MadSci Network: Astronomy

Re: how much gravity (or mass) does it take to bend light, say ... one foot?

Date: Thu Sep 28 07:22:07 2000
Posted By: Meghan Gray, Grad student, Astronomy, Cambridge University
Area of science: Astronomy
ID: 969239382.As

Hi Dave,

Gravitational telescopes are already proving very useful in revealing distant galaxies at very high redshift, but the 'lenses' in question are clusters of galaxies with masses of the order of one hundred thousand billion times the mass of our sun and lying billions of light-years away. Not exactly what you'd call a manuverable telescope!

But let's consider what benefit we might get from a gravitational telescope within our solar system. Let's imagine that we could somehow gather up all the mass in the asteroid belt and use it as a gravitational lens to be observed from Earth. Although there are over 100000 asteroids, they only add up to 0.0005 times the mass of the Earth.

Rather than calculating how much mass would be required to bend light by one foot, a more useful number to calculate would be the *angular* width of the Einstein ring. This is where maximum magnification occurs, if the source and the lens are perfectly aligned (as in the case of galaxy B1938+666), and would be the 'best case' scenario for our telescope. If we assume that our asteroid telescope can be approximated by a point mass, then the Einstein radius would be given by

         ( 4*G*M*D_ds )
ER = sqrt( ---------- )
         ( c*c*D_d*D_s)

where G = gravitational constant
      M = mass of lens
      c = speed of light
      D_d = distance from Earth to lens
      D_s = distance from Earth to source
      D_ds = distance between lens and source
             (we can assume D_ds = D_s - D_d, which isn't always the case
              at cosmological distances)

In the case of our asteroid telescope, where M=0.0005*M_earth and D_d << 1
pc, the Einstein radius for a typical star elsewhere in our Galaxy (D_s ~
10 kpc) would be

ER = 9.71 x 10**(-10) degrees
   = 3.49 x 10**(-6)  arcseconds  (that's pretty small)

To put this into perspective, the resolution of the Hubble Space Telescope would have to be 14 000 times better to resolve this. To make things more difficult, the telescope itself would probably have an angular size much greater than this, which makes it impossible to see the lensed image in the first place (and tells us that the point mass approximation wasn't such a good idea)!

Now we haven't touched on the energy requirements to round up all the asteroids and assemble them into a telescope, let alone maneuvere them into position within the solar system to align them precisely with the object of interest. The benefits of this system are pretty small as well: we could only look at objects within our own galaxy, and the relatively weak boost given by such a small gravitational telescope would, I think, not be worth the effort!

Gravitational lensing studies within our galaxy are taking place using ground based telescopes, but these microlensing searches are more interested in the objects doing the lensing than those being lensed. They are using the changing magnification of distant stars to detect dark objects (sometimes called "MACHOS") throughout the galaxy.

Hope this helps!

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