Uranus orbits far outside Earth, so the superior-planet limit is severe. The fact-sheet ratio is 19.165. The maximum phase angle on these circles is arcsin(1 / 19.165), and the minimum lit fraction is (1 + cos of that angle) / 2 — 2.99° and 99.93%, rounded in the script from the unrounded angle. From Earth the disk is gibbous to full, and at the minimum it is already near full. A crescent is a spacecraft geometry. The place to drag that observer is the Jupiter desk; the wedge here would be even narrower, ±2.99°. NASA’s Basics of Space Flight says superior planets usually appear gibbous, and full at opposition. Opposition repeats on the fact sheet’s synodic period, 369.66 days, close to Earth’s 365.256-day sidereal year because Earth does almost all the catching up. The lineup drawing, with Mars, is the opposition desk.
Educational schematic — circular coplanar orbits, disks exaggerated. Earth is held on the right. The Uranus marker walks clockwise on that frozen view because Earth is faster; the orbit arrows stay counterclockwise. The ratio is 19.165. The fact sheet lists eccentricity 0.0469 and inclination 0.770°. When the inner orbits shrink on the canvas, a magnified inset keeps the Sun and Earth readable; the radii are still the true ratio. The fact sheet lists a planetary ring system. It is left off this drawing so the disk’s phase stays the subject. Not an ephemeris. Not a magnitude. Not a date.
Interactive · From Earth
North up · Earth held on the right · circles at the fact-sheet ratio
As seen from Earth · east to the right · ghost ring is the largest size on these circles
Sun
Uranus
Earth · viewpoint held
Line of sight
0 d
Literacy · words for the phase
Superior planet
NASA’s Basics of Space Flight: the outer planets usually appear gibbous, and full at opposition. Uranus is in that list. The phase angle from Earth stays inside ±2.99° on these circles. Mars is the same rule with a gibbous you can see. Mercury and Venus are the crescent case.
Phase angle
The angle at Uranus between the Sun and Earth. Maximum on these circles: arcsin(1 / 19.165) = 2.99°. Lit fraction = (1 + cos of the phase angle) / 2. Minimum 99.93%. Both are computed from the fact-sheet ratio, then rounded to two decimals.
Opposition and conjunction
Opposition puts Earth between the Sun and Uranus. The disk is full and as large as these circles get. Conjunction puts the Sun in the middle: full again, smallest, and lost in the glare. NASA’s Basics of Space Flight says that far-side lineup appears near the fully illuminated phase. The synodic period on the fact sheet is 369.66 days.
Quadrature
The right angle at Earth. Eastern is the evening side of this sketch; western is the morning side. It is the least-lit moment, and it is still 99.93% lit. A crescent would require leaving the ±2.99° wedge, which only a spacecraft can do. That control lives on the Jupiter desk.
Sources · public NASA pages
Cited, not invented
NASA NSSDCA — Uranus Fact Sheet — semimajor-axis ratio 19.165; sidereal orbit period 30,685.400 days; Earth 365.256 days; synodic period 369.66 days; mean orbital velocity 6.79 km/s (Uranus) and 29.78 km/s (Earth); eccentricity 0.0469; inclination 0.770°. The fact sheet lists a planetary ring system. This desk does not draw it; the phase of the disk is the lesson. The 2.99° and 99.93% figures are computed from 19.165.
NASA Science — Basics of Space Flight, Chapter 1 — superior planets usually appear gibbous, and appear full only when at opposition; at superior conjunction the outer planet appears near its completely illuminated full phase.
Jupiter phases, this site — the spacecraft wedge, with Voyager, Cassini, New Horizons, and Juno cited on that page. The same geometry applies here, with a smaller maximum phase angle.
Classroom picture of a distant orbit and the near-full disk it shows from Earth. Not an ephemeris. Days are counted from a schematic opposition. The phase angle and the lit fraction are computed from the fact-sheet ratio named above. Earthrise preview: NASA / Bill Anders (public domain).