# Explanation of Equatorial Coordinate System?

• saidatta123
In summary, right ascension and declination are two coordinate systems used to identify the positions of celestial objects. Right ascension is based on the vernal equinox, which is fixed by definition. Declination, which is based on the pole, is unaffected by Earth's rotation. Right ascension is the clock-wise [east-west] coordinate due to rotation of the earth. That changes from second to second for all celestial objects. Right ascension is the analog of latitude, and right ascension is the analog of latitude. Because the Earth is rotating, you have to choose a particular instant to do the projection. We choose to do it at noon in London on the day of the vernal equinox.
saidatta123
Can anyone explain very clearly(to a n00b like me) right ascension and declination and how to navigate to stars using this system?

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Declination is the north-south coordinate of a celestial object. That essentially never changes for bodies external to the solar system, save due to precession of the poles. Right ascension is the clock-wise [east-west] coordinate due to rotation of the earth. That changes from second to second for all celestial objects.

Chronos said:
Right ascension is the clock-wise [east-west] coordinate due to rotation of the earth. That changes from second to second for all celestial objects.

I think you may have confused right ascension with hour angle. Right ascension for, say, a star is fairly constant.

Uhh, no.

Chronos, Filip is correct. Right ascension does not change one iota due to the Earth's rotation. That's why star charts are published using right ascension and declination.

I stand corrected. Right ascension is based on the vernal equinox, which is fixed by definition. The location of the vernal equinox, however, is relative because it rotates on the celestial sphere as viewed from earth. Declination, which is based on the pole, is unaffected by Earth's rotation.

saidatta123 said:
Can anyone explain very clearly(to a n00b like me) right ascension and declination and how to navigate to stars using this system?
One simple way to think of it is to imagine projecting the latitude and longitude lines on the Earth onto the celestial sphere. This becomes the coordinate system that is used for defining the positions of the stars. Declination is the analog of latitude, and right ascension is the analog of latitude. Because the Earth is rotating, you have to choose a particular instant to do the projection. We choose to do it at noon in London on the day of the vernal equinox. We also usually measure right ascension using time instead of degrees, with 1 hour of RA equal to 15 degrees, but you can also measure RA in degrees and people often do. As has been mentioned, the RA and Dec of a particular object don't change because of the Earth's rotation, but they do change as a result of the precession of the Earth's axis of rotation. However, this takes 26,000 years to make a complete circle, so the change is slow. For example, here are the coordinates of Aldebaran (Alpha Tauri) in 1950-based and 2000-based coordinates:

B1950 : Dec = +43 30' RA = 16h25m
J2000 : Dec = +43 59' RA = 16h31m

The ecliptic plane is the plane of the Earth's orbit around the Sun. The equatorial plane is the plane of the Earth's equator. The Earth's equator is tilted at an angle to the ecliptic plane. The intersection of those two planes forms a line. This line forms the x-axis of the geocentric equatorial plane.

This line also runs through the center of the Earth, which is the origin of the geocentric equatorial coordinate system. The only thing left to do with this line is decide which direction is positive and which direction is negative. Twice a year (vernal equinox & autumnal equinox), the line formed by the intersection of the ecliptic plane and equatorial plane runs through both the center of the Earth and the center of the Sun. The positive direction for the x-axis runs from the center of the Earth to the center of the Sun on the vernal equinox.

Right ascension measures the position of the star relative to the positive x-axis (the direction of the vernal equinox) around the equatorial plane. You use the right hand screw rule to figure out which direction is positive (positive would be counter-clockwise if viewed from the outside of the system).

And, yes, many astronomical books identify right ascension, which is an angle, by Hour Angle. There's approximately 15 degrees per hour (15.04 if you want to be a little more exact).

Declination measures the North-South position of the star relative to the equator. Positive angles are to the North. Negative angles are to the South.

In order for the right ascension to mean much to you, you need to know the right ascension of the Prime Meridian (0 deg longitude), as well. Just to add confusion, the right ascension of the Prime Meridian is referred to as Greenwich Mean Sidereal Time and is measured in hours, minutes, seconds (but can be converted the same way right ascension is). The difference between the star's right ascension and the Earth's Greenwich Mean Sidereal Time tells you the longitude the star is directly over.

And, while the star's right ascension is almost constant, at least over the short term, Greenwich Mean Sidereal Time is constantly changing, just as the solar time you're more familiar with is, as the Earth rotates. The main difference is that Greenwich Mean Sidereal Time uses sidereal days instead of the more familiar solar days, meaning Greenwich Mean Sidereal Time at midnight Universal Standard Time will shift by about 4 minutes each day. In other words, the stars you see at midnight one night will shift about 1 degree at midnight the next night - and so on. (It isn't just coincidence that the number of degrees in a circle is so close to the number of days in a year - 360 is just a lot easier number to build a numbering system from than 365.)

