How much energy from the Sun could we get if we use Jupiter as a gravitational or atmospheric lens?

How much energy (watts) from sunlight could arrive to the focal point if we use Jupiter as a gravitational lens? and if we use it as an atmospheric lens by using refraction?

How far the focal point would have to be placed for each case?

Ps.: if no energy reached the focal point, then how much energy would reach if we use the Earth instead of Jupiter (with sunlight)?

• None: Jupiter's gravity is millions of times to small and its atmosphere is too opaque. Commented Oct 17, 2020 at 15:42
• Jupiter in Lagrange point L1 will hardly lens some sunlight but instead block it. Maybe a fictional solution to global warming if we knew a way to put Jupiter between earth an sun. But if we ever knew, moving earth in a farther orbit would be comparably much easier. Commented Oct 17, 2020 at 17:35
• @GyroGearloose - Put Jupiter at the L2 Lagrange point, and cover it with mirrors? Commented Oct 17, 2020 at 17:38
• @mmesser314 much easier to surround earth orbit with mirrors, if you really want to heat up earth. BTW, what about putting thus mirrors around Venus, boiling its atmosphere at least some part into space? Commented Oct 17, 2020 at 17:42

A lens deflects light rays, bringing them to a focus. A gravitational lens is typically a galaxy or cluster of galaxies. A galaxy typically has trillions of stars.

The sun deflects light rays a little. See How the Sun Warps Starlight, or Gravitational deflection of light. A ray that skims its surface is deflected by about 1.8 arcsec. These rays would come to a focus 542 AUs away. This is far outside the solar system, about 15 times farther away than Pluto.

The deflection by Jupiter would be far less. The Sun has 1000 times the mass of Jupiter, and the surface gravity is 11 times stronger.

The deflection of starlight by Jupiter is predicted to be 0.00119 arcsec and measured to be just about exactly that. This deflection is about 1500 times smaller than the Sun's. The focal length is 13 light years.

Of course, this is just the rays that skim the surface of Jupiter. Rays that pass it farther away are less deflected, and meet even farther away.

So this isn't a good way to get more energy from the Sun. To use it, you would have to go to the focus, 13 light years away. At that distance, the Sun would be just a dim star. It would be slightly less dim if you were exactly at the focus than if you were nearby. You get a lot more energy from being on Earth, which is much closer to the Sun.

• Thanks for your answer. And by using the earth to gather Sunlight using atmospheric refraction, how far the focal point would it be? also little energy would reach the focal point?
– user277436
Commented Oct 17, 2020 at 18:44