The Sun and Moon appear roughly the same size in the sky. But How Much Bigger Is The Sun Compared To Earth? A simple observation of the Moon’s phases can reveal a surprising amount about the Sun’s size and distance.
Understanding the Moon’s Phases
The Moon’s monthly cycle of phases, from crescent to full and back again, happens because of the changing relationship between the half of the Moon lit by the Sun and the half we can see from Earth.
When the Moon is between the Sun and Earth (New Moon), its lit side faces away from us, making it invisible. When the Moon is on the opposite side of Earth from the Sun (Full Moon), its entire near side is illuminated. Between these extremes, we see varying portions of the lit half, creating the familiar waxing and waning phases.
Figure 1: The Moon’s phases, assuming the Sun is much further than the Moon. The New Moon occurs when the Moon is between the Earth and Sun, while the Full Moon occurs when the Earth is between the Sun and Moon.
First Quarter vs. Half Lit: The Key to the Sun’s Size
A crucial observation is that the “First Quarter” Moon, occurring about a week after the New Moon, coincides with the Moon being half lit. Why is this significant?
“First Quarter” refers to the Moon completing one-quarter of its cycle around the Earth, placing it roughly 90 degrees away from the Sun in the sky. “Half lit” refers to the appearance of the Moon, with half of its visible surface illuminated.
If the Sun were relatively close to Earth, these two events would not occur simultaneously. A nearby Sun would illuminate more than half of the Moon’s near side when the Moon is at the First Quarter position in its orbit.
Figure 2: Top: With a nearby Sun, the Moon would be more than half lit at First Quarter. Bottom: With a distant Sun, the Moon is half lit at First Quarter.
The fact that the “First Quarter” and “Half Lit” Moon occur at nearly the same time indicates that the Sun must be much further away than the Moon. This, in turn, implies that the Sun must be significantly larger than the Earth.
Estimating the Sun’s Size and Distance
By observing that the First Quarter and Half Lit Moon coincide within a day or so, we can deduce that the Sun is at least several times further away than the Moon. Since the Sun and Moon appear the same size in the sky, this greater distance means the Sun must also be proportionally larger.
Figure 3: The further the Sun, the closer the Half Lit Moon is to its First Quarter position.
Further observations, such as measuring the precise angle between the Sun and Moon when the Moon is half lit, allow for a more accurate estimate. Using a simple L-shaped tool to verify a 90-degree angle between the Sun and a half-lit Moon confirms the Sun’s vast distance and size.
Figure 4: Confirming the 90-degree angle between the Sun and a half-lit Moon with a simple tool.
Conclusion: The Sun is Enormous
While these simple methods don’t provide exact figures, they demonstrate conclusively that the Sun is much larger than the Earth and vastly further away than the Moon. The observation of the Moon’s phases, coupled with basic geometry, provides compelling evidence of the Sun’s immense scale compared to our planet. The Sun’s diameter is, in fact, about 109 times that of Earth.
