Lab 02 Worksheet – The Earth And Its Sun

Lab 02 Worksheet – The Earth and Its Sun

Identify the actual assignment question/prompt and clean it: remove any rubric, grading criteria, point allocations, meta-instructions, due dates, repetitive lines, or instructions on submission. Focus on the core task and essential context.

The cleaned assignment instructions are as follows:

Analyze how the length of a shadow can inform us about the seasons and our geographical location on Earth. Conduct an experiment building a simple shadow measurement device to determine the angle of insolation at your current location. Compare your measured angles with theoretical calculations based on the Earth's tilt, the date, and the Earth's position in its orbit. Include calculations of the angle of declination and discussions about the effects of latitude and Earth's axial tilt on shadow length throughout the year.

Paper For Above instruction

The relationship between shadow length and Earth's position in its orbit offers critical insights into seasonal variation and geographical location. Shadows are affected by the angle at which sunlight strikes the Earth's surface, known as the angle of insolation. By examining these shadows at different times of the year and at different latitudes, we can infer information about Earth's axial tilt, the seasons, and the observer's position on the planet.

The experiment begins with constructing a simple shadow measurement device—a makeshift sundial. Using a piece of paper with a small hole (gnomon) and a pencil placed vertically through the center, the height of the pencil and the length of the shadow at noon are measured accurately. The height of the pencil (a) and the length of the shadow (b) are used to calculate the angle of insolation (A) through trigonometric functions, primarily the arccosine of the ratio b/a, which provides the solar elevation angle at solar noon.

Theoretically, the angle of insolation varies depending on the Earth's tilt (approximately 23.5 degrees), the Earth's position in its orbit, and the observer's latitude. During the June solstice, the North Hemisphere experiences maximum tilt toward the sun, resulting in an increased insolation angle and a shorter shadow at noon, especially near the Tropic of Cancer. Conversely, during the December solstice, the South Hemisphere (or the North, depending on location) receives more direct sunlight, with corresponding shadow variations.

To perform precise calculations, the declination of the Sun (the angle between the rays of the Sun and the plane of Earth's equator) is determined through the use of formulas involving the number of days since January 1. The formula sin δ = 0.39795 cos [0.98563 (N - 173)] allows for the calculation of the declination δ, which affects the angle of insolation at any given location and date. Alternatively, the analemma diagram provides a visual means to estimate δ by locating the current date and then determining the corresponding declination angle.

Having measured the shadow length and calculated the insolation angle, comparisons between the measured and theoretical angles help identify the accuracy of the experimental setup and understanding of Earth's orbital mechanics. Differences may arise due to local factors such as atmospheric conditions, measurement inaccuracies, or slight deviations in the device's placement.

Discussion of the results also involves hypothesizing how shadows would change if the experiment were conducted at different latitudes or times of the year. For example, at higher latitudes, shadows tend to be longer during specific seasons, while at equatorial regions, shadows are less variable year-round. During solstices, the shadow length at noon reaches its maximum or minimum depending on the hemisphere and season.

In summary, the examination of shadows provides a tangible demonstration of Earth's axial tilt, orbit around the Sun, and the resulting seasonal variations. It enables observers to connect local phenomena—such as shadow length—with planetary scale processes, deepening understanding of Earth's position in space and the factors that influence climate and daylight.

References

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