Scholars Online Astronomy - Chapter 2: 5-8 Knowing the Heavens

Homework

Reading Preparation
- Study Guide/Reading Notes
Key Formulae to Know
WebLecture
Study Activity
Chat Preparation Activities
Chapter Quiz
Lab Work

Reading Preparation

Reading: Astronomy, Chapter 2: Knowing the Heavens, sections 5-8

Study Notes: notes on your assigned reading from the text

Now we look at some of the consequences of the earth's position and orientation with respect to the sun and moon. Length of day changes as the earth moves around the sun because of the "tilt" of the earth's axis to the plane of its orbit. This changes the amount of sunlight reaching a given square foot of the earth's surface, creating differences in the amount of energy available to heat the atmosphere and oceans, or provide light for photosynthesis. The tilt and annual motion of the earth around the sun give earth its climates, seasons, and calendar.

Section 5: The earth's axis is tilted with respect to the plane of its orbit; this causes sunlight to fall unevenly on the north and south hemispheres at positions in the orbit. The difference in the amount of energy a given area receives gives earth its seasons.
The earth varies in distance from 91 million miles to 93 million miles over the course of its revolution around its slightly elliptical orbit, but this difference, less than 2% of the total distance from the sun, is not enough to cause the change in seasons, and in fact, the earth is closest to the sun aroun January 2, in the middle of the northern hemisphere's winter.
Section 6: Interaction with the moon's gravitational field causes the earth to wobble on its axis, slowly changing the orientation of the axes in space (precession). Over time, this "wobble" points the earth's north pole at different parts of the sky, so that 3000 years ago, the north celestial pole was close to Thuban in the constellation Draco, where it is now closer to Polaris.
Section 7: Because the earth revolves around the sun on an elliptical orbit, it speeds up when we are closer to the sun and slows down slightly when we are further away. Note that the winter from Dec 21 to March 20 has only 89 days, while the summer has 93 days. Since the sun doesn't move at a constant speed in the sky, we must use other periodic events (such as atomic vibrations) as time keepers. Civil time also allows people to coordinate clocks instead of recognizing slight differences in the sun's position.
Section 8: The calendar is based on increasingly accurate observations of the position of the sun and stars. We make adjustments for the slightly less than quarter day extra beyond 365 complet days for the earth's revolution by adding a day to February every four years, but skipping centuries divisibly by 400. Even so, the US Naval station must add a second to its clock every once in awhile to keep the time coordinated with solar positions.
Box 2-2: Sidereal time is the Right Ascension of stars on the meridian, a line projected across the sky from the observer's north point to the point directly overhead (zenith) and then down to his or her south point.

Key Formulae to Know

Time and Right Ascension:

1 day = 24 hours = 360° rotation of celestial sphere.
1 hour rotation = 360/24 = 15° rotation celestial sphere.
1° rotation = (24 hrs * 60 min) / 360 = 4 minutes of time.
1 sidereal day = 23h 56m 4.091s
Time and Solar Declination:

Sun's position March 21: 0°.
Sun's position June 20: 23.5° (north).
Difference in days: 91
Average change per day: 0.258°

Web Lecture

Read the following weblecture before chat: The Earth in Space

Study Activity

Planetarium program exercise

The following picture set is based on observing projects #63-64-65 on p. 43 and was made using Stellarium on my Mac. You should try to complete the observing projects on your own, but if you are unable to create similar views using your planetarium program, you can use the pictures below to make some observations.

Note: Because of the Earth's annual motion, this discussion and its pictions showing the position of the sun against the background sky is accurate within one day of 22 September for any year).

Sunrise, looking east, 22 Sept 2021

Look carefully at this picture of the sunrise. You should be able to see the celestial equator grid faintly in the background, and the ecliptic. Since the sun is at the autumnal equinox, the sun is near the position where the two lines (ecliptic and celestial equator) cross.

The sun at noon....notice the faint celestial coordinate system markings.

The sun at noon -- but with the sky "dark" so that you can see the background stars.

Notice the position of the sun on the ecliptic (orange line), and at 0 ° declination. The blue line is the celestial equator, and the sun is at 12hr RA, between 10hr and 14hr. Since it is noon, the 12hr RA line corresponds to the local celestial meridian -- and to local sidereal time.

