Talk-Polywell.org

Rereading the article about the first measurement of the speed of gravity made 8 years ago by observing the transit of Jupiter in front of a quasar, some questions came to my mind, out from pure curiosity.

That measure was made using the National Science Foundation's Very Long Baseline Array (VLBA). It's maximum base line is about 8.600 km, and max angular resolution goes from 0.17 milliarcsecond at 7 mm wavelengths, to 22 mas at 900 mm.

What'd be the angular resolution of a super-VLBA using as baseline the ~259E6 km separating the earth lagrange points L4 and L5?

With that kind of resolution, what would be the precision of another measurement of the gravity speed using the same method (the mentioned one was ~20%)?

And, would it be enough to tell apart an earth-sized planet 1 UA from its sun at a distance of a few light years from us?

You have to knowledge that two more telescopes at L4 and L5 would complement very nicely the projected infrared James Webb Observatory at L2.

Anyone?


edit Oct 9, 2011: sorry, not speed of light but of gravity

charliem wrote:Rereading the article about the first measurement of the speed of light made 8 years ago by observing the transit of Jupiter in front of a quasar, some questions came to my mind, out from pure curiosity.

Curiosity is the source of all our knowledge, consider yourself lucky to have it.

charliem wrote:What'd be the angular resolution of a super-VLBA using as baseline the ~259E6 km separating the earth lagrange points L4 and L5.

R=f*LAMBDA/B

R= Resolution in Milliarcseconds
f =2060 (more or less for the VLBA)
LAMBDA= Wavelength observed in cm
B= Baseline in Km


Throw inside your numbers and you get:
R = 5,57E-6 mas for 7 mm wavelengths
R = 7.16E-4 mas for 900 mm wavelengths

Unless I made a mistake somewhere, at 10 Ly (9.5E16 mt) this gives us a very very very very theoretical resolution spot size of about :

2*9.5E16*Sin(R/(2*3600E3))=

Spot diameter at 7 mm = 2,6 Km
Spot diameter at 900 mm = 330 Km


In reality the final resolution will depend A LOT on the flux density of the signal as well as from a plethora of other variables that I will not even start to mention as it will take a good couple of pages just to list them.
But one important issue worth mentioning is the number of baselines available. With only one telescope in orbit you will have a poor/useless resolution. Placing 10 of them at different Lagrangian... well... enough to say that I droll just to the thought of it

Edited to fix a wrong symbol definition.

Thanks a lot Giorgio.

Wow. That's even better than I thought.

¡¡A resolution of 2.6 to 330 km at 10 light-years from earth!!

Makes me drool too.

And yes, 10 telescopes (or 50) distributed throughout the earth orbit (or Jupiter's) would, definitely, be much better. Problem is that only L4 and L5 are stable. Even L2, where they are planning to place the James Webb, is a metastable position, and that implies higher operational costs and a shorter lifespan for the instrument (at least L2 is relatively close, so a manned mission to refurbish it, in the Hubble's way, would not be that expensive).

How about a little constellation of telescopes orbiting around L4 and L5?

And some other instruments out of the ecliptic would also be nice, but I suspect that we are gonna have to start it easy and slow...

Who knows, if Elon Musk can indeed take down the launch price per kg to the hundreds of dollars, a whole new world of possibilities opens up.

Bye the way, first we'd have to send a mission to "clean up", cause most probably those two points have to have gathered more dirt than an old carpet.

charliem wrote:Who knows, if Elon Musk can indeed take down the launch price per kg to the hundreds of dollars, a whole new world of possibilities opens up.

That's probably the only real hope we have to ever see a project like this realized.

charliem wrote:Bye the way, first we'd have to send a mission to "clean up", cause most probably those two points have to have gathered more dirt than an old carpet.

I think there has already been a survey of the Lagragian points and they was found to be clean.
I might be wrong on this, I will have to go back and research to see if I remember correctly.

The solar system is essentially empty space, but for some things it looks a bit overcrowded:

http://cfa-www.harvard.edu/iau/Animations/Middle.gif

About earth companions: Earth Lagrange/Trojan asteroids

And: Earth's first Trojan asteroid: 2010 TK7

Giorgio, just one little doubt about your formula for the resolution. R is in milli or microarcseconds?

charliem wrote:Giorgio, just one little doubt about your formula for the resolution. R is in milli or microarcseconds?

It's MilliArcSeconds, The calculations are correct, but I wrote Micro in the symbol description of the first post. I will re-edit it to make it correct.

Thanks for pointing it out