Astro 1010 - Exam 2 Study Guide Notes

Chapter 4: Making Sense of the Universe

Scalars

• Scalars possess magnitude and a unit of measurement.
  • Examples:
    • Mass (e.g., $5 kg$)
    • Time (e.g., $12 seconds$)
    • Speed (e.g., $15 m/s$)

Vectors

• Vectors possess magnitude, a unit of measurement, and direction.
  • Examples:
    • Displacement (e.g., $9 miles$ to the west)
    • Velocity (e.g., $60 miles/hour$ in the negative direction)
    • Acceleration (e.g., $10 m/s^2$ downward)

Acceleration

• Linear acceleration: Occurs when an object speeds up or slows down along a straight line.
• Centripetal acceleration: Occurs when an object moves in a circle; in this case, the direction of velocity ($v$) changes.
• Acceleration caused by Earth's gravity: Approximately $10 m/s^2$ pointing downwards. All objects accelerate at this rate as they fall.

Newton's Laws

• 1st Law of Motion (Law of Inertia): Objects maintain a constant velocity unless acted upon by an outside force.
• 2nd Law of Motion: $F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration.
• 3rd Law of Motion: For every force that acts on one object, an equal yet opposite reaction force is exerted upon another object.
• Law of Gravity: $F = G \frac{m<em>1 m</em>2}{r^2}$, where every mass gravitationally attracts every other mass. The strength of the gravitational pull decreases as the distance between them grows.

Misconceptions About Gravity

• It is false to assume that there is no gravity in space.
• Earth’s gravity keeps the moon in orbit, proving there is gravity in space.
• Astronauts in orbit experience weightlessness because they are falling around the Earth, not due to a lack of gravity.

Tides

• Tides are caused by the moon's gravitational pull being stronger on the near side of the Earth than the far side.
• Spring Tide: The sun and moon work together to enhance tides.
• Neap Tide: The sun and moon work against each other to decrease tides.

Angular Momentum

• Angular momentum is a conserved quantity for a spinning object, meaning it cannot be created or destroyed, only transferred to/from another object.

Chapter 5: Light and Matter

Light

• Light has both particle-like and wave-like properties.

Waves

• Wavelength: The distance from max-to-max or min-to-min.
• Frequency: How many cycles (max to min to max again) a wave goes through in a given time interval, measured in Hertz ($Hz = \frac{1}{second}$).
• Wave speed = wavelength x frequency.
• Wave energy increases with higher frequency.

Electromagnetic Spectrum

• In order of increasing energy and frequency/decreasing wavelength: radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma-rays.
• Radio waves: low energy, low frequency, long wavelength.
• Gamma-rays: high energy, high frequency, short wavelength.
• All are forms of light; visible light is only special to humans because that's the part of the spectrum humans use to see.

Speed of Light

• The speed of light is constant in a vacuum, and nothing can go faster than the speed of light in a vacuum. In non-vacuum, light travels more slowly.
• The index of refraction ($n$) defines how much light is slowed down in a transparent material: $n = \frac{c}{v}$.

Energy

• Mass energy: The energy contained in physical objects.
• Kinetic energy: The energy of motion.
• Thermal energy: The energy of heat.
• Gravitational potential energy: The energy of objects lifted high above the ground.
• Radiant (or radiative) energy: The energy of light.
• Energy is conserved: It can be transformed into other types or transferred to other objects, but the total amount of energy in the universe is constant.

Wien's Law

• Hotter objects emit the most intense light (brighter light) at shorter wavelengths and higher frequencies (hotter objects emit more blue light) than cooler objects. However, a hotter object will emit more light at all wavelengths than a cooler one.

Light/Matter Interactions

• Emission: Hot matter converts thermal energy into radiant energy.
• Absorption: Matter absorbs the radiant energy of light and heats up.
• Transmission: Light passes through matter, like a window. Light always refracts (changes speed and direction) when it is transmitted.
• Reflection: Light “bounces off” of matter, like a mirror.

Spectra

• Spectra: Split light into its individual wavelengths to create a rainbow band.
• Spectrographs (prisms) and diffraction gratings are used to create spectra.
• Types of spectra:
  • Continuous spectra: Caused by a hot, dense object.
  • Emission spectra: Caused by a hot gas.
  • Absorption spectra: Caused by the light from a hot, dense object passing through a cool gas.

What Spectra Tell Us

• The chemical composition of an object.
• Due to the Doppler Effect:
  • Blueshift: Object is moving toward us.
  • Redshift: Object is moving away from us.
  • Spectral line broadening: Object is rotating.

Matter

• Atomic number: # of protons in an atom, which defines the element of the atom.
• Atomic mass number: # of protons + neutrons in an element, which defines the isotope of the atom.
• Molecules: Multiple atoms held together by the attraction of positive and negative electric charges.
• Matter has both wave-like and particle-like properties, just like light.

Chapter 6: Telescopes

Curved Lenses

• Curved lenses use refraction to gather light rays to a focal point.
• Human eyes are lens-based and focus light to the retina. The iris controls how much light is allowed to enter the pupil of the eye and reach the retina.
• Digital cameras mimic the structure of the eye in many ways.

Basic Properties of a Telescope

• Angular resolution: The ability to see fine detail. Better angular resolution allows smaller angles to be seen.
  • Larger telescopes have better angular resolution.
  • Angular resolution can be improved with Adaptive Optical (AO) systems that compensate for atmospheric blurring (the “twinkle” of stars).
  • Angular resolution can also be improved with interferometry, in which multiple telescopes work together to produce a single image.
• Light-gathering area: The ability to collect more light and therefore see fainter objects. Larger telescopes have better light-gathering power.
• Magnification: The ability to make an image appear larger than normal, which depends on the size of the telescope + the eyepiece used.

Types of Telescopes

• Telescopes are either refracting (lens-based) or reflecting (mirror-based).
• Common reflecting telescope designs include the Cassegrain, Newtonian, and Nasmyth/Coude focus models.

Good Observing Sites

• Dark (to minimize light pollution).
• High (to minimize atmospheric blurring).
• Calm (low winds also minimize atmospheric blurring).
• Dry (to reduce cloud cover).

Earth's Atmosphere vs. the EM Spectrum

• Radio, visible, the near-infrared, and the near-ultraviolet can pass through Earth’s atmosphere and reach the ground. Most of the infrared, most of the ultraviolet, gamma-rays, microwaves, and x-rays are absorbed or scattered as they pass through Earth’s atmosphere; we need space telescopes to make observations at these wavelengths.

Famous Non-Visible Light Telescopes

• Radio: Arecibo and Greenbank.
• Infrared: SOFIA and James Webb.
• Visible and ultraviolet: Hubble.
• X-rays: Chandra and XMM-Newton.
• Satellite TV dishes are miniature radio telescopes.
• Apart from light, astronomers observe gravity waves in addition to particles such as neutrinos and cosmic rays.