Formula Used
The calculator first converts right ascension into degrees. It converts declination into signed decimal degrees. The UTC time becomes a Julian date. Greenwich mean sidereal time is then estimated from that Julian date. Local sidereal time equals Greenwich sidereal time plus east-positive longitude.
The hour angle is local sidereal time minus right ascension. Altitude is found with sin(alt) = sin(dec) sin(lat) + cos(dec) cos(lat) cos(hour angle). Azimuth uses atan2 with the hour angle, latitude, and declination. The output is normalized from zero to three hundred sixty degrees.
Optional refraction uses a common near-horizon correction. Zenith angle is ninety degrees minus apparent altitude. Airmass uses the Kasten and Young style estimate when the target is above the horizon.
Understanding Altitude and Azimuth
Altitude and azimuth describe where an object appears in your sky. Altitude measures height above the horizon. A value of zero degrees sits on the horizon. A value of ninety degrees sits at the zenith. Azimuth measures direction around the horizon. North is zero degrees. East is ninety degrees. South is one hundred eighty degrees. West is two hundred seventy degrees.
Why Local Inputs Matter
The same star has different sky angles from different places. Your latitude changes the height of the celestial pole. Your longitude changes local sidereal time. Date and time also matter. Earth rotates, so hour angle changes quickly. This calculator combines observer position, right ascension, declination, and time. It then returns the apparent viewing direction for that exact moment.
Useful Planning Details
Advanced results help with real observations. Hour angle shows how far the object is from transit. Zenith angle gives the distance from overhead. Airmass estimates how much atmosphere the light crosses. Smaller airmass usually means cleaner views. Refraction correction can lift objects near the horizon. This is helpful for low planets, comets, or stars. The compass sector gives a simple direction label. Rise and set sidereal values help plan later checks.
Good Data Practices
Use coordinates with clear signs. North latitude is positive. South latitude is negative. East longitude is positive. West longitude is negative. Enter time in UTC for consistent results. Use right ascension in hours, minutes, and seconds. Use declination in degrees, minutes, and seconds. Select the correct declination sign. Small input errors can shift the result. This is most noticeable near the horizon.
Reading the Output
A positive altitude means the object is above the ideal horizon. A negative altitude means it is below the horizon. Azimuth points to the compass direction. For example, ninety degrees means east. Two hundred twenty five degrees means southwest. The exported files are useful for logs. They keep the inputs and computed values together. This makes repeat observing sessions easier to compare.
Use the result with charts or a planetarium app. Check trees, buildings, and nearby low hills before observing. A mathematical horizon is ideal. A real site may block objects sooner. Recalculate often, because the sky keeps moving each minute.
FAQs
What is altitude in sky position?
Altitude is the object's angle above or below the horizon. Positive values are above the horizon. Negative values are below it. Ninety degrees means the object is directly overhead.
What is azimuth?
Azimuth is the compass direction of the object. This calculator uses zero degrees for north, ninety degrees for east, one hundred eighty degrees for south, and two hundred seventy degrees for west.
Why does UTC time matter?
UTC avoids time zone confusion. Sidereal time depends on the exact moment. A local time entered as UTC will shift the hour angle and give wrong sky directions.
What longitude sign should I use?
Use positive longitude for locations east of Greenwich. Use negative longitude for locations west of Greenwich. This sign is important because it changes local sidereal time.
Does the calculator include atmospheric refraction?
Yes, when the checkbox is selected. Refraction is most important near the horizon. It makes low objects appear slightly higher than their geometric altitude.
What is hour angle?
Hour angle shows how far the object has moved from the local meridian. Negative values are generally before transit. Positive values are generally after transit.
Can I use this for planets?
Yes, if you already have the planet's right ascension and declination for the selected time. Planet coordinates change, so use current ephemeris values.
Why are rise and set times sidereal?
The calculator works from celestial coordinates. Sidereal rise and set values show where the target meets the selected horizon. Convert them with local observing tools when exact clock times are needed.