The sun is so big, why does it look about the same size as the moon?
The size of the disk in front of you depends on how big the object is and how far it is from you.
Hold the coin close to your eyes and it will block distant buildings. The sun and moon are similar: their real sizes are very different, but because of the difference in distance, the disks in front of you will be closer. Drag the distance to see two disks of the same scale.
Guess first
If you hold the same coin closer, what will it look like?
Show answer and explanation
bigger — The actual size remains the same, but the viewing angle becomes larger.
Then connect experience and science
Geocentric radii of the sun and moon
The Sun uses the book s₀/Δ and the Moon uses strict arcsine.
s☉ = 959.63″/Δ；sin s☾ = k·6378.14/r
Time and direction parameters
Lunar declination and hour angle are given teaching inputs, not real-time ephemeris.
π = asin(6378.14/r)
center distance factor
Construct the station center vector using the reference ellipsoid observer coordinates, the length of which is q times the distance from the center of the earth.
q²=(cosδ sinH)²+(cosδ cosH−ρcosφ′sinπ)²+(sinδ−ρsinφ′sinπ)²
From distance factor to corner radius
Keep the true radius of the moon unchanged, and recalculate the opening angle after the distance changes.
s′ = asin(sin s / q)
Expand the calculation
ssun = 959.63″/ΔAU π = asin(6378.14/rkm) sMoon = asin(k × 6378.14/rkm) sstand center = asin(sin scenter of earth/q)
s is the angular radius, and the angular diameter must be multiplied by 2. k is the ratio of the radius of the moon and the radius of the earth selected in the course; q is the distance ratio of the center of the station to the center of the earth, which is calculated according to the components of each direction in this lesson.
give it a try
Compare "the moon is closer" and "the moon is further away"; the difference between standing on the surface and imaginary standing at the center of the earth is given below. Do not use this chart to directly predict a solar eclipse.
No need to memorize symbols
- s
- Angular radius in arc seconds; diameter is 2s
- Δ
- Distance between the sun and the earth in AU
- r
- Distance between the center of the Earth and the Moon, in km
- q
- Distance from center of station/distance from center of earth
- k
- Ratio of the Moon's equatorial radius to that of the Earth
Algorithm, accuracy and scope of application
Covers Chapter 55 Sun and Moon angular radii and strict center correction. The original book k=.272481, the local AA+ has been changed to .2725076, please specify the version when switching and comparing. The station center geometry follows the observer vector in Chapter 11/40 and does not need to be replaced by simplified height correction. Geometric directions below the horizon can still be calculated but cannot be directly observed.
my understanding check
If the moon looks bigger, must it be because the moon is expanding?
No, distance will also affect — In this experiment, only the distance is changed, and the radius of the object remains unchanged.
If the two disks are the same size, can they alone indicate that there must be a solar eclipse now?
No, the directions need to overlap — The same apparent size does not mean that the sun and moon coincide in the sky.
What is the difference between the radius of the center of the earth and the center of the station?
different viewing positions — The distance between an observer on the surface and the Moon is different from the distance from the center of the Earth.
How large it appears is a combination of size and distance; get closer and the same object occupies a larger perspective.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 55 chapter