Assignment #1

Assignment 1: Local Noon and the Altitude of the Sun

Due: in class on January 17, 2008

1. Determine local noon in Eugene and the highest point in the sky reached by the Sun for a random winter day. First off, what is meant by local noon?
In what direction is the Sun (N, E, S, W) at local noon? ________

To perform this exercise, find a flat spot and place a stick (pole) into the ground vertically. (You could also find a flat spot of ground which already has a vertical stick (pole) for this exercise such as the large sundial in the Memorial Quad across from Lillis Hall. The height of the obelisk in the Memorial Quad is ~10.25 meters.) This vertical stick is referred to as a gnomon (see the Figure below). We will measure the length of the shadow cast by the gnomon to accomplish our goals.

Measure and record the height of the pole, H.

Date:
Gnomon Height, H:

Between the times say, 11:15 am and 1:30 pm, measure the length of the shadow cast by the gnomon. Record your measurements in the table below:

Time

Length, L

11:00  
11:15  
11:30  
11:45  
12:00  
12:15  

Time

Length, L

12:30  
12:45  
1:00  
1:15  
1:30  
1:45  

Time

Length, L

2:00  
2:15  
2:30  
2:45  
3:00  
3:15  

2. Plot your data on the graph below:

At what time is the length of the shadow the smallest? ________ At what time is the Sun the highest in the sky? _________ At what time does the Sun pass through the Celestial Meridian, the semi-circle which connects the north point on the horizon, the zenith, and the south point on the horizon? ________ At what time is local noon? ________ Does local noon lead or lag clock time at this time of year? ________

3. What is the maximum altitude above the horizon reached by the Sun (on the day you performed your observations)? ________ Use the table below to estimate your answer. (For a more precise result note that the Altitude A = tan-1 (H/L), that is, the altitude is the inverse tangent of the ratio (H/L).) The longer the shadow (the smaller the H/L), the lower the altitude of the Sun.

For fun, perform this exercise in the summer and compare your answers to those found here.

H/L

Altitude

0 0
0.1 5.7o
0.2 11.3o
0.3 16.7o
0.4 21.8o
0.5 26.6o

H/L

Altitude

0.6 31.0o
0.7 35.0o
0.8 38.7o
0.9 42.0o
1.0 45o
1.25 51.3o

H/L

Altitude

1.5 56.3o
1.75 60.3o
2 63.4o
2.25 66.0o
2.5 68.2o
2.75 70.0o