measuring stellar distances without parallax

[Jamie]

Hi,

I was wondering about using something like a "wavefront curvature
sensor" to measure stellar distances without requiring parallax:

http://en.wikipedia.org/wiki/Wavefront_curvature_sensor

The curvature of the wavefronts of light from stars is proportional to
the distance to the star. As the light from a star travels it becomes
more and more like a plane wave the further it travels:

http://en.wikipedia.org/wiki/Plane_wave

A perfect plane wave wouldn't follow the inverse square law, but would
propagate all energy in a directed beam like a perfect laser. A
wavefront with low curvature would also not follow the inverse square
law over a given distance, proportional to the curvature of the wavefront.

Is there a way to build an instrument that could detect the wavefront
curvature accurately enough to deduce the stellar distance? I was
thinking of using a pinhole to restrict the incoming light to a single
star, and then measuring the intensity of the light 1 meter from the
pinhole, but the pinhole itself will destroy the near planar wavefront
curvature of the light.

Could a crystal be put in the output section of the pinhole to maintain
the wavefront curvature of the star's light? If the light can be
restricted to a single star and the wavefront curvature can be
maintained, then it should be possible to find the distance based on the
light intensity measured over a distance.

cheers,
Jamie

 

[Bill Gill]

Hi,

I was wondering about using something like a "wavefront curvature
sensor" to measure stellar distances without requiring parallax:

http://en.wikipedia.org/wiki/Wavefront_curvature_sensor

The curvature of the wavefronts of light from stars is proportional to
the distance to the star. As the light from a star travels it becomes
more and more like a plane wave the further it travels:

http://en.wikipedia.org/wiki/Plane_wave

A perfect plane wave wouldn't follow the inverse square law, but would
propagate all energy in a directed beam like a perfect laser. A
wavefront with low curvature would also not follow the inverse square
law over a given distance, proportional to the curvature of the wavefront.

Is there a way to build an instrument that could detect the wavefront
curvature accurately enough to deduce the stellar distance? I was
thinking of using a pinhole to restrict the incoming light to a single
star, and then measuring the intensity of the light 1 meter from the
pinhole, but the pinhole itself will destroy the near planar wavefront
curvature of the light.

Could a crystal be put in the output section of the pinhole to maintain
the wavefront curvature of the star's light? If the light can be
restricted to a single star and the wavefront curvature can be
maintained, then it should be possible to find the distance based on the
light intensity measured over a distance.

cheers,
Jamie

My first thought is that the wavefront from even the closest star
would be almost a perfect plane by the time it gets to Earth. There
would not be any place close to enough curvature to be able to
measure it. Keep in mind that Proxima Centauri has a distance of
4.2 light years. With a radius of 4.2 light years the angle that
you could reasonably subtend from the Earth is going to approach 0.
And remember that Proxima Centauri is close. Any other stars
would just get worse.

Bill

 

[Jamie]

My first thought is that the wavefront from even the closest star
would be almost a perfect plane by the time it gets to Earth. There
would not be any place close to enough curvature to be able to
measure it. Keep in mind that Proxima Centauri has a distance of
4.2 light years. With a radius of 4.2 light years the angle that
you could reasonably subtend from the Earth is going to approach 0.
And remember that Proxima Centauri is close. Any other stars
would just get worse.

Hi,

Ya, the measurement precision might make it impossible to do even if the
star's wavefront could be isolated to begin with. Maybe there is a way
to "amplify" the wavefront a known amount with optics to make it less
planar a precise amount before doing the intensity over distance
measurement?

I don't know enough about optics to know if something like that exists.

cheers,
Jamie

 

[[email protected]]

Hi,

I was wondering about using something like a "wavefront curvature
sensor" to measure stellar distances without requiring parallax:

http://en.wikipedia.org/wiki/Wavefront_curvature_sensor

The curvature of the wavefronts of light from stars is proportional to
the distance to the star. As the light from a star travels it becomes
more and more like a plane wave the further it travels:

http://en.wikipedia.org/wiki/Plane_wave

A perfect plane wave wouldn't follow the inverse square law, but would
propagate all energy in a directed beam like a perfect laser. A
wavefront with low curvature would also not follow the inverse square
law over a given distance, proportional to the curvature of the wavefront.

