{"openapi":"3.1.0","info":{"title":"Telescope Optics API","version":"1.0.0","description":"Telescope optics maths as an API, computed locally and deterministically — the magnification, exit-pupil and resolving-power numbers an amateur astronomer or stargazing-app developer picks gear and eyepieces with. The magnification endpoint gives magnification = the telescope's focal length ÷ the eyepiece focal length (a 1000 mm scope with a 10 mm eyepiece is 100×), the focal ratio, and — from the aperture — the useful range from about the aperture in mm ÷ 7 (lowest useful, a 7 mm exit pupil) up to roughly 2× the aperture in mm, beyond which the image only dims and blurs; pass an eyepiece apparent field and it returns the true field of view. The exit-pupil endpoint gives aperture ÷ magnification, the width of the light beam leaving the eyepiece — a big 4–7 mm exit pupil for bright wide views of nebulae, a small 0.5–2 mm for the Moon and planets at high power. The resolution endpoint gives the Dawes limit ≈ 116 ÷ aperture(mm) and the slightly stricter Rayleigh limit ≈ 138 ÷ aperture in arcseconds, plus the limiting magnitude ≈ 2.7 + 5·log₁₀(aperture mm) — bigger glass splits finer doubles and reaches fainter stars, though seeing usually caps real resolution near 1 arcsecond. Everything is computed locally and deterministically, so it is instant and private. Ideal for astronomy and stargazing apps, telescope-shop and eyepiece-calculator tools, and observing-planner utilities. Pure local computation — no key, no third-party service, instant. 3 compute endpoints. For camera/thin-lens imaging use a lens API; for stellar magnitudes a star-magnitude API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/telescope-api","description":"oanor gateway"}],"tags":[{"name":"Telescope"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/exit-pupil":{"get":{"operationId":"get_v1_exit_pupil","tags":["Telescope"],"summary":"Exit pupil","description":"","parameters":[{"name":"aperture_mm","in":"query","required":true,"description":"Aperture (mm)","schema":{"type":"string"},"example":"200"},{"name":"magnification","in":"query","required":true,"description":"Magnification","schema":{"type":"string"},"example":"100"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Exit pupil = aperture ÷ magnification — the width of the beam of light leaving the eyepiece. Match it to the job: a big 4–7 mm exit pupil gives a bright, wide view for nebulae and the Milky Way (but beyond ~7 mm, more than a dark-adapted eye, light is wasted), while a small ~0.5–2 mm exit pupil at high power suits the Moon, planets and double stars. The exit pupil also sets the image brightness per unit area.","inputs":{"aperture_mm":200,"magnification":100},"exit_pupil_mm":2},"meta":{"timestamp":"2026-06-07T08:18:03.694Z","request_id":"c25aba4c-d2fd-4795-a742-8ae6390d2668"},"status":"ok","message":"Exit pupil","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/magnification":{"get":{"operationId":"get_v1_magnification","tags":["Telescope"],"summary":"Magnification and useful range","description":"","parameters":[{"name":"scope_focal_length_mm","in":"query","required":true,"description":"Telescope focal length (mm)","schema":{"type":"string"},"example":"1000"},{"name":"eyepiece_focal_length_mm","in":"query","required":true,"description":"Eyepiece focal length (mm)","schema":{"type":"string"},"example":"10"},{"name":"aperture_mm","in":"query","required":false,"description":"Aperture (mm) for useful range & f-ratio","schema":{"type":"string"},"example":"200"},{"name":"apparent_fov_deg","in":"query","required":false,"description":"Eyepiece apparent field (deg) for true FOV","schema":{"type":"string"},"example":"52"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Magnification = the telescope's focal length ÷ the eyepiece focal length, so a shorter eyepiece magnifies more. Useful magnification runs from about the aperture in mm ÷ 7 (a 7 mm exit pupil, lowest useful) up to roughly 2× the aperture in mm — push past that and the image just gets dim and fuzzy, not more detailed. The true field of view = the eyepiece's apparent field ÷ the magnification, so high power shows a small patch of sky.","inputs":{"aperture_mm":200,"apparent_fov_deg":52,"scope_focal_length_mm":1000,"eyepiece_focal_length_mm":10},"focal_ratio":5,"magnification":100,"true_field_of_view_deg":0.52,"max_useful_magnification":400,"min_useful_magnification":28.6},"meta":{"timestamp":"2026-06-07T08:18:03.768Z","request_id":"98ee3446-a6a8-4640-aca2-20c31a399d55"},"status":"ok","message":"Magnification","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/resolution":{"get":{"operationId":"get_v1_resolution","tags":["Telescope"],"summary":"Resolving power and limiting magnitude","description":"","parameters":[{"name":"aperture_mm","in":"query","required":true,"description":"Aperture (mm)","schema":{"type":"string"},"example":"200"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"Resolving power is set by the aperture alone: the Dawes limit ≈ 116 ÷ aperture(mm) arcseconds is the classic split-a-double-star figure, the Rayleigh limit ≈ 138 ÷ aperture a slightly stricter criterion. Bigger glass resolves finer detail and, gathering more light, also reaches fainter stars — the limiting magnitude ≈ 2.7 + 5·log₁₀(aperture mm). Atmospheric seeing usually caps real resolution around 1 arcsecond regardless of aperture.","inputs":{"aperture_mm":200},"dawes_limit_arcsec":0.58,"limiting_magnitude":14.2,"rayleigh_limit_arcsec":0.69},"meta":{"timestamp":"2026-06-07T08:18:03.856Z","request_id":"22451984-dc3a-4a03-b49d-6d37fa0722b1"},"status":"ok","message":"Resolution","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"notes":"mm, degrees, arcseconds. mag = scope FL ÷ eyepiece FL; exit pupil = aperture ÷ mag; Dawes = 116/aperture, Rayleigh = 138/aperture; limiting mag = 2.7 + 5·log10(aperture mm). For camera/thin-lens imaging use a lens API; for stellar magnitudes a star-magnitude API.","service":"telescope-api","endpoints":{"GET /v1/meta":"This document.","GET /v1/exit-pupil":"Exit pupil from aperture and magnification.","GET /v1/resolution":"Dawes/Rayleigh resolution and limiting magnitude from aperture.","GET /v1/magnification":"Magnification, focal ratio, useful range and true field of view."},"description":"Telescope optics maths: magnification and useful range, exit pupil, and resolving power / limiting magnitude."},"meta":{"timestamp":"2026-06-07T08:18:03.953Z","request_id":"112e00f1-f88e-44d2-ac48-7a177e1bbf4b"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":9200,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":700,"monthly_call_quota":90000,"rps_limit":6,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":2560,"monthly_call_quota":366000,"rps_limit":15,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":7900,"monthly_call_quota":1680000,"rps_limit":40,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/telescope-api"}