2.5 Calcium 50 14 Phosphorus 1.0 11 Potassium 15 2.5 Sodium 23 1.5 Chlorine .17 1.5 Flourine .54 .037 Zinc .079 .032 Aluminum 82 Titanium 6.6 Manganese 1.1 Strontium .36 Nickel 80 Chromium 20 Cobalt 4The abundances for the Earth's core are estimated using solar abundances and including only elements at least as dense as iron.
The following diagrams are based on models and one shouldn't expect too much precision from them.
MicroWatts Half life Mantle PicoWatts/kg /kg (billion abundance of mantle years) (ppb) Uranium-238 94.6 4.47 30.8 2.91 Uranium-235 569. .70 .22 .125 Thorium-232 26.4 14.0 124 3.27 Potassium-40 29.2 1.25 36.9 1.08The Earth loses heat at a rate of .087 Watts/m2, for a global heat los of 4.42e13 Watts.
80% of the Earth's heat is from radioactivity and 20% is from accretion.
The radioactive heating rate 3 billion years ago is twice that of today.
The Earth's core temperature is ~ 7000 K.
Limestone Calcium carbonate CaCO3 Mafic Rock containing iron or magnesium. Abundant below oceans. Denser than feldspar Granite Quartz, mica, feldspar, amphibole minerals Basalt Solidified lava. Mafic Igneous Granite, basalt Feldspar KAlSi3O8, NaAlSi3O8, CaAl2Si2O8
Dipole Field at Magneto- Axis Radius Spin Core Core Volcanic moment equator pause angle (Earth (days) heating Temp (Earth=1) (Gauss) (planet (deg) =1) (1012 (K) radii) Watts) Sun 5000000 109 25.0 4e14 1500000 Jupiter 20000 4.28 80 9.6 10.9 .41 400000 36000 Saturn 600 .22 20 <1 9.0 .44 150000 11700 Uranus 50 .23 20 58.6 4.0 .72 18000 5000 Neptune 25 .14 25 47 3.9 .67 18000 5400 Earth 1 .305 10 10.8 1.0 1.00 48 6000 Yes Europa .0016 .0072 4.5 .24 3.55 1.6 No Mercury .0007 .003 1.5 14 .38 58.6 No Venus <.0004 <.00003 - - .95 243.0 Yes Mars <.0002 <.0003 - - .53 1.03 No Io ? ? ? ? .29 1.77 100 YesThe Earth's magnetic moment is 7.91e15 T m3.
Jupiter's mangnetic field is 0.00120 Gauss at Europa's orbit.
The sun rotates with a period of 25.0 days at the equator and 34.4 days at the poles. This extreme differential rotation powers a magnetic field dynamo.
For an object to have a magnetic field it needs size, heat, and spin.
Core heating drives convective turbulence in the mantle, and turbulence generates magnetic fields. If there is no spin, the fields will have random directions and the field at the surface will be small. Spin herds magnetic fields into a uniform orientation and produces a dipole shape, like the Earth's field. In this case the field at the surface will be larger.
Magnetic fields are generated by turbulence and lost by resistive diffusion, and the equilibrium field strength occurs when these are in balance. The larger the object, the longer it takes for diffusion to smooth away the field and the larger the equilibrium field.
Density Pressure Column Temp Height Escape Gravity N2 O2 N2 CO2 Ar kg/m3 Bar ton/m2 Kelvin km km/s m/s2 kg/m3 frac frac frac frac Venus 67 92.1 1000 735 16 10.36 8.87 2.34 0 .035 .965 Titan 5.3 1.46 120 94 30 2.64 1.35 5.22 0 .984 Earth 1.2 1 10 287 8 11.2 9.78 .94 .209 .781 .00039 .0093 Mars .020 .0063 .16 210 11 5.03 3.71 .00054 .0013 .027 .953 .016No other object in the solar system has a meaningful atmosphere, except for the gas giants.
Titan is the smallest object with an atmosphere and Mercury is the largest object without an atmosphere.
Gas Concentration Contribution (ppm by volume) to warming H2O 36-72% CO2 394 9-26% CH4 1.79 4-9% O3 <=.07 3-7%
M = Mass of a gas molecule P = Pressure T = Temperature Vol= Volume N = Number of gas molecules within the volume D = Density in kg/m3 = N M / Vol k = Boltzmann constant = 1.38*10-23 Joules/Kelvin Mol= Number of moles of gas molecules = N /6.62*1023 V = Characteristic thermal speed of gas molecules E = Mean kinetic energy of a gas molecule = 1/2 M V2Ideal gas law:
P = k T N / Vol = 2/3 N E / Vol = 1/3 N M V2 / Vol = 1/3 D V2 = 8.3 Moles TFor a system in thermodynamic equilibrium each degree of freedom has a mean energy of .5 k T.
A gas molecule moving in 3 dimensions has 3 degrees of freedom and so the mean kinetic energy is
E = 3 * .5 k T = 1.5 k TThis is also equal to the mean kinetic energy of a gas molecule.
