The moon as a gravitational lens

I read a suggestion to use the sun as a gravitational lens to directly
image extra-solar planets. However, the discussion said that the focal
point would be about 600 million miles from the sun which is beyond the
orbit of Jupiter and not readily accessible.
SO........what about a smaller diameter gravity lens like
say...........our moon?
Unfortunately, I can find no reference to the focal distance in terms
of the lens mass and diameter. Can anyone help?
Of course, the effective aperture might be small but the resolution
would be equal to a lunar diameter lens.......

Frogwatch wrote:
I read a suggestion to use the sun as a gravitational lens to directly
image extra-solar planets. However, the discussion said that the focal
point would be about 600 million miles from the sun which is beyond the
orbit of Jupiter and not readily accessible.
SO........what about a smaller diameter gravity lens like
say...........our moon?
Unfortunately, I can find no reference to the focal distance in terms
of the lens mass and diameter. Can anyone help?
Of course, the effective aperture might be small but the resolution
would be equal to a lunar diameter lens.......

Another web reference said that all photon energies are lensed equally
which seems odd to me, sorta like a blade of grass defelcting a ping
pong ball and cannonball equally. However, if this is correct, we
might have a way to make a high resolution gamma ray telescope.

On Wed, 10 Jan 2007, Frogwatch wrote:

I read a suggestion to use the sun as a gravitational lens to directly
image extra-solar planets. However, the discussion said that the focal
point would be about 600 million miles from the sun which is beyond the
orbit of Jupiter and not readily accessible.
SO........what about a smaller diameter gravity lens like
say...........our moon?

The focal length is 1.45 google light years.

Unfortunately, I can find no reference to the focal distance in terms
of the lens mass and diameter. Can anyone help?
Of course, the effective aperture might be small but the resolution
would be equal to a lunar diameter lens.......

William Elliot a écrit :
On Wed, 10 Jan 2007, Frogwatch wrote:


I read a suggestion to use the sun as a gravitational lens to directly
image extra-solar planets. However, the discussion said that the focal
point would be about 600 million miles from the sun which is beyond the
orbit of Jupiter and not readily accessible.
SO........what about a smaller diameter gravity lens like
say...........our moon?


The focal length is 1.45 google light years.

Can you explain how did you calculate that?

Thanks

Frogwatch wrote:
Frogwatch wrote:
I read a suggestion to use the sun as a gravitational lens to directly
image extra-solar planets. However, the discussion said that the focal
point would be about 600 million miles from the sun which is beyond the
orbit of Jupiter and not readily accessible.

The closest focal length of the gravitational lens of the sun is 570
Astronomical Units away. This is WAY further than merely "beyond the
orbit of Jupiter".

SO........what about a smaller diameter gravity lens like
say...........our moon?

The less massive the object, the FARTHER away the gravitational focus.

Unfortunately, I can find no reference to the focal distance in terms
of the lens mass and diameter. Can anyone help?

Sure.
D = c^2 R^2/(4GM)

Of course, the effective aperture might be small but the resolution
would be equal to a lunar diameter lens.......

Another web reference said that all photon energies are lensed equally
which seems odd to me, sorta like a blade of grass defelcting a ping
pong ball and cannonball equally.

A ping-pall ball and a cannonball fall at identical accelerations in a
gravitational field, so it's clear that gravitational focussing is
independent of mass.

--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis

In article .com,
Geoffrey A. Landis wrote:

Sure.
D = c^2 R^2/(4GM)


Definitions, please. D = distance, R radius of the lensing
object?


Back when there was buzz about Heimian physics

ritual admission that it has all the earmarks of crackpottery
and more.

I suggested that one use for an FTL ship would be to put telescopes
in orbit around white dwarfs, to use them as lenses.

I think I may have been wrong, though. It seems to me that as long
an orbital period as possible would be good, so a short focal length isn't
all that useful.
--
http://www.cic.gc.ca/english/immigrate/
http://www.livejournal.com/users/james_nicoll
http://www.cafepress.com/jdnicoll (For all your "The problem with
defending the English language [...]" T-shirt, cup and tote-bag needs)

James Nicoll wrote:
In article .com,
Geoffrey A. Landis wrote:

Sure.
D = c^2 R^2/(4GM)


Definitions, please. D = distance, R radius of the lensing
object?


Back when there was buzz about Heimian physics

ritual admission that it has all the earmarks of crackpottery
and more.

I suggested that one use for an FTL ship would be to put telescopes
in orbit around white dwarfs, to use them as lenses.

I think I may have been wrong, though. It seems to me that as long
an orbital period as possible would be good, so a short focal length isn't
all that useful.
--
http://www.cic.gc.ca/english/immigrate/
http://www.livejournal.com/users/james_nicoll
http://www.cafepress.com/jdnicoll (For all your "The problem with
defending the English language [...]" T-shirt, cup and tote-bag needs)

For Geoffrey Landis:

Thanks for the focal length equation. Perhaps the book I read about
the focal lrength of a solar gravitational lens being 600 million miles
is wrong because your equation has it going as the diameter squared and
inversely prop to mass. I'd have expected a more reasonable focal
distance from this but I'll plug in the numbers.

So.........we find ourselves a low mass black hole whose event horizon
is very small. The focla length drops faster with radius than with
mass so it doesnt have to be too massive. Then we use them as gamma
ray lenses.............

Geoffrey A. Landis wrote:
[the equation for focal length of a gravitational lens is]
D = c^2 R^2/(4GM)

(James Nicoll) asked:
Definitions, please. D = distance, R radius of the lensing
object?

Right. And M the mass of the lensing object, G is the universal
gravitational constant, and c the speed of light.

The bending of a light ray grazing the surface is proportional to the
gravitational acceleration at the surface, so the focal length must be
inversely proportional to the surface acceleration. In fact, if you
note that the surface acceleration a_surface = GM/r^2, that equation is
simply:

D = (1/4) c^2/a_surface

... I suggested that one use for an FTL ship would be to put telescopes
in orbit around white dwarfs, to use them as lenses.

Do keep in mind that a gravitational lens works as a light-bucket, but
it doesn't image.

(or rather, it forms a virtual image that is so huge that it is far
larger than any practical focal plane.)

--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis