Earth and the sky – solar altitude by latitude and season
PhysicsGravitation & AstronomyAges 15–16
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Gravitation & Astronomy
Earth's axis is tilted 23.5°, so the Sun's noon altitude and the length of day change with latitude and with the day of the year. Choose an observing location and a date to see the Sun's path across the sky, and see why regions near the tropics have two days a year when the Sun passes through the zenith while polar regions have midnight sun or polar night. A 3D view shows the tilted Earth, the observer standing on the horizon plane and the angle between the noon sunlight and the horizon, with the same data as the 2D view.
Lesson: Earth and the sky
What it shows
Earth's axis is tilted about 23.4° to its orbit, so the Sun's declination δ swings between +23.4° and −23.4° during the year. At latitude φ the Sun's altitude at local noon is h = 90° − |φ − δ|, and day length follows from the sunrise hour angle, cos H₀ = −tan φ·tan δ. When no sunrise solution exists, the Sun never sets or never rises: midnight sun or polar night. Seasons come from this tilt, which changes both the angle of sunlight and the hours of daylight, not from Earth's distance to the Sun.
How to use
Press Summer solstice, then move the Latitude slider from the equator towards the pole and record the noon altitude and day length shown beside the sky dome. Repeat with Winter solstice. Next choose one latitude, for example with the Honolulu or Caracas button, and drag Day through the year to find the dates when the Sun passes through the zenith. Switch to 3D to see the tilted Earth, the horizon plane and the noon sunlight that form the angle h.
Parameters you can change
- Observer's latitude -66–80 °
- Day of the year 1–365
- Show the Sun's path
Questions to explore
- Around the March equinox, what noon altitude and day length does the simulation give at latitude 21° N?
- Why does day length change very little through the year near the equator but a lot at high latitudes?
- At which latitude is the Sun directly overhead at noon on the June solstice, and why?