E = .5 M V2Hence
k T = 2/3 E
Gamma = Adiabatic constant = 7/5 for diatomic molecules such as H2, O2, N2. Air also has Gamma=7/5 = 5/3 for monatomic molecules such as Helium and XenonThe sound speed for an ideal gas is
SoundSpeed2 = Gamma P / Density = 1/3 Gamma V2For air,
Gamma = 7/5 SoundSpeed = .63 ThermalSpeed = 343 meters/second at 20 CelsiusGas properties simulation
Dist from Mass H2O H2O Density sun (AU) (Earth=1) (Earth=1) frac (g/cm3) Mercury .39 .055 - - 5.60 Venus .72 .82 - - 5.20 Earth 1.00 1.00 .00025 .00025 5.52 Moon 1.00 .0123 - - 3.35 Mars 1.52 .107 .00000027 .0000025 3.95 Phobos 1.52 1.88 Deimos 1.52 1.47 Vesta 2.36 .0000447 - - 3.42 Ceres 2.77 .00016 .000033 .21 2.08 Pallas 2.77 .0000359 - - 2.8 Io 5.20 .0150 - - 3.528 Europa 5.20 .0080 .0033 .4 3.103 Ganymede 5.20 .0248 .012 .5 1.942 Callisto 5.20 .0180 .0084 .5 1.834 Pan 9.54 8.3e-10 .42 Mimas 9.54 .0000063 1.15 Titan 9.54 .0225 .012 .5 1.88 Triton 30.07 .00358 .00067 ~.2 2.061 Pluto 39.48 .00220 2.03 Charon 39.48 .000271 1.72 Jupiter 5.20 317.83 1.326 Saturn 9.54 95.16 .687 Uranus 19.19 14.50 1.270 Neptune 39.48 17.20 1.638 Ceres has an ocean's worth of H2O. Ceres H2O / Earth H2O = .13 Earth mass = 5.972e24 kg
Oceans .954 Ice caps and glaciers .024 Lakes and rivers .006 Underground .016 Atmosphere .00001
Planet Metal & H2O Gas Density H2O mass rock (g/cm3) frac Ceres .00016 .00013 .000033 0 2.08 .21 Europa .0080 .005 .0033 0 3.103 .4 Mars .107 .107 .00000027 .000000004 3.95 .0000025 Earth 1 1 .00025 .0000009 5.52 .00025 Jupiter 317.9 12-45 Most of it 1.33 Saturn 95.2 9-22 Most of it .69 Uranus 14.5 0.5-3.7 9.3-13.5 .5-1.5 1.27 3/4 Neptune 17.2 1.2 10-15 1.0-2.0 1.64 3/4Masses in Earth masses
Mean Temperature Min Max Parent Albedo (K) (K) (K) planet Mercury 340 100 700 Venus 735 735 735 Earth 288 184 330 Moon 220 100 390 Mars 210 130 308 Ceres 168 ? 235 Europa 102 50 125 Jupiter Ganymede 110 70 152 Jupiter Callisto 134 80 165 Jupiter Titan 94 Saturn Titania 70 60 89 Uranus Oberon 75 Uranus Nitrogen freeze 63 Oxygen freeze 54 Triton 38 Neptune .76 Nereid 50 Neptune .155 Pluto 44 33 55 .58 Hydrogen freeze 14The boundary between rocky and icy objects is at Ceres' orbit.
The boundary for frozen nitrogen is at Neptune's orbit.
Freeze Boil Heat Capacity Density (Kelvin) (Kelvin) (J/g/Kelvin) (g/cm3) Water 273 373 4.2 1.00 Ammonia 195 240 4.7 .73 Methane 91 112 1.6 .42 Ethanol 159 351 2.4 .79 Ethane 89 184 .55 Propane 86 281 .58 Hydrogen 14.0 20.3 Nitrogen 63.2 77.4 Oxygen 54.4 90.2 CO 68 CO2 194.7 216.6 Argon 83.8
Air at sea level .00127 Ice .92 Water 1.00 Rock ~ 2 Iron 7.9 Nickel 8.9 Metallic asteroids are composted of mostly iron and nickel Lead 11.3 Uranium 19.1 Gold 19.3 Osmium 22.6 Densest element White dwarf e9 Atomic nuclei 2e17 Neutron star 2e17 Planck density 5.1e96
D = Density R = Radius M = Mass = Density * Volume = 4/3 Pi D R3 A = Acceleration at the surface = G M / R2 = (4/3) π G D RAcceleration is proportional to R
Density Radius Gravity g/cm3 (Earth=1) m/s2 Earth 5.52 1.00 9.8 Venus 5.20 .95 8.87 Uranus 1.27 3.97 8.69 Mars 3.95 .53 3.71 Mercury 5.60 .38 3.7 Moon 3.35 .27 1.62 Titan 1.88 .40 1.35 Ceres 2.08 .074 .27
If a mountain gets too high, pressure deforms the rock and the mountain sags. The height of a mountain is limited by the tensile strength of the rock. For a stout rock such as granite this is ~ 100 MegaPascals (Newton / meter2). The density of granite is ~ 3000 kg/m3.
The pressure at the base of a mountain is
Pressure = RockDensity * Gravity * HeightThe height that gives a pressure of 100 MegaPascals is
Height ~ 103 N/m2 / 10 m/s2 / 3000 kg/m3 ~ 3 km
Gravity Radius Tallest mountain Mountain/Radius (m/s2) (km) (km) (km/km) Earth 9.8 6371 8.9 .0014 Mount Everest Venus 8.9 6052 8 .0013 Volcanic Mercury 3.7 2440 10 .0041 Mars 3.7 3386 21.2 .0063 Mount Olympus. Previously volcanic Io 1.80 1822 18 .0099 Supervolcanos Moon 1.62 1738 7 .0040 No geological activity Titan 1.35 2576 2 .0008 Ice mountains Ceres .27 476 5 .0105 Ice mountains. Round Pluto .66 1173 4 .0034 Ice mountains. Vesta .25 265 Tall Not roundIf a planet is substantially heavier than the earth and if it has enough water for oceans, gravity might make it impossible for dry land to exist.
If we define the roundness of an object as the characteristic mountain height divided by the object's radius, then for the Earth,
Roundness ~ 10 km / 7*103 km ~ 10-3The surface gravity for equal-density objects is proportional to radius, hence the roundness of an object of radius R scales as
Roundness ~ 10-3 * (R / RadiusOfEarth)2For an object a tenth the size of the earth, the roundness is ~ 10-1. If we take this magnitude as the boundary between round and potato-shaped, then the smallest round objects should be a tenth the Earth's radius. The smallest round object in the solar system is Ceres, which has a radius of 487 km. The radius of the earth is ~ 6370 km.
This is a plot of all extraterrestrial planetary systems with at least 3 planets. In the lower right there is an index relating star type with mass. The stars are depicted with the size, brightness, and color that your eye would see.
Planet size is scaled as the cube root of the mass. The solar system is 1/3 of the way down. Jupiter is the orange dot at the far right.
The "metallicity" of a star is defined as Metallicity = Mass of elements heavier than helium / Total mass
If the star has metallicity equal to the sun, orange dots are used for the planets. If the star is more metallic, yellow dots are used, and if it is less metallic, red dots are used.
Planet size tends to increase with star metallicity.
The purple dot indicates the location of the Goldilocks zone for each planetary system, where the temperature is right for liquid water.
Very few of the systems have an Earth-sized planet in the Goldilocks zone.
Most extraterrestrial planetary systems are more massive than the sun's planets. In the "Galactic Museum of Natural History", the solar system might be classified as a "Dwarf planetary system".
Goldreich & Tremaine (1980): "We present an illustrative application of our results to the interaction between Jupiter and the plantary disk. The angular momentum transfer is shown to be so rapid that substantial changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years."
The Earth's atmosphere transmits visible light and radio waves and it blocks all other kinds of radiation.
This is a plot of the radiation intensity of blackbody radiation for various
temperatures. Each curve is colored according to what your eye would perceive.
Visible light ranges from 400 nm to 750 nm.
The strip of color at the right depicts the color as a function of temperature.
Laws of blackbody radiation:
T = Temperature in Kelvin I = Radiation intensity in Watts/meter2 W = Wavelength of the peak of the radiation spectrum for a given temperature F = Frequency of light C = Speed of light = 2.998e8 m/s Stefan-Boltzmann law: I = 5.67e-8 T4 Wein's law: W T = 2.897e-3 Kelvin meters Wave equation: F W = C Temperature Intensity Wavelength Color (Kelvin) (Watts/meter2) (micrometers) The Earth 288 429 9.8 Infrared Candle 1000 56700 2.9 Red Incandescent bulb 2500 2000000 1.16 Orange The sun 5778 60000000 .50 White Sirius 9940 600000000 .29 Blue
phet.colorado.edu: Blackbody radiation
The Planck law gives the intensity of blackbody radiation as a function of temperature and frequency.
Planck constant = h = 6.626e-34 Joule Seconds Frequency = F Hertz Speed of light = C = 2.998e8 meters/second Boltzmann constant = k = 1.381e-23 Joules/Kelvin Temperature = T Kelvin Blackbody intensity = I = 2 h F3 C-2 (ehF/(kT)-1)-1 Watts/Hertz/meter2
The following table gives the power radiated in each band in percentages. A star with a temperature in the range of 4200 Kelvin is optimal for photosynthesis because it is both abundant in visible photons and sparse in UV photons.
Temperature UV Visible IR (Kelvin) % % % 2400 .00067 2.23 97.7 3000 .02 7.2 92.8 4000 .32 20.5 79.2 5000 1.73 34.3 63.8 5772 4.0 42.6 53.4 Sun 6000 4.9 44.4 50.7 UV: 315 nanometers and beyond IR: 680 nanometers and beyond
The luminosity of a star scales with mass as
Luminosity ~ Mass3.5The lifetime scales as
Lifetime ~ Mass / Luminosity ~ Mass-2.5The sun burns for ~ 10 billion years.
The minimum mass for hydrogen fusion is 0.08 solar masses.
These are the stars in a (x,y,z)=(40,40,16) light year volume centered around the sun, with the stars in the volume projected on the (x,y) plane. Dot size and brightness are in scale with the star's radius and surface brightness. The color of the dots reflects what your eye perceives. Overlapping dots indicate binary stars. There are many stars in this volume that are too dim to be seen compared to the sun.
In this figure the brigtnesses have been magnified by 20 to bring out dimmer stars. Any star brighter than the sun is reduced in brightness to be equal to the sun.
In this figure the brightness has been raised to the 1/16 power to bring out the dimmest stars. Brown dwarfs are barely visible as tiny red dots. There are 2 of them between the sun and Altair, one to the right of Alpha Cantauri and one below Sirius.
