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) = 103 = thousands Mega(M) = 106 = millions Giga(G) = 109 = 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. ρ =

Mass Volume

(g/cm3, kg/m3, g/ml, etc.) ρwater = 1.0 g/cm3 ρrock = 3.5 g/cm3 ρiron = 7.9 g/cm3 ρSun′s core = 150 g/cm3

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: DH atom = 1 × 10−8 m DMilky Way = 1 × 1021 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:

decimal point lef = + exponent. 1 0 ← − 1 ← −. = 1.01 × 102

• “Standard” → scientific notation:

Moving the decimal point right = - exponent.

• 0. 0

− → 0 − → 1 − →01 = 1.01 × 10−3

• Reverse this for scientific → “standard” notation.

Make sure you know how to properly enter scientific notation

• n 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 × 1027 kg. has a mass of 6.0 × 1024 kg. Okay, how about MJupiter = 318 MEarth? MJ/ME = 1.9 × 1027kg 6.0 × 1024kg = 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◦ = 2π radians, or more simply: 180◦ = π radians.
• θ is the variable ofen used for angles.

Some Geometry

Sum of angles = 180◦ Area: A = 1

2bh

Some Geometry

Similar Triangles

h2 h1 = b2 b1 A2 A1 = b2 b1 2

Some Geometry

Circles and Spheres C = πD C = 2πR Acircle = πR2 Asphere = 4πR2 V = 4 3πR3

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 = Rθ 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 particles, to the cosmic web of galaxies.

Scales

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

Scales

Small bacteria micrometer (µm) - 10−6 m Small flea millimeter (mm) - 10−3 m Small scientist meter (m) - 100 m Small Jovian moons kilometer (km) - 103 m

Scales

Dwarf planet megameter (Mm)

• 106 m

Sun-like star gigameter (Gm) - 109 m Red supergian star terameter (Tm) - 1012 m Youngest Planetary Nebula petameter (Pm) - 1015 m

Scales

Globular Cluster exameter (Em) - 1018 m Radius of Milky Way disk zetameter (Zm) - 1021 m Typical intergalactic void yotameter (Ym) - 1024 m

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.

Proton

Neutron

• 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.

Location

Location

Location

Location