The Impact of Perigee and Apogee on the Moon’s Apparent Size: A Comprehensive Guide to Supermoons

Introduction

The apparent size of celestial bodies, including the Moon, can change over time, primarily due to their varying distances from the observer on Earth. This phenomenon is crucial for understanding the supermoon effect, which occurs when the Moon is at perigee or apogee.

The Influence of Distance on Apparent Size

The apparent size of a celestial body (such as the Moon) is inversely proportional to its distance d from the observer. This relationship is given by the formula:

[ varphi approx frac{text{D}}{d} ]

where φ is the angle of view that subtends the diameter D of the Moon. As d increases, φ decreases, meaning that the apparent size of the Moon becomes smaller when it's farther from Earth.

The Concepts of Perigee and Apogee

The Moon's orbit around Earth is not a perfect circle but an ellipse. Therefore, it reaches its closest point (perigee) and farthest point (apogee) from Earth at different times. These distances are crucial for determining the Moon's apparent size.

Perigee (perigee lunar, periselene: Greek: γ?ω γ? Earth and περ? peri around) occurs when the Moon is at its closest point to Earth, approximately 363,104 km from the center of the Earth. At this point, the Moon appears larger and is often referred to as a supermoon.

Apogee (apogee lunar, aposelene: Greek: γ?ω γ? Earth and ?π? apo from) occurs when the Moon is at its farthest point from Earth, approximately 405,696 km. At this point, the Moon appears smaller and is called a micromoon.

The Calculation of Apparent Size

To understand the apparent size more precisely, let's consider the mathematical explanation. If D ? d, we can approximate the relationship with the tangent function's Maclaurin series.

[ tan(varphi) approx frac{D}{d} approx 0 implies varphi approx 0 ]

The tangent of an angle can be linearized around 0 using the Maclaurin series:

[ tan(varphi) tan(0) frac{d}{d varphi} tan(varphi) bigg|_{varphi0} varphi mathcal{O}(varphi^2) ]

[ tan(0) frac{1}{cos^2(0)} varphi mathcal{O}(varphi^2) ]

[ 0 1 varphi mathcal{O}(varphi^2) approx varphi quad Box ]

Thus, when the Moon is at perigee, its apparent size is larger due to its proximity to Earth. Conversely, when it is at apogee, its apparent size is smaller.

Conclusion

Understanding the relationship between the Moon's distance (perigee and apogee) and its apparent size is essential for appreciating astronomical phenomena. During a supermoon, the Moon's larger apparent size can be a spectacular sight, drawing attention to the beautiful and complex nature of the celestial bodies.

References

[1] Time and Date: Moon Phases