If we are talking about ordinary stars, I do not understand how this
could form a wavefront. After all, typical stellar radiation consists
of black body radiation by individual sources at certain temperature,
with the typical spectrum distribution.


Regarding laser or actually astronomical maser sources, eVLBI stations
on different continents would certainly be able to do such
measurements, provided that individual cycles could somehow be
distinguished by some significant change in radiation.

 

[mike]

Hi,

I was wondering about using something like a "wavefront curvature
sensor" to measure stellar distances without requiring parallax:

http://en.wikipedia.org/wiki/Wavefront_curvature_sensor

The curvature of the wavefronts of light from stars is proportional to
the distance to the star. As the light from a star travels it becomes
more and more like a plane wave the further it travels:

http://en.wikipedia.org/wiki/Plane_wave

A perfect plane wave wouldn't follow the inverse square law, but would
propagate all energy in a directed beam like a perfect laser. A
wavefront with low curvature would also not follow the inverse square
law over a given distance, proportional to the curvature of the wavefront.

Is there a way to build an instrument that could detect the wavefront
curvature accurately enough to deduce the stellar distance? I was
thinking of using a pinhole to restrict the incoming light to a single
star, and then measuring the intensity of the light 1 meter from the
pinhole, but the pinhole itself will destroy the near planar wavefront
curvature of the light.

Could a crystal be put in the output section of the pinhole to maintain
the wavefront curvature of the star's light? If the light can be
restricted to a single star and the wavefront curvature can be
maintained, then it should be possible to find the distance based on the
light intensity measured over a distance.

cheers,
Jamie

How do you measure curvature with only one point measurement?
If you measure two points, isn't that an analog to parallax?

 

[Bill Gill]

SORRY; there is a star that is MUCH closer - in fact it is about eight
light minutes away from us.
And that is far enough to give us a rather planar wave.

Well, yes, but I don't think the OP was thinking of our sun.

Bill

 

[Martin Brown]

Better ways to measure distance to a star is to identify its type for
particular variable stars there is a known period luminosity
relationship - so measure how quickly it varies and you can work out how
bright it really is. Cepheids were the first such standard candles:

http://en.wikipedia.org/wiki/Cepheid_variable#Uncertainties_in_Cepheid_determined_distances

Measure how bright it appears you you get your distance. This is also
true for Type Ia supernovae which are visible over greater distances:

http://en.wikipedia.org/wiki/Cosmic_distance_ladder

How do you measure curvature with only one point measurement?

You don't. The experiment has already been done to measure apparent
stellar diameters of the brightest stars as seen from Earth.

First by Michelson & Pease in 1921 on the Hale 100" and later by
Hanbury-Brown & Twiss of Jodrell Bank using intensity interferometry
which is in effect a sensitive way of determining deviation of the
stellar wavefront from being an unresolved point source.

Optical astronomers are now applying the tricks and mathematics of radio
astronomy to optical wavelengths with excellent results.

http://en.wikipedia.org/wiki/Astronomical_interferometer

If you measure two points, isn't that an analog to parallax?

If you measure them simultaneously then it is interferometry.

It doesn't depend on the Earth's orbit diameter and is best suited to
measuring bright supergiants like Betegeuse where the usable baselines
of 20m - 200m are able to make a sensible determination.

Basically it is easier in general to let the satellites like Hipparcus
do the job of cataloguing of stellar positions.

Regards,
Martin Brown

 

[Jamie]

Maybe, one of these daze, you might learn something about physics.
*IF* and when that happens, you will know the (plural) stupidities in
your "query".

Hi,

There's no such thing as a stupid question, you agree?

cheers,
Jamie

 

[Jamie]

That line is one of my pet peeves. There are a whole lot of stupid
questions--probably a good quarter of the ones that get asked, if you
define stupid questions as those that the askers could have figured out
for themselves with a moment's thought.

Saying that there are no stupid questions is a fiction designed to get
people to talk in classroom settings--it's a promise that even if you
say something dumb, nobody will put you down for it. Getting people to
talk is the first requirement for a discussion, and even stupid
questions can help by eliciting better ones.

(It doesn't apply here, for all manner of reasons.)

Hi,

Don't forget stupid answers too

cheers,
Jamie