Distance Mass Radius Lum Temp Age Metal Rotation (ly) (K) (my) Sun 1.00 1.00 1.00 5778 4540 Proxima Centauri 4.24 .123 .141 .0017 3042 4850 .21 days Alpha Centauri A 4.36 1.10 1.23 1.52 5790 4850 1.51 Alpha Centauri B 4.36 .907 .865 .500 5260 4850 1.60 Barnard's Star 5.96 .144 .196 .0035 3134 10000 .2 130 days Wolf 359 7.78 .09 .16 .0010 2800 ~200 <3km/s Lalande 21885 8.29 .46 .393 .025 3383 <5000 -.2d Sirius 8.60 2.02 1.71 25.4 9940 250 .50d Sirius B 8.60 .978 .0084 .026 25200 white dwarf Luyten 726-8 A 8.73 .10 .14 .00006 2670 Luyten 726-8 B 8.73 .10 .14 .00004 Wise 1541-2250 ~~9 .012 .1 dim 350 Procyon A 11 1.42 2.05 6.93 6530 3000 -.05d 23 days Procyon B 11 .60 .0123 .00055 7740 white dwarf Altair 16.7 1.79 2.03 10.6 8500 <1000 -.2d .37 days Vega 25.04 2.135 2.26 37 9602 455 .52 Capella A 42 2.7 12 78 4940 520 .4 106 days Capella B 42 2.6 9 78 5700 520 .4 9 days Castor A 49.8 2.15 2.3 30 10300 200 9.5 Castor B 49.8 1.7 1.6 14 8840 200 2.8 Arcturus 36.7 1.10 25.7 170 4290 -.37d <1.7km/s Aldebaran 65 1.7 44 520 3910 .7 643 days Achernar 139 ~7 ~10 3150 15000 250 km/s Canopus 310 8.5 65 13600 7350 .9 Polaris 434 7.54 46 2200 7200 1.12 ~17 km/s Betelgeuse 643 ~18 1180 ~140000 3500 10 Zeta Orionis A 700 28 ~20 100000 30000 140 km/s Zeta Orionis B 700 23 1300 ? Zeta Orionis C 700 20 ? 24000 Rigel 860 24 71 66000 12130 8 .0d 40 km/s Deneb 1400 ~20 ~110 ~54000 8525 A0620-00 3000 11 0 nearest known black hole Eta Carinae ~8000 ~125 5000000 ~38000 <3 Mass, radius, and luminosity are in solar units.Altair is a variable star, with radius varying from 1.63-2.03 and the temperature varying from 6900-8500 K.
Eta Carinae has a mass of 100-150 solar masses and a radius of 85-195 solar radii.
Alpha Centauri A and B: Perigee = 11.2 A.U. Apogee = 35.6 A.U. Orbit time = 80 Years Distance Mass Radius Luminosity Temp Age Metallicity (ly) (K) (my) Sun 0 1.00 1.00 1.00 5778 4540 1.0 Proxima Centauri 4.24 .123 .141 .0017 3042 4850 Alpha Centauri A 4.36 1.10 1.23 1.52 5790 4850 1.51 Alpha Centauri B 4.36 .907 .865 .500 5260 4850 1.60 Mass, radius, and luminosity are in solar units.
Star type Mass Luminosity Color Temp Lifetime Death Remnant (K) (109 yrs) Brown Dwarf <0.08 Red 1000 immortal Red Dwarf 0.1 .0001 Red 2000 1000 Red giant White dwarf The Sun 1 1 White 5778 10 Red giant White dwarf Blue star 10 10000 Blue 10000 0.01 Supernova neutron star Blue giant 20 100000 Blue 20000 0.01 Supernova black hole Mass < 9 solar masses -> End as red giants and then turn into a white dwarf. Mass > 9 solar masses -> End as supernova 9 < Mass < 20 -> Remnant is a neutron star. Mass > 20 -> Remnant is a black hole. 130 < Mass < 250 -> Pair-instability supernova (if the star has low metallicity) Mass > 250 -> Photodisintegration supernova, producing a black hole & relativistic jets.Wikipedia: Main sequence
Year Distance Apparent Type (ly) Magnitude 185 8200 -4 1a(?) 386 15000 +1.5 2 393 34000 0 1006 7200 -7.5 1a Brightest supernova, visible Earth-wide 1054 6500 -6 2 Remnant is the Crab Nebula Pulsar 1181 8500 0 1572 8000 -4 1a 1604 14000 -3 1a 1680 9000 +5 2b 1868 25000 1987 160000 2.9 2pec Large Magellanic Cloud, a satellite galaxy of the Milky WayThe sun is 27200 light years from the center of the galaxy.
This is a plot of the radiation intensity of blackbody radiation for various
temperatures. Each curve is colored according to what your eye would perceive.
Visible light ranges from 400 nm to 750 nm.
The strip of color at the right depicts the color as a function of temperature.
Solar masses / 109 Total mass 1000 (Most of which is dark matter) Stars 55 Gas 7 Black holes 1 Dust .1 Central hole .0042 Number of stars = 3e11 Number of black holes = 1/1000 times the number of stars Number of planets = At least 1 per star Earth-size planets in the goldilocks zone = Around .13 per star Average mass of a star = .18 solar masses Disk diameter = 100000 light years Disk thickness = 1000 light years Star density near sun = .004 stars/lightyear3
Galaxy Central black Distance mass hole mass (million ly) Small Magellanic .007 none found .21 Large Magellanic .01 none found .16 Triangulum .05 <.000000003 2.64 Third-largest galaxy in local group Andromeda 1.0 .0002 2.56 Second-largest galaxy in local group Milky Way 1.2 .0000042 .0 Largest galaxy in local group Virgo M87 17 .0035 53.5 Virgo cluster Virgo M49 .000565 55.9 Virgo cluster NGC 3842 ? .0097 331 Leo Cluster NGC 4889 ? .021 308 Coma Cluster APM 08279 ? .023 23600 Largest black hole observedMasses in trillions of solar masses.
This is a plot of galaxies within a 6x6x6 million light year volume centered on the Milky Way. The size of each dot is proportional to Luminosity1/3, and the sizes of the Milky Way and Andromeda are in scale with the distance between them. The two dots above the Milky Way are the Large and Small Magellanic Clouds.
Color indicates depth, where magenta corresponds to the top of the volume, red corresponds to points at the bottom, and green corresponds to points in the midplane.
This is the same as the previous plot but with dot size scaled as Luminosity1/6, to bring out the dimmer galaxies.
This is a plot of galaxies within a 20x20x20 million light year volume centered on the Milky Way, with dot size scaled as Luminosity1/3.
