Why do the four little dots next to Jupiter line up differently after a while?
Enter the same time, first calculate the true position of the satellite, and then see where it falls next to the planet.
Planets and Small Solar System Objects
There are often several bright spots on both sides of Jupiter in a telescope. They are not stuck on a line, but move on a three-dimensional orbit; when you look at them, they form an ever-changing arrangement in front of you.
Guess first
If the satellite looks close to the planet's disk in the photo, does it mean it must be in front of the planet?
Show answer and explanation
Not necessarily, maybe later — Two-dimensional projection does not provide complete depth and must be judged in conjunction with the Z direction.
Then connect experience and science
First, consider the center of the planet as the zero point
The transverse X is positive toward the west, and the longitudinal Y is along the north pole of the planet; Z is the depth, and negative values are closer to the earth. Not the celestial right ascension and declination.
Unit: planetary equatorial radius
First, calculate how long it has taken light to reach the earth.
What we see is the earlier light. The planetary distance and light travel time are first iterated, and then the satellite phase is calculated at the corresponding moment.
Luminous time = TD − planetary light travel time
Satellites interact with each other and their orbits are not fixed rings
Orbital theory includes periodic perturbations, eccentricities and tilts, followed by coordinate rotation to the Earth's line of sight and corrections for differential light travel and perspective.
Periodic term → 3D coordinate → apparent projection
The front and back and lighting determine whether it is blocked or not.
Looking from the direction of the Earth, the center enters and exits the disk to distinguish between eclipses and occultations; looking again from the direction of the Sun, distinguishes eclipses from occultations. The precise contact time is not sought here.
Separate judgments from the earth's perspective and the sun's perspective
First select the low-precision or E5 route, and then calculate the lighting time, each satellite orbit and apparent projection. The coordinate unit is the equatorial radius of Jupiter; the Earth's projection determines transit/occultation, and the Sun's projection determines eclipse/shadow. They cannot share the same set of criteria.
give it a try
Look at all the satellites first, and then narrow the field of view to near the disk. Hollow points indicate that the center of the model's judgment is blocked or in the shadow, and the position is still retained for learning; it may not be visible in reality.
No need to memorize symbols
- X / Y
- West/Planetary north projection, in units of planetary equatorial radius
- Z
- Depth; negative values are closer to the observer than the center of the planet
- When light travels
- Propagation time from planet to observation point
- Ling / cover / food / shadow Ling
- Different states of center projection in the direction of the earth or the sun
Algorithm, accuracy and scope of application
The two routes of Chapter 44 are fully realized: low-precision uses Chapter 43 of low-precision Earth/Jupiter geometry and satellite maximum period correction; high-precision E5 uses 151 longitudes, 35 latitudes and 44 radius period coefficients in this chapter. First, the B1950 angular variable is used to find the disturbance, then add precession and rotate through Jupiter's orbit/equator to the observation time, date, ecliptic and earth's line of sight. Numerical coefficient facts are checked group-by-group with the original book and AA+, and summations and rotations are organized in a universal vector pipeline without using fixed precomputed satellite tables. Planet/Earth positions are from Chapter 32 truncated VSOP87, not full VSOP87. High-precision includes differential light travel time, perspective and Earth/Sun dual-view center classification, while low-precision does not provide event classification. No contact time root finding, finite satellite size, mutual eclipse and mutual occultation, station center correction or complete modern satellite numerical theory were performed.
my understanding check
With the same abscissa on the map, can we directly determine whether the satellite is in front or behind the planet?
No, depth Z is required — The front and rear positions determine whether it is a forward or a cover, and looking at X/Y alone is not enough.
What are the units of X and Y in the picture?
planet equatorial radius — They are projected coordinates relative to the center of the planet's disk.
Is the central state here equivalent to precise contact time forecast?
not equal to — This lesson only classifies the relationship between satellite centers and planetary projections, and does not cover all events such as limited satellite disc contact, mutual eclipse and mutual occultation.
First calculate the three-dimensional position and light travel time, and then project from the two directions of the earth and the sun; only the arrangement of the bright spots has physical meaning.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 44 chapter
Planets and Small Solar System Objects · All interactive courses