Why does part of the Moon seem to disappear?
We stay on the earth and watch how the bright side of the moon turns towards us little by little as it orbits.
Every day when I look up, the moon is sometimes crescent and sometimes round. Man does not move around the moon: it is the moon that moves around the earth, causing the side illuminated by the sun to face sometimes more, sometimes less, towards the earth. On the left is the position of the sun, earth and moon, and on the right is the moon as we see it from the earth.
Guess first
Is the ordinary crescent moon blocked by the shadow of the earth?
Show answer and explanation
no — Ordinary moon phases come from the change in the proportion of the light-receiving surface facing us as the moon moves around the earth; a lunar eclipse occurs when the earth blocks the sun's light.
Then connect experience and science
Find your Earth first
The earth is in the middle and you stay on the earth. Sunlight shines from the right, illuminating the half of the moon facing the sun. During a new moon, most of the bright side faces away from the Earth.
New Moon: D = 0°, i ≈ 180°
The moon moves sideways to the earth
The moon continues its orbit, reaching a quarter of a circle relative to the sun. People on earth see half bright and half dark, which is called a first quarter moon.
Winding: D = 90°, k ≈ 1/2
The moon moves to the opposite side of the sun
The two sides of the earth are the direction of the sun and the direction of the moon respectively. The light-receiving side faces us, forming a full moon. The diagram does not simulate orbital inclination and lunar eclipse.
Full Moon: D = 180°, i ≈ 0°
Continue around and return to the new moon
After the full moon, the bright area gradually shrinks, passes through the waning quarter, and then returns to the new moon. The change comes from the relative directions of the sun, earth and moon, not from people leaving the earth and changing positions.
k = (1 + cos i)/2 ≈ (1 − cos D)/2
Complete the circle and return to the new moon
The moon completes one revolution relative to the sun, and its bright side faces away from the earth again. Comparing a new moon, a full moon, and two quarter moons, the changes come from opposite directions, rather than the Earth always casting a shadow.
D = 360° in the same direction as 0°; k ≈ 0
Expand the calculation
i ≈ 180° − D k = (1 + cos i)/2 k ≈ (1 − cos D)/2 照明百分比 = 100k
D is the angle around the Earth, and i is the phase angle at the moon. They are not the same angle. The supplementary angle is taken as the far-solar illumination approximation; k only represents the illumination ratio and does not determine the profit and loss direction alone.
give it a try
Drag the moon in orbit, or press "New Moon, First Quarter, Full Moon, Last Quarter" to jump to familiar moon phases. We remain on earth.
No need to memorize symbols
- D
- The orbiting angle of the moon relative to the direction of the sun as seen from the earth, 0° is the new moon
- i
- Phase angle, the vertex is at the center of the moon; this model cos i = −cos D
- k
- Proportion of lunar disk illumination seen from Earth
Algorithm, accuracy and scope of application
The original formula (48.1) calculates the illumination ratio according to the phase angle i. This lesson uses the space relationship between the sun, the earth, and the moon: the sun's rays are approximately parallel, and the moon moves in a circular orbit relative to the sun's direction; derive i=acos(−cos D) from D, and then substitute it into the original formula. This reference diagram with a fixed sun direction describes the relative position and does not mean that the real sun does not move. Excludes small corrections caused by the limited distance between the sun and the moon, the moon's orbital inclination, eclipses, Earth illumination, topography and local horizon. The left and right sides of the bright surface only indicate profit and loss, and do not indicate the actual lunar position angle at any location. No date predictions or precise synodic times.
my understanding check
Where are the observers during this cycle of moon phases?
always on earth — As humans remain on Earth, the moon's orbit changes the proportion of the bright side we see.
When the moon is full, roughly on which side of the Earth is the moon?
The side opposite to the sun — At this time, the light-receiving side of the moon facing the sun is also roughly facing the earth.
Both the upper and lower strings are semi-lit, can they be differentiated by just 50%?
cannot — The illumination proportions are the same, but the moon's position in its orbit and its waxing and waning directions are different.
We stay on the earth, and the moon orbits the earth; how much the light-receiving surface faces us determines the phase of the moon in front of us.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 48 chapter