# How many arcseconds does Sun travel through sky?

• MarkB7
In summary, the question being discussed is how many arcseconds the sun travels through the sky in one Tropical Year. From the perspective of an Earth-centered inertial frame, the answer is approximately 50 arcseconds less than 360 degrees. This is due to the Earth's rotation axis being tilted and undergoing precession. If we stand on Earth and look up, the sun would appear to travel approximately 1296000 x 365 arcseconds a year. However, this does not mean that the sun moves that much relative to the stars. In reality, it moves 360 degrees a year, regardless of our frame of reference. The final conclusion is that the sun travels approximately 473040000 arcseconds in one Tropical Year from the reference
MarkB7
Hi Everyone,

I have a simple question:

How many arcseconds does the sun "travel" through the sky in one Tropical Year?

Mark

Mark, you are trying to resurrect a closed thread. It was closed for a reason.

From the perspective of an Earth-centered inertial frame, the answer is a tiny bit (about 50 arcseconds) less than 360 degrees.

Hi D H,

I'm not resurrecting that thread. I just hope we can come to a consensus on the number.

I mean all the travel of the sun in a year. So it's got to be a lot.

Mark

Mark, you are still confusing the Earth's daily rotation with the Earth's orbit. This is the sole source of your confusion. Imagine what things look like from a reference frame that is not rotating with respect to the remote stars and with origin at the solar system barycenter. The International Celestial Reference Frame, for example. The Earth-Moon barycenter follows a nearly elliptical path in this frame. The time it takes for the Earth-Moon system to complete one orbit in this frame is one sidereal year.

Now flip your point of view to an Earth-centered frame, but keep the same axes. This is an Earth-centered inertial frame (a bit of a misnomer; this is an accelerating but non-rotating frame). From this perspective, it is the Sun that completes one orbit about the Earth in one sidereal year.

What about a tropical year? The Earth's rotation axis is tilted with respect to the Earth's orbital angular momentum vector. Suppose the only bodies in the universe were the Sun and Earth (i.e., no Moon or Jupiter to confuse things) and suppose the Earth's rotation axis was unchanging. With these simplifying assumptions, the line connecting the Earth and the Sun would lie completely on the ecliptic plane twice a sidereal year -- and those equinoctal points would be fixed points in the solar system barycentric frame. The between successive vernal equinoxes, the tropical year, would be one sidereal year.

The Earth's rotational axis is not constant; it instead undergoes a slow precession. Because of this precession, a tropical year is a bit shorter (~20.5 minutes) than a sidereal year. Given that a full orbit (one sidereal year) is 360 degrees by definition, 20.5 minutes corresponds to about 50 arcseconds.

Hi DH,

I think you misunderstand my intention here. I simply want to find out how many arcseconds the Sun travels through the sky in one year.

You are the one continuing the conversation from the closed thread.

Mark

What year (tropical, sidereal, anomalistic), and what reference frame (Earth centered inertial or Earth-centered, Earth-fixed)?

Hi DH,

Thank you! I'm sure you're a nice person : )

So, by tropical year I mean the amount of arcseconds the sun travels from the spot over the vernal equinox to that same spot over the vernal equinox the next year. Of course it doesn't travel, so, apparent travel.

Mark : )

Dang! Rotation with respect to what frame of reference? Do you understand what this question means?

Ummm. Assume we are standing on the Earth and looking up...all year.

That is not a very useful frame of reference. It is just going to lead you to confusion -- and that is exactly what is going on. Forget that frame. Read post #4.

Let's approximate...

365 days * (3,600sec/day) = 13,140,000A very boring analysis

Thank you for responding to my question!

flatmaster said:
Let's approximate...

365 days * (3,600sec/day) = 13,140,000

3,600 arcseconds per day?

I think it's 1296000 arcseconds per day.

So then it would be, approximately, 1296000 x 365?

Mark

Yes, the Sun would travel approximately 1296000 x 365 arcseconds a year if you stood on Earth looking up. (It doesn't actually, but let's clear up one issue at a time.) This does NOT mean the Sun moves 1296000 x 365 arcseconds a year relative to the stars.

Do you understand the difference? Suppose I put you on a merry-go-round and start spinning it at one revolution per second. To you, it would appear that the Sun is moving 360 degrees per second. This is analogous to the 1296000 x 365 arcseconds the Sun moves a year. However, the Sun doesn't move 360 degrees per second relative to the fixed stars; it moves 360 degrees a year, whether you're on a merry-go-round or on the ground.

ideasrule said:
1296000 x 365 arcseconds a year relative to the stars.
You are correct. That would be a lot of difference.

ideasrule said:
However, the Sun doesn't move 360 degrees per second relative to the fixed stars; it moves 360 degrees a year, whether you're on a merry-go-round or on the ground.

I assume you mean 360 degrees per day from the reference frame of standing on one spot of the Earth. Every day, from my reference frame, the sun circles me 360 degrees.

So, can we say the sun travels 473040000 arcseconds every year from our reference frame? Standing in one spot on the solid earth? I think this is the right answer. We see the sun once, twice, 365 times and back to the same spot, making 473040000 arcseconds of angle.

Mark

This is really all that I wanted to come to in this thread: how many arcseconds the sun travels in one year from the reference point of a person standing on one spot of the solid Earth.

Tropical Year: 473040000 arcseconds

Tropical Day: 1296000 arcseconds

Mark

MarkB7 said:

I'm afraid you are. Thread closed.

## 1. How do we measure the Sun's movement through the sky?

The Sun's movement through the sky is measured in arcseconds, which is a unit of angular measurement. This is calculated using a system called Right Ascension and Declination, which divides the sky into 360 degrees and then further into 60 arcminutes and 60 arcseconds.

## 2. What is the average number of arcseconds that the Sun travels through the sky in a day?

The average number of arcseconds that the Sun travels through the sky in a day varies depending on the time of year. On the equinoxes, the Sun travels approximately 86164 arcseconds in a day, while on the solstices it travels approximately 86399 arcseconds.

## 3. How does the Earth's rotation affect the Sun's movement through the sky?

The Earth's rotation is what causes the Sun to appear to move across the sky. As the Earth rotates on its axis, the Sun appears to rise in the east and set in the west, traveling through the sky at a rate of 15 degrees per hour, or 900 arcseconds per minute.

## 4. What factors affect the Sun's movement through the sky?

The Sun's movement through the sky is affected by several factors, including the Earth's rotation, the Earth's orbit around the Sun, and the tilt of the Earth's axis. These factors cause the Sun's position in the sky to change throughout the day and throughout the year.

## 5. How many arcseconds does the Sun travel through the sky in a year?

The Sun travels approximately 31,536,000 arcseconds through the sky in a year. This number is calculated by multiplying the average number of arcseconds the Sun travels in a day (86399) by the number of days in a year (365).

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