As someone else mentioned, the long term position of the stars isn't stationary due to precession of the Earth's axis, which leads to a somewhat strange situation. If it doesn't happen to be the vernal equinox, you need a different method to find the positive direction of the x-axis. The solution is to look at the star (or a point in space relative to a few stars) that would be directly behind the Sun on the vernal equinox. This star (or point in space) is called the First Point of Aries. You'd think this point must lie in the constellation Aries, but, thanks to precession, the First Point of Aries actually lies in the constellation Pisces (it's too hard to go back and change books already printed so the term has never been changed even though the point has moved).

Someday soon (at least in astronomical terms) the First Point of Aries will enter the constellation Aquarius. And, at that time, there will be much singing.

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@saidatta123: any of this any use to you?

BobG, let me disagree with something I think you said. Right Ascension can be measured in degrees, or it can be measured in hours, minutes and seconds. The conversion between the two is not approximately 15 degrees per hour, it is exactly 15 degrees per hour. The first one divides the circle into 360 degrees, the second divides it up into 24 hours. It's not correct to say that the conversion factor is 15.04 degrees per hour.

phyzguy said:
BobG, let me disagree with something I think you said. Right Ascension can be measured in degrees, or it can be measured in hours, minutes and seconds. The conversion between the two is not approximately 15 degrees per hour, it is exactly 15 degrees per hour. The first one divides the circle into 360 degrees, the second divides it up into 24 hours. It's not correct to say that the conversion factor is 15.04 degrees per hour.
BobG was correct. In that part of his post he was talking about hours, minutes, and seconds as they are measured typically. He later gave the reason for that factor of 15.04 degrees versus 15 degrees per hour. One rotation of the Earth with respect to the Sun takes 24 hours. One rotation with respect to the stars takes only 23.9344696 hours. That difference of 3 minutes and 55.9084 seconds between a mean solar day and a mean sidereal day is what results in that factor of 15.04 degrees per (solar) hour.

D H said:
BobG was correct. In that part of his post he was talking about hours, minutes, and seconds as they are measured typically. He later gave the reason for that factor of 15.04 degrees versus 15 degrees per hour. One rotation of the Earth with respect to the Sun takes 24 hours. One rotation with respect to the stars takes only 23.9344696 hours. That difference of 3 minutes and 55.9084 seconds between a mean solar day and a mean sidereal day is what results in that factor of 15.04 degrees per (solar) hour.

I understand what you are saying, but BobG's post says,

"And, yes, many astronomical books identify right ascension, which is an angle, by Hour Angle. There's approximately 15 degrees per hour (15.04 if you want to be a little more exact)."

To me, this implies that you would convert hour angle from hours to degrees using a conversion factor of 15.04 degrees per hour. This is wrong. The following is from the Wikipedia entry,

"The angle may be expressed as negative east of the meridian plane and positive west of the meridian plane, or as positive westward from 0° to 360°. The angle may be measured in degrees or in time, with 24h = 360° exactly."

This is correct. I understand that sidereal time and standard time run at slightly different rates. The point is that right ascension and hour angle are both measured using sidereal hours, not standard hours.

I think phyzguy is correct. Context is everything. The hour angle for star locations is in sidereal hours. When calculating your ground location, your position is changing at 15.04 degrees per solar hour (which would be the normal way of keeping track of time).

Fortunately, mixing up your conversions won't result in much of an error for the average backyard astronomer.

Although, being more of a satellite guy than an astronomer, I'd be perfectly happy if they did away with hour angles completely and just used degrees (which is how right ascension is measured for satellites).

## 1. What is the Equatorial Coordinate System?

The Equatorial Coordinate System is a method used to locate objects in the sky based on their position relative to the Earth's equator and the celestial equator. It is a type of spherical coordinate system that uses right ascension and declination to pinpoint the location of celestial objects.

## 2. How is the Equatorial Coordinate System different from the other coordinate systems?

The Equatorial Coordinate System is different from other coordinate systems, such as the Horizon Coordinate System or the Ecliptic Coordinate System, because it is based on the Earth's rotation and not its orbit around the sun. This makes it a useful tool for tracking the motion of objects in the night sky.

## 3. What is the purpose of using the Equatorial Coordinate System?

The Equatorial Coordinate System is used by astronomers and scientists to locate and track celestial objects, such as stars, planets, and galaxies. It also allows for precise measurements and calculations of the positions and movements of these objects.

## 4. How is the Equatorial Coordinate System measured?

The Equatorial Coordinate System is measured using two angles: right ascension and declination. Right ascension is measured along the celestial equator, similar to longitude on Earth, and is usually denoted in hours, minutes, and seconds. Declination is measured perpendicular to the celestial equator, similar to latitude on Earth, and is usually denoted in degrees, minutes, and seconds.

## 5. Can the Equatorial Coordinate System be used for all objects in the sky?

Yes, the Equatorial Coordinate System can be used to locate and track all objects in the sky, including stars, planets, galaxies, and even comets and asteroids. However, it is most commonly used for objects that are far away and have a relatively fixed position in the sky, such as stars and distant galaxies.

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