Background Concepts Review Some of this material is covered in a - PowerPoint PPT Presentation

Background Concepts

Review Some of this material is covered in a MasteringAstronomy practice assignment called Math Review.

The Metric System We will use the metric system almost exclusively. (English units are entirely evil.) • Mass unit: gram (g) • Length unit: meter (m) • Force unit: Newton (N) • Energy unit: Joule (J) • Time unit: seconds (s) • Temperature: Celsius degrees ( ◦ C)

The Metric System Commonly used metric prefixes and suffixes: nano ( n ) = 10 − 9 = billionths micro ( µ ) = 10 − 6 = millionths milli ( m ) = 10 − 3 = thousandths centi ( cm ) = 10 − 2 = hundredths kilo ( k ) = 10 3 = thousands Mega ( M ) = 10 6 = millions Giga ( G ) = 10 9 = billions Notice how most of the exponents go by 3’s.

Temperature Scales In addition to the Celsius scale, we also need to talk about temperature in terms of energy. For that we use the Kelvin scale. (But never the Fahrenheit scale.)

Density Density: a measure of how tightly mater is “packed,” and an important clue to the makeup of an object. Physicists use the symbol ρ for density. Mass (g/cm 3 , kg/m 3 , g/ml, etc.) ρ = Volume ρ water = 1 . 0 g / cm 3 ρ rock = 3 . 5 g / cm 3 ρ iron = 7 . 9 g / cm 3 ρ Sun ′ s core = 150 g / cm 3

Scientific Notation Scientific notation makes it easier to represent very large or very small numbers. Consider: Diameter of a Hydrogen atom ∼ 0.00000001 m. Diameter of Milky Way galaxy ∼ 1,000,000,000,000,000,000,000 m. Using scientific notation: D H atom = 1 × 10 − 8 m D Milky Way = 1 × 10 21 m Far easier to recognize, to compare, to calculate with.

Scientific Notation Simple rules for scientific notation: • One and only one digit before the decimal point. • “Standard” → scientific notation: − . = 1 . 01 × 10 2 decimal point lef = + exponent. 1 0 − 1 ← ← • “Standard” → scientific notation: Moving the decimal point right = - exponent. → 01 = 1 . 01 × 10 − 3 0 . 0 → 0 → 1 − − − • Reverse this for scientific → “standard” notation. Make sure you know how to properly enter scientific notation on your calculator. Look for “EXP” or “EE” or “SCINOT” key. Talk to me if you need help!

Scaling and Ratios Ofen is is far easier to see relationships between values by comparing them to something more familiar. When we do so we are using ratios and proportions.

Scaling and Ratios Is the following easy to compare?: has a mass of 1 . 9 × 10 27 kg. has a mass of 6 . 0 × 10 24 kg. Okay, how about M Jupiter = 318 M Earth ? M J / M E = 1 . 9 × 10 27 kg 6 . 0 × 10 24 kg = 318 Beter? I hope so. We will make use of this a lot.

Angles Angular Measure • Angles are measured in degrees . • There are 360 ◦ in a circle. (Why?) • There are 60 minutes in a degree: 1 ◦ = 60 ′ . • There are 60 seconds in a minute: 1 ′ = 60 ′′ . • 1 ◦ = 3600 ′′ . • Angles are also measured in radians . • 360 ◦ = 2 π radians, or more simply: 180 ◦ = π radians. • θ is the variable ofen used for angles.

Some Geometry Sum of angles = 180 ◦ Area: A = 1 2 bh

Some Geometry Similar Triangles h 2 = b 2 h 1 b 1 � 2 � b 2 A 2 = A 1 b 1

Some Geometry Circles and Spheres C = π D C = 2 π R A circle = π R 2 A sphere = 4 π R 2 V = 4 3 π R 3

Some Geometry Arc Length (s) In the small angle approximation ( θ small), the difference between the curved arc length, s , and the “base” of the triangle formed by the angle, d , is negligible. s = R θ s ≈ d θ MUST be in radians.

Angular Size We can’t really tell how far away something in the sky is. We don’t know the linear size , only the angular size without knowing the distance. An object could be big and far away, or small and close, and have the same angular size, θ .

Angular Size Some Useful “Rules of Thumb”

Scales Astronomical investigations really do encompass the entire Universe: Virgo Consortium - Millenium Project From the smallest of to the cosmic web of particles, galaxies.

Scales atometer (am) - LIGO limit 10 − 18 m femtometer (fm) - Neutron 10 − 15 m Longest picometer (pm) - 10 − 12 m gamma ray nanometer (nm) - Proteins 10 − 9 m

Scales micrometer ( µ m) - Small bacteria 10 − 6 m millimeter (mm) - Small flea 10 − 3 m meter (m) - 10 0 m Small scientist Small Jovian kilometer (km) - 10 3 m moons

Scales megameter (Mm) Dwarf planet - 10 6 m gigameter (Gm) - Sun-like star 10 9 m Red supergian terameter (Tm) - 10 12 m star Youngest petameter (Pm) - Planetary 10 15 m Nebula

Scales Globular exameter (Em) - 10 18 m Cluster Radius of zetameter (Zm) - Milky Way 10 21 m disk Typical yotameter (Ym) - intergalactic 10 24 m void

Scales Great “Powers of 10” video: https://www.youtube.com/watch?v=KEHCCsFFIuY

“Never trust an atom. They make up everything.” • 91% of the atoms are Hydrogen (H) • 8.9% are Helium (He) • Everything else is only 0.1% • By mass this is 74%, 24%, and 2% respectively. • This ratio holds true all across the Universe.

Atoms In an atom: • The number of protons , the atomic number, determines what element it is. Protons have a positive charge. • If only the number of neutrons varies, we call these different isotopes . Neutrons have no charge. Neutron Proton • If the number of protons and electrons (negative charge) is NOT the same, we call this an ion. • The number of protons plus neutrons is the mass number . It is close to, but not exactly, the mass of the atom in amu.

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