**Observing the diameter of celestial objects actually means observing their apparent size. The apparent size ratio is used as a reference for determining the diameter of celestial objects.**

** SCIENCE **– Outer space objects are natural objects in the sky, such as the Sun, Moon, planets, and stars. The apparent diameter of a celestial object is not its actual diameter, but rather how large it appears from Earth. Two celestial objects with different actual diameters may have the same apparent diameter.

In this experiment, we will compare the apparent diameters of the Moon and the Sun and examine the influence of their distances from Earth on their apparent diameters. We will demonstrate and calculate the ratio of the farthest and closest distances of the Moon and the Sun from Earth. We will determine a method using the ratio of apparent diameters at the observed distances to determine the angular diameter of the Moon (apparent diameter measured in radians or degrees). We will also investigate various tools for measuring angles, such as a cross-staff and sextant.

Starting the Experiment This experiment aims to determine the influence of Earth’s distance on the apparent diameter of celestial objects.

**Materials**

- Vernier caliper
- Ruler
- A sheet of yellow paper
- Scissors
- Hole punch with a diameter of 0.63 cm
- White index card
- Insulation tape
- Long ruler
- Thin string, 3 meters long

**Procedure**

- Prepare a data table as shown in the table below.
- Use the vernier caliper to draw a circle with a diameter of 2.5 cm on the yellow paper. Cut out the circle and label it as diameter D.
- Use the hole punch to create a hole in the center of the edge of the index card. The diameter of this hole is 0.63 cm and will be referred to as D.
- Attach the yellow circle to a wall parallel to your eyes. The view from 3 meters away from the wall should be unobstructed. Use insulation tape to attach one end of the string to the center of the circle.
- Insert the other end of the string into the hole in the index card.
- Stand near the wall and hold the bottom of the index card with both hands so that the hole is facing upwards.
- Stand up and stretch both arms forward so that the hole on the index card is centered on the yellow circle.
- Look through the hole on the index card while closing one eye. In the same position, slowly move backward from the yellow circle and let the index card move along the string. Stop when the outer edge of the yellow circle and the edge of the hole on the index card match.
- In this position, continue to hold the index card with one hand stretched forward. Then, pull the stretched string between your open eye and the yellow circle.
- Ask a friend to measure two distances: d₁/d₂, the length of the string from your face to the yellow circle, and d₂, the length of the string from your face to the hole on the index card (see the following image). Record these distances in the data table in columns 4 and 5 for trial 1.

- The comparison between the ratio of diameters and the ratio of distances is:

*D*₁ / D₂ = *d*₁ / d₂

*D*₁ / D₂ = 2,5 cm / 0,63 cm = 4 / 1

Use the measured distances in step 10 to calculate the ratio of distances (d₁)/(d₂) by dividing the numerator by the denominator. Record this distance ratio in the data table in column 7 for trial 1.

- Repeat steps 6 to 11 four more times and record the results for trials 2 to 5.
- Calculate the average of the measured distances for d₁ and d₂. Record the averages in columns 4 and 5 of your data table.
- Calculate the average for (d₁)/(d₂). Record the average in column 7 of your data table.

**Results**

Both the diameter ratio and the distance ratio are the same or approximately 4:1. Since the diameter ratio and the distance ratio are the same, the apparent small hole will have the same size as the yellow circle when viewed from the distance of the circle.

**Why?**

When you move away from the wall, the apparent diameter (the size of an object observed from a certain distance) of the yellow circle decreases. Since the ratio of the diameter of the circle to the hole is 4:1, the yellow circle appears to be the same size as the hole on the index card when the distance ratio from the eye is also 4:1.

The same applies to celestial objects, which are natural objects in the sky such as the Sun and the Moon when viewed from Earth. The ratio of the actual diameter of the Sun to the actual diameter of the Moon is 400:1.