Does the same moon have the same address when viewed from the center of the earth and from where you are standing?
When you reach out to look at a nearby object, changing the viewing position will change the direction; in astronomical calculations, you must also write down where to look from.
Planets and Small Solar System Objects
The ephemeris often first tells you the position of celestial objects "as seen from the center of the Earth." But you are standing on the surface of the earth, and the two lines of sight are not exactly the same. This difference is usually more important the closer the celestial body is; the Moon in particular cannot be ignored casually.
Guess first
The ephemeris says "viewed from the center of the earth", does that mean that the direction you see from the ground must be exactly the same?
Show answer and explanation
uncertain — If the starting point of observation differs by one Earth radius, near-celestial objects will have considerable parallax.
Then connect experience and science
Let’s first recognize two observation points:
One is in the center of the earth and the other is on the ground. The geocentric direction of the ephemeris is not a place where your body can really stand. It is a reference point for unified calculations.
Geocenter: center of the earth; station center: observation location
Subtract the observer's position
Subtract the vector from the center of the earth to the observer from the vector from the center of the earth to the celestial body, and you get the vector from the center of the earth to the celestial body.
Station center vector = geocentric celestial body vector − observer vector
The closer the distance, don’t ignore this step
The Moon's parallax is close to 1°; planets are generally much smaller. The small-angle approximation is often sufficient for planets, but the strict version should be used for the moon.
sin π = sin(8.794148″) / Δ
Also make the coordinate system consistent with the units
The same vector subtraction can be done in equatorial or ecliptic coordinates. Zodiacal exercises also change the apparent radius because the observer's distance from the celestial object also changes.
λ, β, radius and local sidereal time must be consistent
Expand the calculation
rstand center = rcenter of earth − r观察者 αstand center = atan2(ystand center,xstand center) δstand center = atan2(zstand center,√(xstand center²+ystand center²))
First unify the unit, origin and coordinate axis of the vector, and then subtract. When the observer vector depends on latitude, altitude and local stars, you cannot just subtract the Earth's radius from the celestial distance.
give it a try
First use the lunar example to change the hour angle, and then change to the Mars example. The reading on the right is the actual angle difference, and the difference in observation points on the left is drawn more clearly.
No need to memorize symbols
- α,δ / α′,δ′
- Center of the earth/station center right ascension and declination
- π
- Equatorial horizon parallax, in degrees
- H
- Local hour angle defined from the center of the Earth, positive to the west
- ρsinφ′,ρcosφ′
- Observer position calculated from reference ellipsoid
- λ′,β′,s′
- Station center yellow longitude, yellow latitude and visual radius
Algorithm, accuracy and scope of application
Implement the 40.6/40.7 three-dimensional vector method in Chapter 40 and verify it with the 40.2/40.3 independent formula; also provide 40.4/40.5 small parallax approximation and printed page 282 ecliptic coordinate/viewing radius correction. Original book 40.a Mars uses given geocentric coordinates and horizon parallax, and the hour angle is preset to −71.2041667° (equivalent to 288.7958333°); TD sidereal time is not miscalculated from UT. Moon is an imaginary original book exercise, α15°, δ5°, π59′. The small parallax constant is 8.794148″ of AA+ (8.794″ in the original book), which is given by sinπ=sinπ☉/Δ; the corresponding tolerance is used for the rounding examples in the verification book. The geographical latitude and height call the original globe function, and the normal line does not pretend to be a real plumb line. Theta of the ecliptic exercise is local sidereal time, not mixed with GMT or longitude. It does not include atmospheric refraction, real-time ephemeris or lunar terrain; it does not realize the inverse solution of all geocentric states from station-centered coordinates.
my understanding check
How to deal with the vector from the center of the earth to the center of the station?
Subtract the observer's position vector — The direction and size of parallax depend on geometric relationships and cannot be uniformly added to constants.
Between the moon and distant planets, which one usually requires more careful treatment of centroidal parallax?
Moon — The Moon is closer and the Earth's radius is larger in proportion to distance.
Is parallax correction the same thing as atmospheric refraction?
no — Parallax changes the starting point of observation; refraction changes the light path. This lesson only does the former.
The coordinates must indicate where to look. First, move from the center of the earth to your current location, and then talk about the direction in front of you.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 40 chapter
Planets and Small Solar System Objects · All interactive courses