At this moment when you see the planet, is it still in the same position just now?
It takes time for light to travel to the earth, and the telescope receives the news that started earlier.
Planets and Small Solar System Objects
Taking a picture of a distant planet does not show its "immediate" position. The computer must first estimate how long the light has traveled, and then go back to that time to find the position of the planet until the distances calculated before and after are consistent with each other.
Guess first
Light takes time to travel, so does the position of the planet you see correspond to that?
Show answer and explanation
The position of light as it leaves the planet — Propagation time must be considered together with planetary motion.
Then connect experience and science
First change from the heliocentric position to the direction of the earth
Subtract the heliocentric vectors of the planet and the Earth to get the direction from the Earth. The time spent on the road alone is not taken into consideration at this point.
rgeocenter = rplanet − rearth
What we see is the planet as the light leaves it
First guess the light travel time, then find the past planet positions, and recalculate the distance until the light travel time is stable. The Earth's position when receiving light.
τ=0.0057755183Δ day; t transmitting=t receiving−τ
Reprocessing observers in motion
Light aberration is not light time. Here, we add annual optical aberration according to 23.2 of the original book, and then make small corrections to FK5.
Light travel time and light travel difference are calculated separately
Finally converted to the same day apparent equatorial coordinates
Add nutation and use the angle of intersection to change longitude and latitude into right ascension and declination. This is still the geocentric position, without location, atmosphere or terrain.
Add Δψ; use ε to transform to equatorial coordinates
Expand the calculation
rcenter of earth = rplanet(t−τ) − rEarth(t) Δ = |rcenter of earth| τ新 = 0.0057755183 × Δ λ = atan2(y,x)；β = atan2(z,√(x²+y²))
The vector components x, y, z and Δ are represented by AU, and τ is represented by day. The earth is fixed at the receiving time and repeatedly updates the planet's luminous time; this chain only reaches the geometric/light travel time position, and the apparent position needs subsequent correction.
give it a try
Use the Venus book example to compare "geometric position", "light travel time correction" and "complete chapter apparent position". Do not treat the results of this lesson as local horizon coordinates.
No need to memorize symbols
- Δ
- Distance from the center of the earth AU
- τ
- When light travels, day
- λ / β
- Earth's Yellow Longitude and Yellow Latitude
- α / δ
- Geocentric right ascension and declination
Algorithm, accuracy and scope of application
Realize the first route and Example 33.a of Chapter 33 of the original book: Appendix III planet/Earth heliocentric coordinate subtraction; maintain the earth position at the time of reception and the planet position at the time of iterative transmission; calculate the annual optical aberration using the earth's true longitude + 180° according to 23.2, and then perform the 32.3 FK5 correction, nutation and equatorial conversion of the true ecliptic angle. Rely on the complete table 22.A nutation function of the existing nutation or solar-coordinates extension package, and no longer copy another set of models. The final values of the original Venus book on December 20, 1992 are α≈316.17291° and δ≈−18.88801°. The intermediate quantities in the book are rounded, so the corresponding tolerances are retained in the calculation. Reference date-mean dynamical ecliptic to FK5 day true equator; not local apparent bearing or modern complete VSOP87. The Earth itself has no geocentric direction for the purposes of this lesson and explicitly rejects this input.
my understanding check
What to do first to calculate the direction to the earth?
Planet vector minus Earth vector — Space vectors are subtracted to preserve direction.
Are light travel time correction and annual light travel aberration the same thing?
no — The former is due to the different starting times of light, and the latter is related to the combination of the observer's movement and the speed of light.
Is geocentric right ascension and declination the direction on your compass?
no — Location, earth rotation and horizon coordinate conversion are also required.
Light brings news from the past; only by separating the departure time, receiving position and coordinate correction can the direction ahead be calculated.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 33 chapter
Planets and Small Solar System Objects · All interactive courses