This is a plot of galaxies within a 160x160x160 million light year volume centered on the Milky Way, with dot size scaled as Luminosity1/3.
The Virgo Cluster is to the right and the Fornax Cluster is to the upper left. The Z=0 plane is chosen so that it contains the Virgo Cluster, the Fornax Cluster, and the Milky Way. This is why most of the points have the same color.
Distance Mass Speed with Speed Escape Gravity (millions of (solar respect to according velocity time light years) masses) Milky Way to Hubble (km/s) (billions (km/s) law (km/s) of years) Sun 1.6e-11 1.0 - - 41.9 2.3e-10 Alpha Centauri .0000044 1.1 - - .084 .031 Andromeda 2.54 1.0e12 -120 58 105 14.5 Virgo Cluster 54 1.2e15 1254 1240 790 41.0 Coma Cluster 321 6950 7400 Edge of universe 14000 300000 300000 Hubble constant = 23 km/s/(million light years) Hubble velocity = Hubble constant * Distance Solar mass = 1.99e30 kg Light year = 9.46e15 meters Age of universe = 13.8 billion years Distance to the edge of the universe = Speed of light * Age of universeAndromeda and the Milky Way are close enough for gravity to have reversed the Hubble expansion. The Virgo and Coma clusters are far enough away to be a part of the Hubble expansion. The edge of the universe is the horizon beyond which galaxies recede faster than the speed of light.
"Escape velocity" is the escape velocity of the Earth from the given object.
"Gravity time" is the amount of time it would take for the object's gravity to pull the Earth toward it, if the Earth were released from rest with respect to the object.
If an object's escape velocity is smaller than the Hubble velocity, then the gravity from that object cannot reverse the Hubble expansion.
The Andromeda galaxy will collide with the Milky Way in 4 billion years and in the distance future, the merged galaxy will collide with the Virgo Cluster.
The Earth's atmosphere became abundant in oxygen 600 million years ago, concurrent with the emergence of multicellular life.
Planet property If too little If too much Mass Cannot capture atmosphere Becomes gas giant No volcanism Cannot generate a magnetic field Distance from Too hot Too cold for surface water star Inside the snow line Atmospheric Cosmic rays reach the surface Blocks too much sunlight thickness Atmosphere loses heat at night for photosynthesis Water content If you don't have oceans then you No dry land don't have enough photosynthesis to generate an oxygen atmosphere Planet spin Does not generate a large-scale Fine magnetic field Planet spin tilt Fine Extreme seasons Star temperature Not enough blue light for Too much UV light photosynthesis Star metallicity Small planets Too many gas giants Star mass Planet is so close to the star that it Fine is tidally locked to the star Moon mass Planet tilt becomes unstable, causing Fine extreme seasonsA moon of a gas giant can potentially be protected from the solar wind by the gas giant's magnetic field. It can also potentially have volcanism from tidal heating by the gas giant.
The Earth has been beset by asteroids, supervolcanoes, global ice ages, runaway global warming, supernovae, gamma ray bursts, and the industrial age.
Millions of years ago 66 Cretaceous–Paleogene extinction, caused by a 10 km asteroid. Dinosaurs become extinct. 201 Triassic-Jurassic extinction. Cause unknown. 252 Permian-Triassic extinction. Runaway global warming 370 Late-Devonian extinction. Cause unknown. 445 Ordovician-Silurian extinction events. Global glaciation.
kg/m3 Planck density 5 *1096 = PlanckMass / PlanckLength^3 Solar system 2 *10-8 = Mass of sun / (30 AU)^3 Milky Way 3 *10-21 = 1.2e12 solar masses / (100000 lightyears)^3 Matter .12*10-27 = Mean density of protons & electrons in the universe Dark matter .66*10-27 = Mean density of dark matter in the universe Dark energy 1.67*10-27 = Mean density of dark energy in the universeAs the universe expands the matter and dark matter density decrease and the dark energy density is constant.
In the early universe the dark matter density was vastly greater than the dark energy density. In the future dark energy will overwhelm dark matter and the universe will expand unchecked.
Telescope Diameter Resolution Year (meters) (microrad) Human eye .005 291 Lippershey's telescope ? ? 1608 First telescope. Refractor Galileo's telescope #1 .015 34 1609 Refractor Galileo's telescope #3 .038 10 1620 Refractor Newton's telescope .033 12 1668 First reflecting telescope Herschel telescope 1.20 2.5 1789 Reflector Yerkes refractor 1.02 2.5 1897 Refractor. End of refractor age Hale 60-inch 1.52 2.5 1908 Mount Wilson observatory Hooker 100-inch 2.54 2.5 1917 Mount Wilson observatory Hale 200-inch 5.08 2.5 1948 Palomar Observatory Keck 10 2.5 1993 Mauna Kea Observatory Hubble 2.4 .20 1990 Earth orbit Webb Space Telescope 6.5 .10 ? L2 Lagrange point Thirty Meter Telescope 30 .20 ? Mauna Kea Observatory
Refraction depends on wavelength, which introduces "chromatic aberration". This limits the size of refracting telescopes. Reflecting telescopes don't suffer this limitation.
1608 Lippershey constructs the first refracting telescope 1663 Gregory publishes a design for a "Gregorian" reflector 1668 Newton constructs the first reflecting telescope, a "Newtonian" reflector 1672 Cassegrain publishes a design for a "Cassegrain" reflector 1910 Ritchey-Chretien reflecting telescope, the basis for modern reflectors
A person with 20/20 vision can distinguish parallel lines that are spaced by an angle of .0003 radians, about 3 times the diffraction limit. Text can be resolved down to an angle of .0015 radians.
