What would you be most likely to find if you returned to the solar system in 10.0 billion years?

We will find nothing

Explanation:

Our sun is a third generation star, it has been transforming hidrogen in helium in a nuclear fusion reaction (640 millons of tons of hidrogen into 600 millions of tons of helium per second) the difference 40 millions of tons are realese as energy, from that energy Planet earth recieves 25 000000 KW/sq. mile at outside our atmosphere (Solar Constant) which implies 1000 w/m² at ground level.

The proccess of tansfoming hidrogen into helium will continue until approximately 75 % of the sun nucleus become helium (approximately 4000 millions of years or 4 billion of years the sun (depending on its mass will probably expand maybe up to earth orbit we will find out that the solar system does not exist long time ago