# Stars closer than thought. How the sun affects the light path

1. Jan 24, 2004

### luiscar

Distance to star, much little
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

### mathman

The general relativity correction of light rays is barely measurable for rays grazing the sun. That is why the 1919 measurements had to be done during a solar eclipse. For rays not passing near the sun, the effect can be ignored.

3. Jan 30, 2004

### Creator

Luisar;
First....
Parallax is NOT determined by the angle between the star, earth, and sun. It is rather simply a measure of the angular change in position of the star with respect to the 'background' of stars (which are assumed to be at such a greater distance that we can call them 'fixed' for the sake of a 6 month time period).

Creator

4. Jan 30, 2004

### Creator

Luis
Having said the above about how the measurement of parallax itself is made, I would like to compliment you on your insight; and say that you are absolutely correct that the relativistic (light deflection) effect of the sun can be an appreciable percentage of the total amount of parallax for certain stars.

Consider this:
The largest parallax (that of which you mentioned Alpha Centari) is only 0.76 arcsec., corresponding to ~4.3 ly. (1.0 arcsec. of parallax = 1 parsec distance)

We only have <1000 parallaxes of relatively close stars due to the atmospheric limitations of earth-based telescopes; the least value being around 0.03 arcsec.,(corresponding to about 100 ly.).

Hipparcos & Hubble telescopes (due to their increased resolution) have increased it to several thousand stars, lowering our threshold to about 1 milli-arcsec.!

THus, for more sensitive stellar parallaxes (100 ly. and beyond), starlight deflection (or correction) due to solar gravity can be an apprecible percent of the total.

To get an idea of the amount of deflection possible take the case of the guide star originally proposed for the Gravity Probe B Experiment. One of the five relativistic effects needed to be subtracted from the data to get an accurate fix was the deflection of light due to the solar grav. field.

The deflection in this case (for the star Rigel) varied along two axis from 0.0 arcsec to a maximum of 14 milli-arcsec. This amount therefore would be quite apprecible when taking parallax measurements down to milli-arcsec. sensitivity (or even down to tens of milli-arcsec).

Notice, when talking about the corrections for stellar parallax, now the angle with the sun does matter, and is reflected in the variation in the correction at different times of the year.

So, in general, although a parallax measurement itself is independent of solar angle (for any particular star), the correction for starlight deflection is positionally dependent and is one of the adjustments needed in acquiring accurate parallax values.

Good question.

Creator

Last edited: Jan 31, 2004
5. Jan 31, 2004

### Nereid

Staff Emeritus
For HIPPARCOS, several relativistic corrections were explicitly considered, and (IIRC) at least one was included in the analysis. Volume 1 of their published results (available free on the web) gives the gory details.

Another circumstance where relativity must be included is in VLBI (very long baseline interferometry), done at radio wavelengths. AFAIK, the folk who routinely use this method to say that this plate on the Earth's surface is moving towards that plate at x.y mm per year, and who can measure the movement of the solar system around the centre of the Milky Way (and more?) must make all the appropriate calculations of relativistic effects - both GR and SR - and include those which matter.