Resolution Resolution Diopters for parallel for letters (meters-1) lines (radians) (radians) 20/20 .0003 .0015 0 20/40 .0006 .0030 -1 20/80 .0012 .0060 -2 20/150 .0022 .011 -3 20/300 .0045 .025 -4 20/400 .0060 .030 -5 20/500 .0075 .038 -6"Diopters" is a measure of the lens strength required to correct vision to 20/20.
The resolution of a telescope is limited by diffraction.
Wavelength of light = L Mirror diameter = D Resolution angle = θ = 1.22 * L / DIf we assume blue light with L=440 nm,
D θ Eye .005 .00011 10 cm telescope .1 .0000054 Hubble telescope 2.5 .00000021 1 Degree = 60 arcminutes = 3600 arcseconds 1 arcsecond = 4.8e-6 radians
The atmosphere blurs light from outer space, limiting telescopes to a resolution of 5e-6 radians or 1 arcsecond. This is the resolution of a 10 cm telescope. A telescope larger than 10 cm has the same resolution as a 10 cm telescope. The advantage of the larger telescope is more light.
Telescope Resolution Reason for diameter (radians) resolution limit (meters) < .1 5e-7 / Diameter Diffraction > .1 5e-6 AtmosphereA space telescope doesn't experience atmospheric distoration and the limit is from diffraction only. The 2.5 meter Hubble space telescope has a better resolution than the 10 meter Keck Earth telescope.
Telescopes equipped with "adaptive optics" can correct atmospheric distortion and reach a resolution better than 5e-6 radians.
Astronomers measure brightness in a goofy unit called "magnitudes". It was defined by Hipparcos in Ancient Greece and it's still with us.
The "Apparent luminosity" of a star is its brightness as viewed from the Earth.
The "Absolute luminosity" is the power generated by a star in Watts.
Distance to star = R meters Luminosity = L = 3.29⋅1028 * 10-M/2.5 Watts Flux = l = L / (4 π R2) Watts/meter2 Absolute magnitude = M = m + 87.71 - 2.17 log10(R) Apparent magnitude = m = M - 87.71 + 2.17 log10(R) Flux corresponds to the brightness of an object as viewed from the Earth.The fainter an object, the larger its apparent magnitude "m".
Distance Luminosity Flux Absolute Apparent from Watts Watts/m2 magnitude magnitude Earth (L) (l) (M) (m) Sun 1 AU 3.8e26 1360 4.8 -26.7 Full Moon .00257 AU 4.8e15 2.6e-3 32.1 -12.7 Mars .52 AU 2.3e16 3.1e-7 30.4 -2.9 Jupiter 4.2 AU 1.5e18 3.1e-7 25.8 -2.9 Saturn 8.5 AU 6.8e17 3.4e-8 26.7 -.5 Uranus 18.2 AU 1.5e16 1.6e-10 30.9 5.3 Discovered 1781 Ceres 1.77 AU 4.3e13 4.9e-11 37.2 6.6 Discovered 1801 Neptune 29.1 AU 3.8e15 1.6e-11 32.3 7.8 Discovered 1846 Pluto 28.7 AU 1.8e13 7.8e-14 38.2 13.6 Discovered 1930 Alpha Centauri A 4.36 ly 5.9e26 2.7e-8 4.4 0.0 WISE-0855 7.2 ly 3.4e21 5.9e-14 17.5 13.9 Rogue planet Sirius 8.58 ly 9.8e27 1.2e-7 1.4 -1.5 Brightest star Exo-Sun 10.0 ly 3.8e26 3.4e-9 4.8 2.0 Exo-Earth 10.0 ly 5.4e16 4.8e-19 29.5 26.6 Betelgeuse 640 ly 5.8e31 1.3e-7 -6.0 .4 Massive star Andromeda 2560000 ly 9.9e36 1.3e-9 -21.6 4.2Values for solar system objects are for when they are closest to the Earth.
Uranus is at the limit of human vision. It's conceivable that an ancient civilization could have detected Uranus. Ceres is just beyond human vision.
WISE-0855 is a brown dwarf with a mass somewhere between 3 and 10 Jupiter masses. It has a temperature of 240 Kelvin and was detected by the WISE infrared space telescope.
"Exo-Sun" and "Exo-Earth" are values for if the sun and the Earth are at a distance of 10 light years.
GRB 080319B is the most luminous recorded gamma ray burst.
The horizontal lines represent the limits of the Pan-STARRS, Keck, Hubble, and Webb telescopes. Exo-Earth is detectable by the Keck telescope.
Flux Apparent limit magnitude Watts/m2 limit Human eye 3.4e-11 7 Pan-STARRS 5e-18 24 Keck 10 meter 1e-19 28 Hubble 1e-20 31 Webb 5e-22 34
Observable from the ground? Gamma ray No X ray No Ultraviolet No Visible Yes Infrared No Millimeter Yes, if the air is dry Radio Yes
The SOFIA tel escope can see in the infrared because it flies on a Boeing 747 at an altutude of 12 km, which is above most of the atmosphere's water.
