Astronomy Midterm

Numbers in Astronomy:

• Scientific Notation (Powers-of-Ten Notation)

  • 500,000,000 is written as 5 x 108

Distances in Astronomy:

• Light-year: the distance light travels in a year

• Light Speed: Constant; nothing moves faster than light (the fastest speed in the universe)

• 1 Light-Year = 9.461 x 1012km

Light Travel Time:

• If a star is 100 light-years away, it takes 100 years for the light from that star to reach Earth

• A star 500 light-years away can be destroyed by a “Star Destroyer,” and we will have no idea about this destruction for another 500 years.

• Cosmic Microwave Background (CMB): the oldest light in the universe from when the universe was just 380,000 years old

• Astronomers use the patterns in CMB light to determine the total contents of the universe, understand the origins of galaxies, and look for signs of the very first moments after the Big Bang.

A Tour of the Universe:

• 8 planets in the solar system

  • Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune

• Milky Way Galaxy

  • Spiral Galaxy with a black hole in the center

Celestial Poles + Celestial Equator:

• As Earth rotates around its axis, the sky appears to turn in the opposite direction around those celestial pores.

  • North: do not rise and set, circle the Zenith

  • Equator: poles are on the horizon, stars rise from the east and set in the west

  • Intermediate Latitude: ncp is between overhead and the horizon, stars set at an angle at the horizon

• Latitude: north or south of the equator

• Longitude: west or east of the meridian

Celestial Cordinates:

• Declination -> Latitude

• Right Ascension -> Longitude

Subdivison of Degrees:

• A degree can be subdivided into 60 arcminutes

  • Commonly abbreviated as 60 arcmin or 60'

• An arcminute can be subdivided into 60 arcseconds

  •  Commonly abbreviated as 60 arcsec or 60"

1 degree  = 60 arcmin = 60'

1 degree  = 60 arcsec = 60"

Small- Angle Formula:

• Tan(Θ) = D/d

  • For small angles, tan(Θ) ≈ 0

  • Θ = D/d

  • In this case, 0 is in radians.

• Radians to Degrees

  • 360 degrees = 2π radians

  • 1 rad = 360/2π  

  • Θ = D/d x 360/2π

• Convert to arcseconds 

  • Θ =  D/d  x 360/2π   x 60 x 60 arcseconds

  • Θ =  D/d  x 206265 arcseconds

Example: The distance to Jupiter is 944 million km. The angular diameter of Jupiter is measured to be 31.2 arcsec. What is the actual diameter of Jupiter?

D =  (31.2 x 944 x 1010)/206265

D = 142791 km

Newton’s Three Laws:

• First Law: Every object will continue to be in a state of rest or move at a constant speed in a straight line unless it is compelled to change by an outside force

• Second Law: The acceleration of an object is proportional to the net outside force acting on it

  • F = ma

    • Where…

    • F - net outside force (N)

    •  m - mass of the object (kg)

    •  a - acceleration (ms-2)

• Third Law: Whenever one object exerts a force on a second object, the second object exerts an oppositely directed force of equal strength on the first object.

Kepler’s Laws:

• First Law is that the path of an object through space is called its orbit.

• The Second Law says that as a planet travels in an elliptical orbit, its distance from the Sun varies. 

  • Speed is faster when it's near the Sun (Perihelion)

  • Speed is slower farther from the Sun (Aphelion)

• Kepler's third law relates the sidereal period of P of an object orbiting the Sun to the semimajor axis 'a' of its orbit.

  • P2 = a3

    • The period P must be measured in years

    • The semimajor axis, a must be measured in astronomical units (AU).

    • This equation applies only to a special case like a planet that orbits the Sun.

• Example: The average distance from Venus to the Sun (a) is 0.72 AU. Use this to determine the sidereal period of Venus.

  • P2 = a3

  • a = 0.72 AU

  • P2 =(0.72)3

  • √P2 = √0.373

  • P = 0.61 years

Eccentricity:

Newton’s Form of Kepler’s Laws:

• p2 =4π2G(m1m2) a3    

  • Where:

    • p = sidereal period in seconds

    • a = semimajor axis in meters

    • m1 = mass of object 1 in kg

    • m2 = mass of object 2 in kg

Example: Lo is one of the four large moons of Jupiter. It orbits at a distance of 421,600 km from the center of Jupiter and has an orbital period of 1.77 days. Determine the combined mass of Jupiter and Lo.

