Parallax
Hold a finger up at arm's length and look at it with one eye closed, then the other. The finger jumps against the background. Bring it closer and the jump gets bigger; hold it further away and the jump gets smaller.
That is parallax, and it is the mechanism behind the origin setting.
Parallax is the change in an object's apparent direction caused by a change in the observer's position.
Distance decides the size of the shift
The two eyes in that experiment are a fixed distance apart, and yet the finger's jump varied. What varied was the distance to the finger.
The diagram keeps the baseline the same and changes only the distance. The near object swings across the background, and the far one barely moves.
This is why parallax matters only in the Solar System's near neighbourhood. The baseline available on Earth, at most one Earth radius from the centre to the surface or about 4,000 miles, is very large compared with a room and negligible compared with the distance to a star.
The numbers
The table gives the size of the shift for each kind of body. The shift is what you get by moving from the centre of the Earth to a point on its surface, and most of what the origin setting does in practice follows from it.
| Body | Typical shift |
|---|---|
| The Moon | up to about 1° |
| Venus, at its closest | around half an arcminute |
| Mars, at its closest | around a third of an arcminute |
| Jupiter and beyond | a couple of arcseconds at most |
| The stars | far too small to measure, even for the nearest |
A degree is two full Moon-widths. That is large enough to see and large enough to matter, and the Moon is the only body it applies to.
Everything else on the list is smaller than the width of the line a chart is drawn with.
Why the Moon is the exception
The Moon is about sixty Earth radii away, so the baseline from the Earth's centre to its surface is a sixtieth of the distance to it, which is a very large fraction by astronomical standards.
Two observers on opposite sides of the Earth see the Moon in different places against the stars. This is the reason a solar eclipse is total along a narrow track and partial on either side of it. The Moon covers the Sun for observers in one strip and misses for observers a few hundred miles away, because they are looking at it from different places.
Any calculation involving the Moon and a specific location on the ground — eclipse circumstances, occultations, precise rising times — has to account for it.
Height contributes too
The surface is not all at the same distance from the centre. Standing higher lifts you a little further from the Earth's centre and adds a little to the baseline.
The contribution is in proportion to the extra distance, and the proportion is small: Denver's mile is about one part in four thousand of the Earth's radius, so it adds just under an arcsecond to the Moon's shift. This is the arithmetic behind the claim made back in Height Above Sea Level — that height changes almost nothing.
The effect is small but it is not zero, and that is why the location record has a height field at all.
What comes next
The next three pages take the origins one at a time. The first is Geocentric, the origin nearly every chart ever cast has used, and the next page gives the reasons it became the default.
Next: Geocentric.