Min & Max Aperture Year wavelength (m) (meters) Square kilometer Array 1000 2019 .01 4.3 Australia and South Africa Green Bank II 100 2000 .0026 3.0 Green Bank, West Virginia. Largest steerable dish Arecibo 300 1963 .03 1.0 Puerto Rico Green Bank I 91 1962 Collapsed and rebuilt as Green Bank II Jodrell Bank 76 1951 Jansky 30 1931 Astron 10 2011 .01 1.0 High Earth orbit. Used for large-baseline interferometry
Min & Max Aperture Year wavelength (meters) (mm) CSO 10.5 1986 .3 2.0 Mauna Kea Caltech Maxwell 15 1987 .3 2.0 Mauna Kea ALMA 12 2011 .3 9.6 Atacama Desert, Chile 54 12-meter dishes and 12 7-meter dishes LMT 50 2011 .85 4.0 Sierra Negra, Mexico Large millimeter Telescope CCAT 25 2017 Cerro Chajnantor, Chile Wavelength range similar to ALMA CSO = Caltech submillimeter observatory CCAT = Cerro Chajnantor Atacama Telescope ALMA = Atacama Large Millimeter Array
Diameter Resolution Mass Min Max Year Location (m) (urad) (tons) (mm) (mm) Planck 1.9 4100 .21 .3 11 2009 L2 WMAP 1.6 12000 .76 .32 1.30 2001 L2 COBE .19 1.41 1989 Geocentric
Aperture Year Min Max Location (meters) (mm) (mm) WMAP 1.6 2001 .003 .015 L2 Lagrange point NASA Observes cosmic microwave background Spitzer .85 2003 .003 .180 Sun orbit NASA WISE .40 2009 .003 .025 Earth orbit NASA Herschel 3.5 2009 .055 .672 L2 ESA SOFIA 2.5 2010 .001 .655 Boeing 747 at an altitude of 12 kmSOFIA = Stratospheric Observatory for Infrared Astronomy
Aperture Resolution Low High Focus Mass Year (m) (urad) (keV) (keV) (m) (tons) Hitomi soft .3 12 5.6 2.7 2016 Geocentric JAXA Hitomi hard 5 80 12 2.7 2016 Geocentric JAXA XMM-Newton .70 24 .1 12 7.5 3.2 1999 Geocentric ESA NuSTAR .32 46 3 79 10.15 .17 2012 Geocentric NASA Swift .30 .61 2004 Geocentric NASA GSFC INTEGRAL .31 3500 3 10000 4.0 2002 Geocentric ESA RKA NASA Chandra 1.2 2.4 .1 10 10 4.8 1999 Geocentric NASA SAO CXCNuSTAR has a collecting area of 847 cm2 at 7 keV and a collecting area of 60 cm2 at 78 keV. The field of view is 12 arcminutes.
The Hitomi lost attitude control and went into an uncontrollable spin, destroying the telescope.
Year Low High Mass (MeV) (MeV) (tons) Hitomi 2016 .06 .6 2.7 Geocentric JAXA Fermi 2008 30 300000 4.3 Lagrange #2 NASA
Aperture Magnitude Field of Exposure Full-sky CCD Year (meters) limit view (seconds) survey time (Gpixels) (degrees) (days) Pan-STARRS 3.6 24.0 3.0 60 8 1.4 2010 Hawaii LSST 8.4 24.5 3.5 15 2 3.2 2021 El Penon, ChileThe Pan-STARRS and LSST telescopes are designed to find solar system objects, which is why they use short exposures.
Frequency = F Wavelength = W Planck constant = h = 4.1357⋅10-15 eV seconds Speed of light = C = F W = 2.9979⋅108 meters/second Energy = E = h F Aperture diameter = D Diffraction angle = A = 1.22 W / D Energy Wavelength Temperature (eV) (nm) (Kelvin) Gamma ray 1000000 .0012 X-Ray 1000 1.2 290000 Bohr energy 13.6 91 32000 UV-Extreme min 12.4 100 29000 UV-C min 4.43 280 10350 UV-B min 3.94 315 9200 Human UV limit 3.10 400 7244 Violet 3.06 405 7155 Blue 2.79 445 6512 Cyan 2.58 480 6037 Green 2.33 532 5447 Yellow 2.10 589 4920 Orange 2.03 610 4750 Red 1.91 650 4458 Human IR limit 1.63 750 3864 1 electron Volt 1 1222 2371 Infrared .12 10000 290 Millimeter .0012 106 2.90 300 GHz Radio 109 .0029 300 MHz 1800 Herschel discovers infrared light by its effect on a thermometer 1801 Ritter discovers UV rays by their effect on AgCl 1835 Melloni builds a thermoelectric infrared detector 1878 UV rays are found to kill bacteria 1879 Stefan-Boltzmann law: Power = Constant * Area * Temperature^4 1901 Planck hypothesizes that E=hF 1905 Einstein discovers the photoelectric effect 1960 UV rays found to be harmful to DNA
"Ridge A" in Antarctica is a 4 km high plateau where the environment is cold, dry, and has no wind, making it the best place in the world for a telescope. Resolution is up to 3 times higher than what can be achieved by telescopes at the equator. It is also ideal for submillimeter astronomy, which requires cold dry air.
Properties of Ridge A: Altitude = 4053 meters. Distance from the South Pole = 1000 km. Distance from Dome A = 144 km. Dome A is the highest ice feature in Antarctica, with an altitude of 4091 meters. Annual snowfall = 2 cm. Average temperature = -70 Celsius.
Modern mathematics and physics was launched when Simon Stevin popularized decimal numbers in Europe. Cartesian geometry and the calculus followed shortly after. Mathematics has been on a roll ever since.
Decimal numbers enable precise calculation, which is essential for science. Shortly after decimal numbers were popularized, the logarithm and the slide rule were invented. The slide rule enables fast multiplication and division.
1585 Stevin popularizes decimal numbers in Europe 1614 Napier develops logarithm tables 1622 Oughtred develops the slide rule 1604 Galileo publishes the mathematical description of acceleration. 1637 Cartesian geometry published by Fermat and Descartes. 1684 Leibniz publishes the calculus 1687 Newton publishes the Principia Mathematica, which contained the calculus, the laws of motion (F=MA), and a proof that planets orbit as ellipses.
