# Distance to star, much little

1. Jan 24, 2004

### luiscar

Considering the effects of the relativity theory in terms of the curvation of space, I am wondering if for the calculation of the distance to the stars using the parallax method (below 100ly), the effect that the sun is creating a deformation in the solar system is taken into consideration.
The escape velocity of the solar system from the earth orbit is around 42Km/s. I do not know how to calculate how this may affect a light ray travelling from outside the solar system and arriving at the earth orbit, but for sure it has an effect.
Furthermore, imagine the following:
1. There is a star 4.2ly away from the sun
2. It is located in a direction perpendicular to the earth diameter

If we mesure the angle formed between the star, the eart and the sun at the beginning and the we measure the angle six months later (consider the 90ºeffect), the values we would obtain would be:

89º 59'59.18''
90º 0'0.52''

That means that the angle difference is 0.0005%

42Km/s / 300000Km/s = 0.014%

So actually, the sun effect may affect a lot.

So my point is that if the sun is curving the lightpath, maybe we are mesuring a more little angle difference than which is actually, and , therefore saying that the star distance is more than which actually is.

Any ideas on how the light path is affected when travelling through the solar system?

2. Jan 24, 2004

### Labguy

"Any ideas on how the light path is affected when travelling through the solar system?"

Almost none at all, or at least too small to be measurable. A similar question was posted before, and I don't remember the website citation, but any effect on a parallax measurement would be, at most, just one part in many billions. The light is not passing very near our single big-body (Sun) as in the 1919 eclipse experiment. In fact, since we measure from Earth, we will always be at one AU. The parallax measurements should be as accurate as our instruments are.

3. Jan 24, 2004

### LURCH

I've never looked into the exact details of how parallax range-finding is done, but I know how I would do it:

I would want to get the widest parallax angle I could. Therefore, I would draw a straight line from the distant object under observation to the sun. I would try to make my measurements when I am as far away from that line as possible. So, drying in a straight line through the sun that is at a 90o angle to the original line, I would take my measurements as earth passed through this second line. I think it is reasonable to guess that this is how astronomers make their measurements.

As you probably know, the curvature of light that results from our Sun's gravitational field is so slight that we have to wait for a solar eclipse to see light that has passed close enough to the sun that the effect is measurable at all. But using the above method for parallax range-finding, one would be observing the light that has never passed close earth than 1 astronomical unit from the sun.

4. Jan 24, 2004

### luiscar

Well, you say slight. I do agree, it is slight, but nevertheless, it lasts for 1 hour-light (1080MMKm). At this distance, the escape velocity is still a big number (around 15Km/s over the earth's ground escape velocity) and you have been at light speed for 1h

You know slight + long time = some effect.

If you calculate the effect that would have in the trigonometry of a "Galileo spaceship" going at c.

My calculations say that we would be sayng that a star is at 4ly when it is actually at 1ly.

5. Jan 24, 2004

### Nereid

Staff Emeritus
HIPPARCOS, the most accurate set of parallax measurements made to date (at least, in the optical band), did take relativistic corrections into account.

See Volume 1 of the report; it's online:
http://astro.estec.esa.nl/Hipparcos/CATALOGUE_VOL1/catalog_vol1.html

I don't recall which section covers the relativistic correction, probably 1.2.

6. Jan 24, 2004

### Labguy

See: http://instruct1.cit.cornell.edu/courses/astro101/lec14.htm

about 8/10ths down the page. Notice the distances are in parsecs (3.26ly).

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