Geoastronomy

Dan O'Brien, May 14, 2021

Learning activities to understand some of the spatiotemporal effects of the Sun's rays on the Earth - suitable for Project-Based Learning.

Table of Contents

  1. Frames of Reference
    1. Sun Always to the Right
    2. On the Plane of the Ecliptic, Sun Always to the Right
    3. Always Looking South
    4. Polar Axis Frames
    5. Transforming between Surface Cartesian Coordinate Axes
  2. 3D Simulations
    1. Earth 3D Simulation (Using 2D Equations)
    2. Earth 3D Simulation (Using 3D Equations)
    3. Earth 3D Simulation with only One Time Measure
  3. Trigonometry Problems
    1. Finding the Polar Tilt in the Sun's Direction
    2. Finding the Length of the Day
    3. Finding the Length of the Day (Older Version)
    4. Where and When is the Sun Directly Overhead?
    5. Angle between the Sun and the Zenith
    6. Horizontal Sundial with Hour Lines
  4. Sun Hours
    1. Sun Hours (Best Fit)
  5. Map Projection
    1. Terminator Line - Equirectangular Projection
  6. Make Your Own Sundial!
    1. Horizontal/Vertical vs Equatorial Dial Plates
    2. Horizontal or Vertical Dial Plate
    3. Card Stand for Equatorial Sundial
    4. Equatorial Sundial - Dial Plate Parallel to Equator
  7. Photos
    1. Equatorial and Horizontal Sundials in Action - AM
    2. Equatorial and Horizontal Sundials - Setup
    3. Vertical Sundial in Action - AM Only (Shaded After)
    4. Horizontal Sundial (Roughly) Zeroed at 12:16pm Local Time
    5. Equatorial Sundial (Roughly) Zeroed at 12:18pm Local Time
    6. Horizontal & Equatorial Sundials in Action - PM
  8. Worksheets, Lesson Plan & Slide Deck PDFs
    1. Lessons 1-3 Wksht May 2021
    2. Lessons 4-6 Wksht May 2021
    3. Slide Decks
    4. Lessons 1-3 Lesson Plan

1.

Frames of Reference

  • 1. Sun Always to the Right
  • 2. On the Plane of the Ecliptic, Sun Always to the Right
  • 3. Always Looking South
  • 4. Polar Axis Frames
  • 5. Transforming between Surface Cartesian Coordinate Axes

1.1.

Sun Always to the Right

– Dan O'Brien

1.2.

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1.3.

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1.4.

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1.5.

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2.

3D Simulations

  • 1. Earth 3D Simulation (Using 2D Equations)
  • 2. Earth 3D Simulation (Using 3D Equations)
  • 3. Earth 3D Simulation with only One Time Measure

2.1.

Earth 3D Simulation (Using 2D Equations)

– Dan O'Brien

2.2.

–

2.3.

–

3.

Trigonometry Problems

  • 1. Finding the Polar Tilt in the Sun's Direction
  • 2. Finding the Length of the Day
  • 3. Finding the Length of the Day (Older Version)
  • 4. Where and When is the Sun Directly Overhead?
  • 5. Angle between the Sun and the Zenith
  • 6. Horizontal Sundial with Hour Lines

3.1.

Finding the Polar Tilt in the Sun's Direction

Write down an expression for the tilt of the polar axis, θ(T), resolved in the Sun's direction. You can drag the North Pole around the blue circle.
– Dan O'Brien

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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4.

Sun Hours

  • 1. Sun Hours (Best Fit)

4.1.

Sun Hours (Best Fit)

The city data has been imported from Excel...make sure you can do this yourself first.
– Dan O'Brien

5.

Map Projection

  • 1. Terminator Line - Equirectangular Projection

5.1.

Terminator Line - Equirectangular Projection

– Dan O'Brien

6.

Make Your Own Sundial!

  • 1. Horizontal/Vertical vs Equatorial Dial Plates
  • 2. Horizontal or Vertical Dial Plate
  • 3. Card Stand for Equatorial Sundial
  • 4. Equatorial Sundial - Dial Plate Parallel to Equator

6.1.

Horizontal/Vertical vs Equatorial Dial Plates

If you can find β' in terms of β and α, can you find the same thing for a vertical dial plate at the same latitude?
– Dan O'Brien

6.2.

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6.3.

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6.4.

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7.

Photos

  • 1. Equatorial and Horizontal Sundials in Action - AM
  • 2. Equatorial and Horizontal Sundials - Setup
  • 3. Vertical Sundial in Action - AM Only (Shaded After)
  • 4. Horizontal Sundial (Roughly) Zeroed at 12:16pm Local Time
  • 5. Equatorial Sundial (Roughly) Zeroed at 12:18pm Local Time
  • 6. Horizontal & Equatorial Sundials in Action - PM

7.1.

Equatorial and Horizontal Sundials in Action - AM

10:59am local time on phone; 14-min delay based on longitude and Greenwich meridian data so sundials should read 10:45
– Dan O'Brien

7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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8.

Worksheets, Lesson Plan & Slide Deck PDFs

  • 1. Lessons 1-3 Wksht May 2021
  • 2. Lessons 4-6 Wksht May 2021
  • 3. Slide Decks
  • 4. Lessons 1-3 Lesson Plan

8.1.

Lessons 1-3 Wksht May 2021

Lessons 1-3 Wksht May 2021
– Dan O'Brien

8.2.

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8.3.

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8.4.

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Information