The two planets "joined", did they collide in the sky?
Seen from the Earth, two bright spots passing through the same direction line may still be separated up and down.
Planets and Small Solar System Objects
The news says Mercury conjunct Venus. If you look up for them, you may still see two separate bright spots. To "combine", you must first explain which coordinates are the same: In this lesson, we use the original ephemeris to find the moment when the right ascension is the same, and then see how much difference in declination they have.
Guess first
Does "the same right ascension" ensure that two celestial bodies completely coincide in the sky?
Show answer and explanation
No, it may be worse in declination — There can be different declinations on the same right ascension line, just like different latitude positions on the same longitude line.
Then connect experience and science
The same right ascension can still be separated up and down
Viewed from the Earth, two bright spots can pass through the same right ascension line, but one is to the north and the other to the south. They don't necessarily coincide.
Right ascension combined: Δα = 0
Use the original book’s ephemeris to track changes before and after
Choose from the Mercury-Venus five-day data, or the Vesta and sidereal exercises. Move the moment and observe the right ascension difference from negative to positive.
Interpolate Δα by 3 or 5 points
Find the instant when the difference is zero
The algorithm finds roots within the central half table interval; the resulting declination difference is then interpolated from the same set of samples.
Δα(n₀)=0; Δδ(n₀) gives the north-south difference
Don't interpret combination as collision
Conjunction is only a coordinate relationship as seen from the Earth; actual distances are not given in this lesson. The conjunction of right ascension does not necessarily coincide with the minimum angular separation.
Same right ascension ≠ same point ≠ closest approach
First expand the right ascension difference into a continuous quantity, and then use the selected three-point or five-point polynomial to find the zero point n₀; bring the same n₀ back to the declination difference. The zero point answer is the same as the right ascension, and the declination difference answers how far away it is.
give it a try
Click "Moment of Conjunction" to view the Mercury-Venus results in the original book; after switching to Example 1, drag the moment to see the right ascension direction of Vesta passing through the star.
No need to memorize symbols
- α / δ
- Right ascension / declination, the algorithm internally uses degrees
- n
- Relative central time, unit is table interval; 1 day for Mercury, 5 days for Vesta
- Δα / Δδ
- The coordinate difference of the first celestial body minus the second celestial body
- TD
- Original book kinetic time markers, not converted to civil time
Algorithm, accuracy and scope of application
Meeus 2nd Edition, Chapter 18, Example 18.a (printed pp. 117–118) and Vesta and Beta Libra Exercise (p. 119). Using the ephemeris coordinates of the original page, the right ascension is first continuous, and the three-point/five-point Lagrangian interpolation is equivalent to the difference form in Chapter 3; the interval is divided into two to find the zero point of Δα, and then the declination is interpolated. Mercury Center 1991-08-07 0TD, Vesta Center 1996-02-17 0TD; sidereal coordinates include self-corrections for the epochs given in the book. Smoothed ephemeris only applies to short intervals given, and does not calculate planetary positions, ecliptic conjunctions, or moments of minimum angular distance for any calendar year. All coordinates must have the same reference point.
my understanding check
When finding right ascension conjunction in this lesson, which difference is zero?
Right ascension difference — The definition is that the right ascension is the same, and other quantities are not required to be zero at the same time.
In this example, when Mercury and Venus are conjunct, they are still about 2.14° apart. Is this reasonable?
Reasonable — Their right ascension is the same, but their declination still differs by about 2.14°.
Is the time of conjunction necessarily the time when the angular distance between the two stars is smallest?
uncertain — The two coordinates change together with time. The same coordinates and the minimum angular distance are different conditions.
Let’s first clarify “which coordinates are the same”. Conjunction does not mean collision, nor does it necessarily appear to be the closest moment.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 18 chapter
Planets and Small Solar System Objects · All interactive courses