Physics 5 The Universe, with Prof. D. Tytler Spring 2000

Solutions to homework 1

 

  1. Most stars which you see at night are 20-200 million AU away.
    How large would the Earth's orbital diameter appear (what angle) from these two distances?

    The Earth's orbital radius is 1 A.U. by definition. For small angles, we may approximate the two angles (in radians) as: 2AU/(20 million AU) = .0000001 radian = .02 arc-sec, and 2 AU/(200 million AU) = .00000001 = .002 arc-seconds, respectively. These are just ratios of 2 sides of a triangle, the short side (numerator) formed by a line connecting the Earth and Sun (an A.U.) and the long side formed by a line connecting the Earth and star distance, which is nearly the same as the 3rd triangle side formed by a line connecting the Sun and the distant star since the angle is so small.

Once you have an angle, conversion to arc-seconds from radians is just a matter of multiplying by a given constant, given as 206265.

See pages 12, 13, 18, and p. 456-8.

2. List 4 motions in astronomy, in increasing order of time period (time for one complete cycle of motion).

The clue in the question is the work PERIOD.
This implies something which repeats itself again and again, like an orbit or a
spin. The stars do have orbits, around the galaxy, which you could use.
The intent of the question is to look through the book.


  1. motion of rotating Earth (about 24 hours)
  2. motion of revolving moon (about 1 month)
  3. motion of revolving Earth (about 1 year)
  4. motion of precessing (wobbling) of Earth's axis (about 26,000 years)
  5. motion of Sun revolving around Galaxy center (about 200 million years)


3. Why are constellations so irregularly shaped?

See figure 2-2 p.27.
Historical reasons. Ancient astronomers (6000 yr ago) grouped bright stars
into constellations. Such stars are distributed somewhat randomly.
In the last 100 years we have put straight line boundaries on these constellations,
to ensure that each part of the sky was in one constellation.
Connecting and creating borders around randomly spaced objects creates
irregular shapes.


4. Define and differentiate between the Ecliptic and the Zodiac.

The Ecliptic is the apparent path of the Sun throughout the year.
It is a circle on the sky. Zodiac is the band of 12 constellations (all well known, your astrological "sign" is named after one of these), which together contain the
ecliptic. The orbits of the planets lie in the zodiac constellations.

5. Define, and differentiate between, planetary conjunctions and oppositions.

Include diagram(s).

See p. 77, fig 4-6.
Both are when one planet, the Earth and the sun are nearly aligned
(never happens exactly because orbits has slight tilts). Conjunction is the order: Earth -- sun -- planet. Opposition is the order: Sun -- Earth -- planet. Planets are easiest to see when at opposition: nearest to Earth, and highest in the sky at midnight, because opposite the sun.

6. How is modern astronomy different than other sciences? How is it different from
astrology? One key difference for each is enough.

Different from most sciences:

1) Not much experimentation in astronomy: we can not make a star, or cut up a planet to look inside.
2) Astronomy deals with the largest sizes, and whole history of the universe.

Different from astrology: Both are equally ancient.
Astrology is not a science, it does not use experiments to test ideas and
build a set of proven theories, and it does not seek to understand why,
but rather is a set of traditional rules and beliefs.

7. What information is needed to get the distance to a star using parallax?

Take two photos of the sky, several months apart. Measure the angle by which the star moves. The angle is obtained from the distance on the photo, once the camera
has been calibrated (e.g. photo of a ruler at a known distance). Also need to know 1 AU.


8. The smallest angle which can be measured using modern telescopes on the Earth is 0.001 arc-seconds. At what distance could we just detect the parallactic (due to parallax) motion of a star?

Same concept as Question 1, but now we are given the angle, and need to find
the distance. We can use proportion. Diameter (not radius) of orbit = 2 AU. One may use a formula from the text (see Q1), but understanding proportions is easier:
At 1 pc, 1 AU will give an angle of 1 arc-seconds.
At 1 pc, 2 AU will give an angle of 2 arc-seconds.
At X pc, 2 AU will give an angle of 0.001 arc-seconds. This angle is 2000 times
smaller, so X must be 2000 pc.

9. Make a list of all the key words which we have used so far, and give the definition of each.

See text and the text's website. These terms will reoccur, so
learn them well. Below are the words used so far:

Astronomy: Study of everything in the Universe, its origin, contents, and evolution

Astrology: The use of ancient rules to predict the future of human

Spectroscopy: The study of spectra and spectral lines

Cosmology: The study of the structure and evolution of the Universe

Constellation: A configuration of stars in the same region of the sky

Galaxies: groups of millions of stars, our solar system is on the edge of Milky Way Galaxy

Milky Way: Our Galaxy; the band of faint stars seen from the Earth in the plane of our Galaxy’s disk

Polaris: The pole star

Astronomical Unit: 1 AU = the average distance between the Earth and the Sun (93 million miles)

Telescopes: Tools of the astronomy trade, a way to collect light to study outer space

Theory: A hypothesis that has withstood experimental or observational tests

Ecliptic: The apparent annual path of the Sun on the celestial sphere

Zodiac: A band of 12 constellations around the sky, centered on the ecliptic

Conjunction: The geometric arrangement of a planet in the same part of sky as the Sun

Opposition: The configuration of a planet when it is at an elongation of 180 degrees and thus appears opposite the Sun in the sky

Precession: A slow, conical motion of the Earth’s axis of rotation caused by the gravitational pull of the Moon and the Sun on the Earth’s equatorial bulge

Sidereal Month: The period of the Moon’s revolution about the Earth with respect to the stars

Synodic Month: The period of revolution of the Moon with respect to the Sun or the length of one cycle of lunar phases also called the lunar month

Eclipse: The cutting off part or all the light from one celestial object by another

Solar Eclipse: An eclipse of the Sun by the Moon

Lunar Eclipse: An eclipse of the Moon by the Earth; a passage of the Moon through the Earth’s shadow

Ptolemaic system: The definitive version of the geocentric cosmogony of ancient Greece

Epicycle: A moving circle in the Ptolemaic system about which a planet revolves

Deferent: A stationary circle in the Ptolemaic system along which another circle moves, carrying a planet, of the Sun, or the Moon

Geocentric Theory: An Earth-centered theory of the Universe

Heliocentric Theory: A Sun-centered theory of the Universe

Hypothesis: An idea or collection of ideas that seems to explain a specified phenomenon

Arc Minute: One-sixtieth of a degree

Arc Second: One-sixtieth of an arc minute

Light year: The distance light travels in vacuum in one year

Par Second: A unit of distance, 3.26 light years

Lunar Phases: The appearances of the illuminated areas of the Moon as seen by Earth

Ellipse: A conic section obtained by cutting completely through a circular cone with a plane

Parallax: The apparent displacement of an object due to the motion of the observer

Retrograde Motion: The apparent westward motion of a planet with respect to background stars