Is the day when the earth is closest to the sun the hottest day?
Perihelion and aphelion refer to distance extremes and cannot directly replace seasons or temperatures.
Planets and Small Solar System Objects
The planet's orbit is not a perfect circle, so its distance from the sun varies. We first use the formula in the original book to find the closest perihelion or aphelion in a given year, and then look at the correction of the earth's influence by the moon, and the extreme value refinement of the distance curve.
Guess first
Is it a contradiction that the Earth passes perihelion during the winter in the Northern Hemisphere?
Show answer and explanation
No contradiction, seasons are not only determined by distance — The tilt of the earth's axis determines the distribution of sunlight in the northern and southern hemispheres, and perihelion is not the hottest day in the world.
Then connect experience and science
First distinguish between distance and season
Perihelion is the closest point to the sun, and aphelion is the farthest point. The earth's seasons mainly come from the tilt of the earth's axis, and cold and warm cannot be read directly from these two words.
Distance extreme value ≠ temperature extreme value
Use a valid event number
The perihelion k takes an integer, and the aphelion k takes a half integer; any decimal is not a legal event number in this formula.
Perihelion k∈Z; aphelion k∈Z+0.5
The Earth also needs to correct for the influence of the Moon
The Earth polynomial first corresponds to the Earth-Moon mass center. The original book gave 5 periodic terms, and changed the time to be closer to the extreme value of the distance between the center of the earth and the sun.
JDE = Polynomial + Earth Period Correction
Actuarial science needs to return to the distance curve
The Earth model can then use the truncated VSOP87 distance to find extreme values nearby. This lesson on other planets still shows the approximate polynomials and their limitations in the original book, and does not pretend to be precise predictions.
Find the minimum or maximum of R(t)
First select k according to the planet and perihelion/aphelion point, and find the average event polynomial; add the specified periodic term to the earth branch. This moment is an event estimate, and finding the extreme value directly on R(t) belongs to another refinement route.
give it a try
Compare the average and corrected results for "Earth's 1990 perihelion". The polynomial error in the original book of the outer planet may be several weeks, so do not treat it as a precise moment.
No need to memorize symbols
- k
- Integer or half-integer number of perihelion and aphelion points
- R
- Distance from the center of the sun in AU
- JDE
- Number of days during TT kinetics
- center of mass of earth and moon
- The center of mass that the Earth and Moon orbit together
Algorithm, accuracy and scope of application
Realize the event polynomial of the 8 planets in this chapter, select the nearest integer/half integer k; add the 5 geocentric corrections of the original book to the earth, and use the appendix of Chapter 25 to truncate the earth distance of VSOP87 to search for the golden section extreme value within ±4 days of the predicted value. The outer planets are not connected to the complete VSOP87 hourly actuarial calculation. The original book points out that the error can be half a month for Jupiter, more than a month for Saturn, and even worse for farther planets. The average error of the original Earth 5 correction book from 1980 to 2019 is about 3 hours. This experience cannot be extended to the guarantee of this interface from 1900 to 2100. The refinement results are still limited by the truncated distance model and are not modern precision almanacs.
my understanding check
In the perihelion formula in the original book, what should k be?
integer — Use half integers for aphelion, other decimals cannot represent events in this formula.
What is the Earth Cycle Correction correcting?
The difference between the center of mass of the Earth and the Moon and the center of the Earth — The moon affects the earth, and the extreme moment of the distance between the earth and the center is different from the center of mass of the earth and the moon.
The outer planet polynomial gives a lot of decimals, does that mean the error is small?
no — The original book clearly states that Jupiter, Saturn and the outer planets may have time errors of several weeks or more.
The extreme value of the distance must be found for the closest or furthest distance; the approximate time, period correction and fine ephemeris should be marked respectively.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 38 chapter
Planets and Small Solar System Objects · All interactive courses