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Astro 1010 - Exam 2 Study Guide

Chapter 4: Making Sense of the Universe

Scalars

  • Scalars have magnitude and a unit.
    • Mass (example: 5 kg)
    • Time (example: 12 seconds)
    • Speed (example: 15 m/s)

Vectors

  • Vectors have magnitude, unit, and direction.
    • Displacement (example: 9 miles to the west)
    • Velocity (example: 60 miles/hour in the negative direction)
    • Acceleration (example: 10 m/s² downward)

Acceleration

  • Linear acceleration: when you speed up or slow down along a straight line.
  • Centripetal acceleration: when you move in a circle (direction of v changes).
  • Acceleration caused by Earth’s gravity is about 10 m/s² (pointing down). All objects accelerate at this rate as they fall.

Newton’s Laws

  • 1st law of motion (the law of inertia): objects maintain a constant velocity unless acted upon by an outside force.
  • 2nd law of motion: F = ma
  • 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{m1m2}{r^2}, that is, every mass gravitationally attracts every other mass, but the strength of the gravitational pull decreases as the distance between them grows.

Misconception: There Is No Gravity in Space

  • THIS IS A FALSE STATEMENT.
  • The fact that Earth’s gravity keeps the moon in orbit around us proves there is plenty of gravity in space!
  • Astronauts in orbit experience weightlessness due to the fact that they are falling around the Earth, not due to a lack of gravity.

Tides

  • Caused by the moon’s gravitational pull being stronger on the near side of the Earth than the far side.
  • Spring tide: sun and moon work together to enhance the tides.
  • Neap tide: sun and moon work against each other to decrease the tides.

Angular Momentum

  • Conserved quantity for a spinning object. That is, momentum cannot be created or destroyed for an object, only transferred to/from another object.

Chapter 5: Light and Matter

Light

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

Waves

  • Wavelength: 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 = 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 of the above are forms of light; visible light is only special to humans because that’s the part of the spectrum we use to see.
  • The speed of light is constant in vacuum and nothing can go faster than the speed of light in vacuum. In non-vacuum, light travels more slowly. How much light is slowed down in a transparent material is defined by its index of refraction, 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.
  • Wein’s law: hotter objects emit the most intense light (that is, brighter light) at shorter wavelengths and higher frequencies (that is, hotter objects emit more blue light) than cooler objects. However, a hotter object will emit more light at all wavelengths than a cooler one. There’s a formula for this on the equation sheet.

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). Note that 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.

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

Chapter 6: Telescopes

Curved Lenses

  • Curved lenses use refraction to gather light rays to a focal point
  • Human eyes are lens-based. They 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 also 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. This depends on the size of the telescope + the eyepiece used.
  • Telescopes are either refracting (lens-based) or reflecting (mirror-based). Common reflecting telescope designs include the Cassegrain, Newtonian, and Nasmyth/Coude focus models. (note: you DON’T need to be able to sketch them)

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
  • Other than light, astronomers observe gravity waves in addition to particles such as neutrinos and cosmic rays.