Planetary Angular Distance Calculator
Compute the angular separation in degrees between any two celestial objects using their right ascension and declination coordinates. Use it to plan conjunction observations, check alignment of planets, or assess how close two stars appear in the sky.
About this calculator
Angular separation between two objects on the celestial sphere is found using the spherical law of cosines. Given Object 1 at (RA₁, Dec₁) and Object 2 at (RA₂, Dec₂), the angular distance θ is: cos(θ) = sin(Dec₁)·sin(Dec₂) + cos(Dec₁)·cos(Dec₂)·cos(ΔRA), where ΔRA is the difference in right ascension converted to degrees (hours × 15°). Solving for θ gives the great-circle arc between the two points in degrees. Right ascension is entered in hours (1 hour = 15°), and declination in degrees with sign (negative for south). A result near 0° means the objects appear nearly superimposed — a conjunction. Results above ~5° generally mean the pair won't fit in a typical telescope eyepiece. Observer latitude is used in some extensions of this tool for altitude and visibility checks.
How to use
Example: Jupiter at RA = 4.5 h, Dec = +20°, and Saturn at RA = 4.8 h, Dec = +18°. Step 1 — convert ΔRA to degrees: (4.8 − 4.5) × 15 = 4.5°. Step 2 — apply the formula: cos(θ) = sin(20°)·sin(18°) + cos(20°)·cos(18°)·cos(4.5°). Step 3 — compute: (0.342 × 0.309) + (0.940 × 0.951 × 0.9969) ≈ 0.1057 + 0.8909 = 0.9966. Step 4 — θ = arccos(0.9966) ≈ 4.76°. The calculator returns 4.76°, a close but distinct pairing visible in binoculars.
Frequently asked questions
What does angular separation mean in astronomy and how is it measured?
Angular separation is the apparent angle between two objects as seen from Earth, measured in degrees, arcminutes, or arcseconds. It describes how far apart objects look in the sky, regardless of their true physical distance from each other. The full Moon, for reference, spans about 0.5°. Two stars separated by less than about 1 arcminute (0.017°) are typically unresolvable to the naked eye. Astronomers measure this angle along the great circle connecting the two objects on the celestial sphere.
How close do two planets need to be for an event to be called a conjunction?
A conjunction is traditionally defined as two celestial bodies sharing the same right ascension — meaning one passes directly 'above' or 'below' the other in the sky. In practice, conjunctions of interest are often those where the angular separation falls below about 1–2°, making them a striking naked-eye sight. A separation under 0.1° is sometimes called an appulse or near-occultation and is very rare. This calculator lets you quantify any separation precisely so you can decide whether the event is worth observing.
Why does right ascension need to be converted from hours to degrees in the angular separation formula?
Right ascension is historically measured in hours, minutes, and seconds of time because the celestial sphere appears to rotate at 15° per hour due to Earth's spin. To use it in trigonometric formulas alongside declination (which is already in degrees), you must convert: multiply hours by 15 to get degrees. Failing to convert is a common mistake that produces wildly incorrect angular separations. This calculator handles the conversion automatically, accepting RA in decimal hours and internally multiplying by 15 before applying the spherical cosine rule.