• p2 =4π2G(m1m2) a3    

• m1+m2 =  4π2a3p2G

• a = 421000 x 1000 = 4.216 x 108m

• p = 1.77 x 24 x 60 x 60 s = 1.529 x 105s

• m1+m2 =1.90 x 1027kg

Interplanetary Exploration:

• Cassini Mission:

  • Launched in 1997

  • The science goal was to study Saturn, its complex rings, and moons

  • Its mission ended in 2017 when it intentionally plunged into the atmosphere of Saturn

  • Sent probe to Titan, one of the moons of Saturn

  • Revealed Titan to have rain, seas, and rovers and shrouded in a thick Nitrogen rich atmosphere

  • Studied the composition and formation of Saturn's rings

• Voyager 2 Mission

  • Launched in 1977

  • It is the only spacecraft to study all four of the solar system's giant planets at close range

  • Voyager 2 discovered a 14th moon at Jupiter

  • At Uranus, Voyager 2 discovered 10 new moons and two new rings

  • Voyager 2 was the first human-made object to fly by Neptune

  • At Neptune, Voyager 2 discovered five moons and four rings

Escape Velocity:

• If an object is hurled with enough speed, it can escape a planet altogether

• Vesacpe = 2GMR 

  • Where:

  • Vesacpe: escape velocity

  • M: mass of the planet

  • G: universal gravitational constant

  • R: radius of the planet

Seasons:

• Created by the Earth's tilt of 23.5*

• June -> the Northern Hemisphere "leans into" the Sun and is more directly illuminated

• In December, the Southern Hemisphere leans into the Sun

• In September and March, Earth leans "sideways" - neither into the Sun nor away from it, so the two hemispheres are equally favored with sunshine.

Foucault Pendulum:

• A suspended 60m pendulum with a mass of about 25 kg from the dome of the Pantheon in Paris and started the pendulum swinging evenly.

  • After a few minutes, he noticed that the path of the pendulum changed.

Obliquity:

• The angle Earth's axis is tilted with respect to Earth's orbital plane, known as obliquity

• Over the last million years, obliquity has varied between 22.1 and 24.5 degrees

  • The obliquity change due to the influence of other planets

• Earth's axis is currently tilted by 23.5*, halfway between its extremes

  • This angle is slowly decreasing in a cycle of 41000 years

Moon’s Syncronous Rotation:

• The moon is rotating in such a. way that it takes exactly the same time to rotate around its axis as well as to orbit around the Earth.

Ocean Tides:

• The moon exerts gravitational forces on different points on Earth

  • This causes the Earth to distort slightly into an oblate spheroid

• Facing the Moon: water flows towards it

• Facing opposite the Moon: water produces tides (inertia)

• When Sun and Moon are lined up, tides are greater than normal

Moon and Sun Eclipses:

• Solar Eclipse: occurs when the moon gets in between the Sun and the Earth

  • Umbra: the darkest part of the shadow

  • Penumbra: the lighter region

• Path of Totality: where you can view the total eclipse (duration of totality is 7 mins)

• Lunar Eclipse: occurs when the Moon enters the shadow of Earth

  • Earth’s shadow could cover around 4 Moons

  • Lunar Eclipse is visible to anyone who can see the moon (unlike the Solar)

Equations for Wavelength and Frequency:

• Wavelength (λ): Shortest distance between two equivalent points

• Frequency (F): How many wave cycles pass a point per second

• Wave Speed (V)

  • V = Fλ

  • C = Fλ

  • C = 3 x 108ms-1

The Electromagnetic Spectrum:

• Objects in the universe send out electromagnetic radiation in various ranges

• Low frequency waves are blocked by Earth's ionosphere

Types of Radiation (from low to high frequency):

• radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays

Blackbody Radiation:

• the relationship between an object's temperature, and the wavelength of electromagnetic radiation it emits

Spectroscopy:

• In 1672 Sir Issac Newton did an experiment where he permitted sunlight to pass through a small hole and through a prism 

  • He realized that sunlight (which appears white) is made of  all colors of the rainbow

  • Upon enter the prism, light gets refracted (bent)

    • Not all colors bend the same amount

• How much the light bends depends on the wavelength

• Violet is bent the most - Red the least

• Called dispersion

Photon:

• A discrete bundle of electromagnetic energy

• E=hf

  • Where:

  • E: energy of the photon

  • h: Planck's constant = 6.626 x 10^(−34) Js

  • f: frequency of the wave the photon represents

Doppler Effect:

• the change of the frequency of a wave in relation to an observer who is moving relative to the source of the waves

Redshift and Blueshift:

• the change in the frequency of a light wave depending on whether an object is moving toward or away from us

  • Moving toward blueside: blueshift

  • Moving toward redside: redshift

Astronomical Instruments:

• Telescopes

  • Collect faint light from an astronomical sources

  • Focus all the light into a point or an image

  • Aperature: diameter of the opening through which light travels

Types of Telescopes:

• Refractor: telescope with a long tube and a lens on one side

  • Cons: 

    • The glass or lens must be perfect for the light to pass through

    • Difficult to make large piece of glass without flaws and bubbles in them

    • Chromic Aberration: images appear blurring because each wavelength of light focuses at a slightly different spot

    • The lens needs to be supported only around the edges

    • The force of gravity will cause the lens to sage and distort the path of the light rays

• Reflector: uses a concave mirror as its optical element

  • Pros:

    • Because light is reflected from the surface only, we do not have to worry about flaws and bubbles within the glass

    • Light doesn’t need to pass through the mirror so it can be supported from the back

    • Mirror is more stable

Visible Light Detectors:

• CCD: Astronomers use charge-coupled devices (CCD) to capture the images digitally

  • CCD is a semiconductor divided into an array of small light sensitive squares called pixels

  • Do not capture color information