Pluto is so far away, are we seeing its current position?

First find its position around the sun, and then subtract the time it takes for the light to travel to the earth.

Light from distant objects takes time to reach Earth. The example of Pluto is obvious: the light distance can be several hours. When calculating the direction from the Earth, the position when it is emitting light is used, while the Earth is still taking the position when it is receiving light.

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Guess first

How many hours does it take for light to travel from Pluto to Earth? Will we see the position of Pluto at exactly the same time?

Show answer and explanation

No, it was the light that was emitted earlier — The position of Pluto needs to be calculated at the time of emission and then combined with the position of the Earth at the time of reception.

Then connect experience and science

First find the position using the sun as the origin

The 43 periodic terms calculate the heliocentric longitude, ecliptic latitude and distance of Pluto, and the reference equinox is J2000.

Table 37.A: Σ(A sin α + B cos α)

Then move the observation position to the earth

Adding the geocentric sun vector at the same receiving time changes the heliocentric Pluto position to the geocentric position.

Geocentric Pluto = Heliocentric Pluto + Geocentric Sun

Let the light path participate in iteration

Estimating the light travel time based on the distance from the Earth's center, and then recalculating Pluto by going back to an earlier luminous time; usually converges quickly.

τ = 0.0057755183 Δ days

Don’t forget the scope of application

This fit cannot be extrapolated arbitrarily beyond 1885–2099. The output is the J2000 astrometric direction, not the local elevation or apparent position with all corrections.

Applicable dates and coordinate systems must be stated together

First, use the basic angles of Jupiter, Saturn, and Pluto to construct each α, and accumulate 43 corrections for ecliptic longitude, ecliptic latitude, and distance respectively; then add them to the geocentric sun vector. The light travel time τ is measured in days and cannot be directly added to the position as an angle.

give it a try

First read the calculation example of 1992-10-13 in the original book, and then switch the light travel time. The 43 items here are only valid from 1885–2099.

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No need to memorize symbols

L / B / R: Heliocentric longitude, yellow latitude and heliocentric distance
α / δ: Geocentric J2000 celestial measurements of right ascension and declination
Δ / τ: Earth-center distance and light travel time
TT / JDE: Kinetic time and corresponding consecutive days

Algorithm, accuracy and scope of application

Realize the heliocentric L/B/R (J2000) of all 43 items in Table 37.A, then rotate the equatorial vector according to 37.1, and iterate the optical path to obtain the geocentric J2000 astrometric coordinates. The sun's reception time vector is calculated through Chapter 26 of the solar-coordinates expansion package, without the homepage orbit. No nutation, optical aberration to apparent position, local parallax or modern numerical ephemeris are added; the accuracy cannot exceed the original book fit and the solar truncation model used. Dates outside of 1885–2099 are strictly rejected.

my understanding check

Table 37. Where is the origin of the coordinates directly given by A?

solar center — Calculate the heliocentric position first, and then convert it to the geocentric position.

When taking into account the light distance, do we have to move the Earth back to the same earlier time?

No, the earth takes the reception time — The observer is at the current location of the Earth when receiving the light.

Can the formula in this chapter be used directly to calculate the year 2500 AD?

Can't — The original book clearly limits the period to 1885–2099.

To calculate the position of distant celestial objects, you must also distinguish where to look from, which set of coordinates to use, and when the light will start.

Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 37 chapter

Planets and Small Solar System Objects · All interactive courses