Experiment #2: Determining The Size Of The Moon Reports Example

This experiment, including all measurements, was performed at LOCATION in Denver, Colorado.

The purpose of this experiment is to provide an actual measurement of the angular diameter of the moon while in the zenith and near the horizon. In this report, the measurements will be examined and compared to the theoretical measurements; furthermore, the claim that the size of the moon is larger when it is near the horizon will be tested and the diameter of the moon will be estimated.

Procedure:

For the first part of the experiment, the angular diameter of the moon was measured. Using a ruler, the observer measured the apparent diameter of the moon by extending the arm holding the ruler. The diameter of the moon was estimated by using the thumbnails as markers for both sides of the moon as it appears on the ruler. The measured diameter was recorded.
Next, the distance of the ruler to the eye of the observer was measured by using a two-foot ruler and a measuring tape. The measured distance was recorded.
For the next part of the experiment, the angular diameter of the moon while near the horizon was measured. Again, doing the same measurement procedure in the first part of the experiment, the measurement was performed by the observer using a ruler. The observer extended his arms, and using his thumbnails as markers for both sides of the moon as it appeared on the ruler, the measured diameter of the moon was recorded. In addition, the distance of the ruler from the eyes of the observer was measured.

Data and Calculation

For the first part of the experiment, the measured diameter of the moon was about 5 millimeters while the distance of the ruler to the eyes of the observer was measured to be about 54 centimeter. To solve for the angular diameter of the moon, it is important to note that for small angles, the small angle approximation can be used. The small angle approximation states that:
θ''=206265Dd
(Equation 1)
The θ is the angular diameter in arc-seconds, D is the diameter of the moon, and d is the distance of the ruler to the eyes of the observer. Thus, using (Equation 1), the angular diameter of the moon can be calculated as follows:
θ''=206265Dd
θ''=2062654 mm540 mm=1910''

Thus, the angular diameter of the moon as calculated was 1910ʺ.

For the next part of the experiment, the measurements were as follows: the diameter of the moon is 4 millimeters while the distance between the eyes and the ruler is 540 millimeters. Using (Equation 1) again, the angular diameter was calculated to be 1910ʺ.
For the final part, the calculation of the diameter of the moon involves the distance of the earth to the moon which is 3.8 x 10^5 km. Since the angular diameter of the moon is calculated to be 1910ʺ, the small angle approximation can be used. The calculation for the diameter of the moon is as follows:
θ''=206265Dd
D=(θ''×d)206265=1910''×3.8 ×105 km206265=3519 km

Conclusion and Analysis

The calculated angular diameter of the moon is 1910ʺ which falls within our desired range of 1800 ± 360ʺ. Thus, the first part of the experiment was successful. However, it is important to consider that to perform similar experiments, errors would arise from measurement limitations such as inaccuracy in measuring the diameter of the moon using the ruler.
The angular diameter of the moon while it was near the horizon was shown to be equal to the measured angular diameter when it was not near the horizon. This tells us that the claim that the size of the moon is larger when it is near the horizon is fallacious. Moreover, the claim could be interpreted as a result of illusion probably arising from the idea that objects appear larger because it appears farther. In this case, the moon looks farther when it is in the horizon because our perception is that objects in the horizon is far.
Finally, the calculated diameter of the moon is 3519 km which deviates from its actual diameter which is 3474.8 km by 1.27%. This small error could be from the measurement limitations. Still, the calculated diameter is precise; therefore, the experiment is successful.

Experiment #3: Observing the Moon’s Phases

The observations for this experiment was performed at LOCATION in Denver, Colorado.
The purpose of this experiment is to familiarize to the different phases of the moon, and to associate them to the positions of the Earth, Sun and the Moon.
Procedure:
The experiment was done by observing the moon at a certain location which is at LOCATION. The observations were once a week for four weeks. For each observation, the phase of the moon was drawn and the time of the observation was recorded. Table 1 shows the observation date and time.
Data and Calculation
The moon on February 3 at around 5:56 PM was observed to be fully illuminated; in other words, the moon on February 3 was a full moon. Figure 1 shows the phase of the moon on February 3 and the probable positions of the Earth, Sun and Moon during that day.
Figure 1. The full moon casted no shadow; the earth is between the Sun and the moon.
On February 10, the moon casted shadow. The illuminated part of the moon is only about 60%, or three-fifths of the façade of the moon. Figure 2 shows the phase of the moon as observed and the position of the Earth, Sun and the Moon.
Figure 2. The moon is almost half illuminated. The positions of the Earth, Sun and the Moon is shown.
The moon of February 17 is almost entirely covered in darkness. However, there was still a small portion of the moon that was illuminating as Figure 3 shows.
Figure 3. The shadow on the moon almost engulfed the entire face of the moon.
Lastly, the moon on February 24 has almost 50% illumination, but area of the darker portion is bigger than the glowing region. Figure 4 shows the phase of the moon and the positions of the Earth, Moon and Sun.
Figure 4. The phase of the moon as well as the positions of the Earth, Sun and Moon on February 24.

Conclusion and Analysis

The positions of the Earth, the Moon and the Sun is the reason for the different phases of the moon. The portion of the moon facing the sun is always illuminating due to its reflective property. However, as the moon revolves around the Earth, we see its different phases. In the figures above, the sun is located on the right side; thus, sunlight is coming from the right. Now, the moon is just reflecting the sunlight; hence, the portion of the moon facing the sun is illuminating. Due to the revolution of the moon around the Earth, we see the moon’s different angles composed of the illuminating and the darker portion.