The sun at noon 22 Sept 2021, with background constellations.

This shows the same picture, but with the constellations drawn in. We say that "the sun is in Virgo", because it shows up against the background constellation Virgo, moving out of Leo and toward Libra. None of these constellations are visible for observing, since the sun's light is too bright.

Sunset 22 September 2021

This shows the sun at sunset, with the sky dark so that we can determine the other nearby objects. Mercury lies to the east of the sun in the sky at this time, and so sets later than the sun. Since it is below the ecliptic, it will be very near the horizon at sunset, and very difficult to see. The best time to find Mercury is at maximum elongation east (after sunset) or west (before sunrise), when it is north of the ecliptic.

Further to the east, you can see Venus, in the constellation Libra. It is bright enough to be visible in the SW sky at sunset and for about an hour after, before it, too, follows the sun below the horizon.

The northern sky, 22 September 2022 as seen from Seattle (latitude 47°).

This shows the sky looking north. The lines of RA converge on the celestial north pole, 47° above the north point. Stars that are within 47 ° of the pole at 90° (in other words, with a declination of 90-47 = 43° or more) will be circumpolar, and always be above the horizon (although not visible during daylight hours).

Notes on Working with a Planetarium Program

Mercator Projection, 22 September 2022.

Study the map above. You are looking S on September 22, 2022, around 9 pm PDT, from Seattle, WA (47°N latitude, 122° W longitude).
Find the green line: this is the horizon. It is marked with the directional points; S is to the left and NW to the right of this segment of the sky. Stars below the green line have already set.
Find the orange line (passing through the Sun, near Spica, and through Antares). This is the ecliptic. The sun will move eastward along this path over the next months. What star does it pass near id mid-November? in August?
Find the blue line (passing through the Sun, the West pont on the horizon, and going up near Altair). This is the celestial equator. Stars above and to the right have north declinations, stars down and to the left have south declinations. Note that the path of the sun for the next six months lies in the south declination.
Find the planets -- this map shows Jupiter and Saturn due south, with Venus, Mars, and Mercury east of the sun. Are any of these planets planets at this time (above the horizon line? What about the Moon and Uranus? Which coordinate circle are they near, the ecliptic or the celestial equator?
Try to create the same type of projection for today's date (whatever day you attempt this exercise) in your Stellarium program. You should use your own location. The sun should be near or below the western horizon, depending on your latitude. Where are the planets? are any visible? Where is the moon? Can you explain why the sun is in nearly the same part of the sky as it was on this date in 2009, but the Moon and planets may have changed position?

UNL Tools Exercises

Interactives: Work through the exercises unders the Seasons.
Class Action: Test your control of the concepts by answering the Questions for the Basic Motions and Ancient Astronomy module.
Labs:
- Read through the materials for the Motions of the Sun, then use the simulator to see how the sun's position changes. Set the position for your latitude. How high is the sun above your south horizon at solar noon today?
- Under The Rotating Sky: You might want to finish the sidereal time and hour angle demo to make sure that you know how sidereal time works.

Optional websites:

Use the links and information at the US Naval Observatory Astronomical Applications page to determine the time of sunrise, sunset, moonrise, moonset, and the phase of the moon for your location.

If you are still having problems envisioning coordinate systems, checkout the Thinkquest Project Coordinate System Unit. Thinkquest is a set of projects by students, for students.

Chat Preparation Activities

Essay question: The Moodle forum for the session will assign a specific study question for you to prepare for chat. You need to read this question and post your answer before chat starts for this session.
Go over the list of Key Words and Key Ideas at the end of the chapter. If you don't remember the definition of the key word, review its use (the page number on which it is explained is given).
Read through the Review Questions and be prepared to discuss them in class. If any of them confuses you, ask about it!
Mastery Exercise: The Moodle Mastery exercise for the chapter will contain sections related to our chat topic. Try to complete these before the chat starts, so that you can ask questions.

Chapter Quiz

Required: Complete the Mastery exercise with a passing score of 85% or better.
Go to the Moodle and take the quiz for this chapter to see how much you have learned about observational astronomy!

Lab Work

Read through the lab for this week; bring questions to chat on any aspect of the lab, whether you intend not perform it or not. If you decide to perform the lab, be sure to submit your report by the posted due date.

Lab instructions: Basic Observing: Coordination Systems

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