-240 Eratosthenes measures the Earth's circumference to 20% error. -240 Aristarchus proves that the sun is at least 10 times larger than the Earth using lunar eclipses. 150 Ptolemy publishes The Almagest with the geocentric model 550 Aryabhata publishes accurate measurements of size of the sun and moon 1543 Copernicus publishes a heliocentric model. 1600 Brahe measures accurate planet positions 1608 Lippershey invents the telescope 1609 Galileo builds a telescope and begins observing 1609 Kepler proves that planets orbit as ellipses using Brahe's data 1613 Galileo publishes observations of the phases of Venus, which support the heliocentric model 1632 Galileo publishes the "Dialogue Concerning the Two Chief World Systems", which contained a comparison of the systems of Ptolemy and Copernicus 1672 Richter and Cassini measure the parallax of Mars, producing a precise value for the size of the sun 1687 Newton publishes the Principia Mathematica, which contained the calculus, the laws of motion (F=MA), and a proof that planets orbit as ellipses. 1718 Halley finds that the stars move. He found that Sirius, Arcturus and Aldebaran were 1/2 of a degree from the positions charted by the Ancient Greek astronomer Hipparchus 1783 Herschel finds that the solar system is moving with respect to the stars 1826 Olbers' paradox. If the stars in the universe are uniformly distributed and if the universe is infinite, then the sky would appear infinitely bright with stars. 1863 Bessel measures the first stellar parallax, showing that the stars are more than 4 light years away. This also implies that stars are as luminous as the sun. The parallax of stars is too small to see without a telescope. 1905 Einstein publishes special relativity 1915 Einstein publishes the general theory of relativity. Einstein shows that general relativity is consistent with the existence of a cosmological constant. At the time the cosmological constant was a proposed explanation for why the universe hasn't collapsed gravitationally. 1920 Shapley finds that the sun is not at the center of the galaxy. Because starlight is absorbed by interstellar gas, we only see the nearby stars and it appears as though we live at the center of a disk of stars. Shapley measured the distances to globular clusters and found that they are centered on a point (the galactic center) that is far from the sun. 1922 Friedmann finds a solution to the equations of general relativity that are consistent with an expanding universe. 1923 Hubble measures the distances to Andromeda and Triangulum and finds that they are outside the Milky Way. These were the first objects to be shown to be outside the Milky Way. 1929 Hubble's law published. For distant galaxies, the recession velocity is proportional to distance. 1933 Zwicky's analysis of the Coma cluster of galaxies shows that they contain unseen matter that is not due to stars. 1965 Penzias and Wilson discover the cosmic microwave background radiation. 1970 Rubin and Ford measure galactic rotation and show that galaxies contain matter that is not due to stars. 1980 Guth and Starobinsky propose the theory of inflation to explain why the universe is flat 1998 Observations of supernovae show that the expansion of the universe is accelerating and the the cosmological constant is positive. Previous to this it was not known if the universe was destined for collapse (big crunch) or for infinite expansion (big chill). 2003 WMAP mission measures the Hubble constant to 5% precision, as well as other cosmological parameters. Previous to this, the Hubble constant had an error of ~ 20%. This settled once and for all the question of the overall structure of the universe.
-260 Aristarchus established that the distance to the sun is at least 20 times the distance to the moon.
In 499, Aryabhata publishes a measurement of the distance to the sun.
Brahe's data consisted of measurements of angles between different objects. This data could be used to establish the shape of orbits but not their size. For example, if the size of the solar system were doubled along with the speeds of the planets, the angles would stay the same and you wouldn't be able to tell the difference.
In 1639, Horrocks used a transit of Venus to measure the distance to the sun, but this method is incapable of giving an accurate value, and it can only be done once per century.
In 1672, Richter and Cassini measured the parallax of Mars which gives a result for the distance to the sun that is more accurate than the Venus method. The Mars method has an advantage over the Venus method in that it can be done once every 26 months, when Mars is at closest approach.
In 1676, Romer used the moons of Jupiter to measure the time it takes for light to cross the Earth's orbit. This gives a value for R/C.
In 1729, Bradley measured the deflection of starlight due to the Earth's motion, which gives a measurement of V/C, or equivalently, a measurement of R/C.
In 1849, Fizeau produced the first measurement for the speed of light that was independent of the Earth-sun distance R.
Speed of light = C Earth-sun distance = R Earth orbital velocity = V Earth orbital time (1 year) = T = 2 π R / V Time for light to cross the Earth's orbit= t = 2 R / C
The unit of energy used for atoms, nuclei, and particle is the "electron Volt", which is the energy gained by an electron upon descending a potential of 1 Volt.
Electron Volt (eV) = 1 eV = 1.602e-19 Joules Kilo electron Volt = 1 keV = 103 eV Mega electron Volt = 1 MeV = 106 eV Giga electron Vlt = 1 GeV = 109 eV
Proton + Proton -> Deuterium + Positron + NeutrinoHydrogen fusion requires a temperature of at least 4 million Kelvin, which requires an object with at least 0.08 solar masses. This is the minimum mass to be a star. The reactions in the fusion of hydrogen to helium are:
P + P --> D + Positron + Neutrino + .42 MeV P + D --> He3 + Photon + 5.49 MeV He3 + He3 --> He4 + P + P + 12.86 MeV
As the core of a star star runs out of hydrogen it contracts and heats, and helium fusion begins when the temperature reaches 10 million Kelvin.
A heavy star continues to fuse elements until it reaches Iron-56. Beyond this, fusion absorbs energy rather than releasing it, triggering a runaway core collapse that fuses elements up to Uranium. If the star explodes as a supernova then these elements are ejected into interstellar space.