Mercury and Venus orbit inside ours, so neither can ever appear more than a limited angle from the Sun. Drag through an apparition and watch the planet swing out, turn round, and come back.
What is greatest elongation?
Elongation is the angle between a planet and the Sun as seen from Earth; greatest elongation is the moment an inner planet — Mercury or Venus — is furthest from the Sun during one apparition. Mercury never gets even 30° from the Sun and Venus never 50°, and after that moment each appears to close back in on the Sun.
Why are Mercury and Venus only seen at dawn or dusk?
Because both orbit inside Earth's orbit, the angle between them and the Sun as seen from Earth has a ceiling, and they can never stray far from it. Elongation peaks when the sightline from Earth just grazes the inner orbit; beyond that the planet appears to swing back toward the Sun. So they only show low in the east before sunrise or low in the west after sunset, never high in the sky at midnight.
What is the difference between eastern and western elongation?
At greatest eastern elongation the planet lies east of the Sun and appears in the western sky after sunset as an evening star; at greatest western elongation it lies west of the Sun and appears in the eastern sky before sunrise as a morning star. Venus is close to half lit at greatest elongation, while Mercury's eccentric orbit makes the angle differ noticeably from one apparition to the next.
Why Mercury only appears near dawn or just after sunset
Mercury and Venus never stray far from the Sun in our sky. Their limit comes from the angle made by our view into their inner orbits.
To find Mercury, start with its angle from the Sun
Mercury can be bright enough for the unaided eye, but it remains close to the Sun. The angle between planet and Sun in our sky is elongation; when that angle is small, twilight overwhelms the planet.
An eastern greatest elongation offers an evening view, while a western one belongs before sunrise. East and west describe sky direction and do not mean the planet is physically farthest from the Sun.
The easiest date is not always the brightest
Venus can reach roughly 47 degrees from the Sun, whereas Mercury usually reaches only the twenties. Brightness also depends on distance and phase: a nearby planet looks larger but may show only a thin illuminated crescent.
Move the date and compare elongation, distance, and illuminated fraction together. Greatest elongation answers whether the planet is separated from sunlight; maximum brightness is a different balance of the other measurements.
The easiest day to find it is not necessarily the brightest
An inner planet's brightness depends on both distance and phase. When Venus is near Earth its disk looks larger, but the lit part facing us may be only a thin crescent; farther away more of it is lit, yet the whole planet's apparent diameter shrinks.
As you drag the date, watch elongation, distance and illuminated fraction together. Greatest elongation answers “is it far enough from the Sun?”, while brightness results from the other two factors working together, so the two dates usually do not coincide.
Why they never leave the Sun
Greatest elongation is where the line of sight grazes the planet's orbit.
Both orbit inside Earth's orbit, so the line from us to the planet can never swing more than a certain angle away from the line to the Sun. The limit is reached where our line of sight is tangent to the planet's orbit, and for a circular orbit that angle is the arcsine of the planet's distance from the Sun in AU.
Venus's orbit is almost a circle, so the circular formula predicts its greatest elongations to within a degree. Mercury's is not. At an eccentricity of 0.206 the Sun sits well off the centre of its orbit, and the greatest elongation depends on whether the apparition happens near Mercury's perihelion or its aphelion. Quoting one figure for Mercury would be wrong by up to five degrees.
The turning points are the greatest elongations. Zero is conjunction, and the sign says which side of the Sun the planet is on.
Before looking for Mercury or Venus, check which side of the Sun it is on. Greatest eastern elongation favours the western sky after sunset; greatest western elongation favours the eastern sky before sunrise. Greatest elongation marks a local maximum in angular separation, not necessarily the highest altitude or darkest twilight. Latitude and the ecliptic's angle to the horizon still control the useful viewing window.
The circular limit in the table uses only the ratio of semi-major axes; the actual range retains the effect of orbital eccentricity. Mercury differs enough that 22.8 degrees should not be treated as a fixed value when checking a particular elongation.
Half lit at greatest elongation, for Venus
That Venus shows phases at all is the observation that broke the geocentric model. In Ptolemy's arrangement Venus rides an epicycle that keeps it between us and the Sun, so it could only ever be a crescent. Galileo saw it gibbous.
Crescent, half, gibbous — Venus runs through the same geometry as the Moon: half the ball is always lit, and only our viewing angle changes. The moon-phase lesson lets you drag that angle and watch.
Mercury does not obey the rule, and a textbook that states it without qualification is quoting the circular case. Mercury's phase angle at greatest elongation runs from 74 to 106 degrees, so its disc there is anything from 37 to 64 per cent lit.
Brightest is neither closest nor furthest from the Sun
The peak lands near 39 degrees of elongation with about a quarter of the disc lit, roughly five weeks either side of inferior conjunction. It happens twice in each apparition, once in the evening sky and once in the morning, and it is the brightest any planet ever gets: bright enough to cast a shadow from a dark site, and to be found in daylight if you know where to look.
Brightness here is pure geometry: sunlight received, lit fraction, and distance. Real photometry adds a phase function for the atmosphere and the scattering angle, which moves the peak by a few days. Nothing on this page is a magnitude prediction.
Why they never leave the Sun
Planet
Eccentricity
Circular-orbit limit
Actual range, 16 years
Mercury
0.206
22.8°
18°–28°
Venus
0.0068
46.3°
45°–47°
FAQ
Why are Mercury and Venus never visible at midnight?
That is the whole reason neither is ever visible at midnight, and why both are always twilight objects: low in the west after sunset, or low in the east before sunrise, and nowhere else.
Is Venus always half illuminated at greatest elongation?
If the line of sight is tangent to a circular orbit then the Sun-planet-Earth angle at greatest elongation is exactly 90 degrees, and a planet lit from 90 degrees away shows exactly half a disc. Venus obliges: at every greatest elongation over the last sixteen years its disc is between 49 and 51 per cent lit.
Why is Venus not brightest at greatest elongation?
Between greatest elongation and inferior conjunction Venus keeps coming closer, so its disc grows; at the same time the lit crescent keeps getting thinner. What reaches us is the lit area, which is the product of the two, and the product peaks somewhere in between.
Orbital elements from NASA/JPL, "Keplerian Elements for Approximate Positions of the Major Planets" (Standish & Williams, 1992), valid 1800–2050. Positions are geometric — no light-time or aberration — because this is a diagram of the ecliptic plane, not a simulation of a telescope view.