How much solar energy concentrates at Jupiter's focal point via gravitational lensing?

Question

How much solar energy concentrates at Jupiter's focal point via gravitational lensing?

Answer 1

Solar energy - from our Sun at Jupiter's focal distance? A negligible amount. Gravitational lensing doesn't have a focal point so much as a focal region that begins roughly at a point, and that point (which really shouldn't be called a focal point) can be calculated, ProfRob gives the formula here.

Jupiter's gravitational lensing distance is so far (about 10 times the Sun's or about 5500 astronomical units), that Jupiter essentially appears 1/10th the size of the Sun from that distance, so it doesn't really work at focusing the Sun's rays. You still get a lot more light direct from the Sun, which at that distance, would just be the brightest dot in the sky, with Jupiter blocking more light than it lenses in the observer's direction. You get more light from the Sun when Jupiter isn't blocking the sun at that distance.

Gravitational lensing works best when the lensing object is either very massive, so it pulls in light from a sizable area, or if it's larger than the object that's being studied. That is, You could use Jupiter's gravitational lensing to study an exoplanet, which is incredibly tiny to our observation light years away, but the gravitational bending of light by Jupiter gives a very distorted image of the incredibly tiny/distant object, but that distorted image would have a great deal more information. In that scenario, Jupiter would focus much more light from the very distant, very dim object, but only because the object is effectively so small by our observation.

Maybe somebody here knows how to run the math for gravitational lensing brightness, but it varies on how pin-point the object you want to get a better look at is, so it's not a simple one line formula.

With the case of the Sun and Jupiter, the Sun being larger, it doesn't really work. A black hole could image something larger than itself, but a black hole bends a lot more light than Jupiter does and it's so called "focal point" begins much closer.

A magnifying glass, which focuses sunlight to a point (and this only works because the sun is so distant that the rays of light are essentially parallel), that focused sunlight can never be hotter than the surface of the Sun itself. That's a law (xkcd did a nice bit about that)

The focused (but very blurred) image that a planet makes at it's gravitational lensing point wouldn't come close to hot enough to cook ants, if that's your goal. A better way to think about it would be looking through a telescope, but the image is spread out into a ring but not that bright. Maybe with a perfect scenario, like a black hole or neutron star and a star in the distance, you might get some brightness, but still much less concentration than a magnifying glass can give you because it doesn't focus at a point, it's more of a range.

If you make your question more specific, somebody might be able to give you a more exact mathematical answer.