The Scale of the Cosmos Lecture 2
POWERS OF 10 & SCIENTIFIC NOTATION • In science and especially in astronomy, you have to deal • with very large numbers and very small numbers. • For example, the number of kilometers in a light year is • approximately 9,500,000,000,000 (9.5 trillion). • The diameter of the hydrogen atom is 0.000000013 • centimeters (13 billionths).
To manage large numbers and small numbers, professionals make use of powers of 10 and scientific notation. 10,000,000,000 (10 billion) years is the approximate age of the Milky Way Galaxy (MWG). Instead of writing out the large number in expanded form (i.e., 10,000,000,000) it is written as as a power of 10…1010). 10 9 8 7 6 5 4 3 2 1 10,000,000,000. 1010 The number of place values to move the decimal behind the 1.
The diameter of the MWG is approximately 100,000 (100 thousand) light years. 5 4 3 2 1 100,000. 105 The number of stars in the MWG is approximately 100,000,000,000 (100 billion). 11 10 9 8 7 6 5 4 3 2 1 100,000,000,000. 1011
Large numbers have a positive exponent when written as a power of 10. Small numbers have a negative exponent when written as a power of 10. Consider the small number 0.000000001 (1 billionth): 1 2 3 4 5 6 7 8 9 0.000000001 10-9 The number of place values to move the decimal behind the 1.
Positive Exponents Negative Exponents 100 = One 101 = Ten 102 = One Hundred 103 = One Thousand 104 = Ten Thousand 105 = One Hundred Thousand 106 = One Million 107 = Ten Million 108 = One Hundred Million 109 = One Billion 1010 = Ten Billion 1011 = One Hundred Billion 1012 = One Trillion 100 = One 10-1 = One Tenth 10-2 = One Hundredth 10-3 = One Thousandth 10-4 = Ten Thousandth 10-5 = One Hundred Thousandth 10-6 = One Millionth 10-7 = Ten Millionth 10-8 = One Hundred Millionth 10-9 = One Billionth 10-10 = Ten Billionth 10-11 = One Hundred Billionth 10-12 = One Trillionth
SCIENTIFIC NOTATION A number is put into scientific notation if it is in the form d x 10n (large number) or d x 10-n (small number) where d is a decimal between 1 and 10 (i.e., 1 ≤ d < 10). The distance to the Sun is about 150,000,000 km 150,000,000 = 1.5 x 108 8 7 6 5 4 3 2 1 150,000,000. 1.5 x 108
10 9 8 7 6 5 4 3 2 1 38,000,000,000. 3.8 x 1010 1 2 3 4 5 6 7 0.000000478 4.78 x 10-7 1 2 3 4 5 0.000031 3.1 x 10-5
To multiply or divide powers of ten you: Add the exponents when you multiply Subtract the exponents when you divide 103* 104 = 103+4 = 107 105* 107 = 105+7 = 1012 1012= 1012-3 = 109 103 108= 108-5 = 103 105
ARITHMETIC OF NUMBERS IN SCIENTIFIC NOTATION (2.1 x 103) . (1.5 x 106) = (2.1 . 1.5) x (103. 106) = 3.15 x 109 Multiply the Decimals Add the Exponents 7.2 x 1017=7.2x 1017=2.4 x 107 3 x 1010 3 1010 Divide the Decimals Subtract the Exponents
When it comes to the arithmetic of numbers in scientific notation, let your fingers do the walking…USE YOUR CALCULATOR. Your calculator will handle all of the decimal calculations and the addition/subtraction of the exponents. All you have to do is to set your calculator to scientific notation mode then key in the numbers in the arithmetic problem. Note – DO NOT enter a number as “3” “x” “10” “^4”, it will treat the “3” and the “10^4” as separate numbers. Use the “exp” or “EE” button (for “exponent”) as in “3” “EE” “4”. (Often written in shorthand form as 3e4).
SAMPLE PROBLEMS Light travels at the speed of c = 300,000 km/s. The distance from Earth to the Sun is 150,000,000 km. How long does it take light travel from the Sun to Earth? Distance = Speed . Time Speed =Distance Time Time =Distance Speed Time =Distance=150,000,000 km Speed 300,000 km/s Time = 500 seconds 500 s . 1 min/60 s = 8.3 minutes The Earth is 8.3 light-minutes from the Sun.
The metric system as opposed to the British system of units is used in science. There are two versions of the metric system: MKS = Meters (m) Kilograms (kg) Seconds (s) CGS = Centimeters (cm) Grams (g) Seconds (s) It is customary to use CGS in stellar astronomy and MKS in the other branches of astronomy. We will be using the MKS system of units. The meter is the unit of distance in the MKS system. It is approximately one yard in length (39.3 inches). The kilogram is the unit of mass (weight). It is approximately two pounds of weight at Earth’s surface.
Scales of Size and Time Astronomy deals with objects on a vast range of size scales and time scales. Most of these size and time scales are way beyond our every-day experience. Humans, the Earth, and even the solar system are tiny and unimportant on cosmic scales.
A Campus Scene 16 x 16 m (52 x 52 ft)
A City View 1.6 x 1.6 km (1 x 1 mile)
The Landscape of Pennsylvania 160 x 160 km (100 x 100 miles)
The Earth Diameter of the Earth: 12,756 km
Earth and Moon Distance Earth – Moon: 384,000 km
No atmosphere. Diameter: 3500 km Sidereal Period: 27.3 days Synodic Period: 29.5 days Distance from Earth: 385,000 km Maria – Younger Surface 3 billion years old Highlands – Older Surface 4.5 billion years old EARTH’S MOON
Earth Orbiting Around the Sun Distance Sun – Earth = 150,000,000 km
Earth Orbiting Around the Sun In order to avoid large numbers beyond our imagination, we introduce new units: 1 Astronomical Unit (AU) = Distance Sun – Earth = 150 million km (93 million miles)
SUN Sunspots (Magnetic Storms) Solar Flares & Prominences Boiling Earth-Sized Convection Cells Diameter: 1,400,000 km Rotation Period: 25 days Surface Temperature: 5,800 K Core Temperature: 15,000,000 K
The Solar System Approx. 100 AU
MERCURY With no atmosphere, Mercury is heavily cratered by 4.5 billion years of meteoritic impacts. Nearest the Sun of all the planets. 60,000,000 km (0.4 AU) Diameter: 5000 km Orbital Period: 88 days Rotational Period: 58 days Although not much bigger than Earth’s Moon it is much denser, 5.5 times that of water compared to the Moon’s 3.5 times.
Thick atmosphere of carbon dioxide and sulfuric acid. VENUS Venus has a hot thick atmosphere. It is so thick that optical-based telescopes cannot penetrate to the surface. Closer to the Sun than Earth, the temperature at the surface is a blistering 800o F. Diameter: 12,100 km (almost a match for Earth) Orbital Period: 225 days Rotational Period: 243 days (retrograde) Distance from Sun: 110,000,000 km (0.7 AU) Soviet Venra Spacecraft photograph of the surface of Venus.
MARS Diameter: 6800 km Orbital Period: 1.88 years Rotational Period: 24h Distance from Sun: 225,000,000 km (1.5 AU) Gigantic gorge in the surface of Mars (Valles Marinaris) stretching 3000 km across. It would reach across the entire continental United States. Polar Cap Dry Ice & Water Ice Thin atmosphere of carbon dioxide and water.
ASTEROID BELT Gaspra Ida The Asteroid Belt is located between 2 and 4 AU from the Sun. It contains billions of rock boulders. The two at the right are 20-60 km in size. Dactyl
JUPITER Atmospheric cloud bands due to high winds. Extensive atmosphere of methane and ammonia. Diameter: 143,000 km Orbital Period: 12 years Rotational Period: 10h Distance from Sun: 680,000,000 km (5 AU) Great Red Spot Jupiter is the largest of the planets in the solar system. It is large enough to fit all of the other planets inside of it…twice! It can easily engulf over 1000 Earths. It has an extensive atmosphere tens of thousands of kilometers thick. It is believe to have been the first planet to form in the solar system, 100 million years after the Sun formed from a large cloud of gas and dust in the rotational plane of the Milky Way Galaxy.
Moon-wide ocean encrusted in ice Most volcanically-active object In the solar system THE GALILEAN SATELLITES • This composite includes the four largest moons of Jupiter which are known as the Galilean satellites. From left to right, the moons shown are Ganymede, Callisto, Io, and Europa. • The Galilean satellites were first seen by the Italian astronomer Galileo Galilei in 1610. In order of increasing distance from Jupiter, Io is closest, followed by Europa, Ganymede, and Callisto.
SATURN Diameter: 121,000 km Orbital Period: 29 years Rotational Period: 10h 30m Distance from Sun: 1,400,000,000 km (9.5 AU) Extensive system of rings
Atmospheric clouds URANUS NEPTUNE Diameter: 50,000 km Orbital Period: 164 years Rotational Period: 15h Distance from Sun: 4,500,000,000 km (30 AU) Diameter: 51,000 km Orbital Period: 84 years Rotational Period: 15h Distance from Sun: 2,900,000,000 km (19 AU)
OORT CLOUD & KUIPER BELT • Diagram of the Oort cloud, showing a few cometary orbits. Most Oort cloud comets never come close to the Sun. Of all the orbits shown, only the most elongated ellipse represents a comet that will actually enter the solar system (which is smaller than the dot at the center of the figure on this scale) and possibly become visible from Earth. • (b)The Kuiper belt, the source of the short-period comets, whose orbits hug the ecliptic plane.
PLUTO Discovered in the 1930’s by Clyde Tombaugh, Pluto was long considered the 9th planet in the solar system. Although it built up in the same way as the planets, it is now better classified as a Kuiper Belt Object (KBO). Along with newly-discovered KBO Eris and the asteroid Ceres, it is now also classified as a dwarf planet. The Kuiper Belt is a region outside Neptune’s orbit where billions of ice boulders (the building blocks of the planets) are located. The second KBO after Pluto was discovered in 1992, although their presence was predicted circa 1950 by Gerard Kuiper. Pluto Charon Diameter: 2,200 km Orbital Period: 248 years Rotational Period: 6 days Distance from Sun: 5,900,000,000 km (40 AU)
(Almost) Empty Space Around Our Solar System Approx. 10,000 AU
The Solar Neighborhood Approx. 17 light years
The Solar Neighborhood New distance scale: 1 light year (ly) = Distance traveled by light in 1 year = 63,000 AU = 1013 km = 10,000,000,000,000 km (= 1 + 13 zeros) = 10 trillion km Approx. 17 light years Nearest star to the Sun: Proxima Centauri, at a distance of 4.2 light years
The Extended Solar Neighborhood Approx. 1,700 light years
The Milky Way Galaxy Diameter of the Milky Way: ~ 75,000 ly
The Local Group of Galaxies Distance to the nearest large galaxies: several million light years
The Universe on Very Large Scales Clusters of galaxies are grouped into superclusters. Superclusters form filaments and walls around voids.
For next time • Read Units 5 and 6 • Remember that the homework is due on Monday