telescope - Equation to find distance between objective and eyepiece

1 A.U. is same as infinity. The difference in terms of eyepiece position is infinitesimal, you can't measure it. Anything beyond a few kilometers away is pretty much "at infinity".

Regardless of that - from the practice of designing and building telescopes, calculations only offer you a starting point. You do the math, and the distance is 105 cm. But in practice lenses will deviate from the ideal focal length. Even if they didn't deviate at some temperature, put them in a cold environment, and the focal length will change a fraction of mm.

So take the calculations as a starting point, and build the instrument in such a way as to allow fine adjustments of the position of the eyepiece. There's a device called focuser that allows such fine adjustments. Or simply rely on friction to move the eyepiece back and forth until the image looks best, and hold it there.

When using the instrument in practice, you'll forget the ideal distance. What you will do is adjust the position of the eyepiece until the image looks best. You will do that every time you observe, and often multiple times during the same observation.

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If you want some math, take a look at the thin lens equation, and apply it to the objective lens.

f = focal length of the lens

o = distance from lens to object

i = distance from lens to image

Then the thin lens equation is:

1/f = 1/i + 1/o

i = 1/(1/f - 1/o)

If o = infinity, then i = f.

But what happens if o = 1 A.U.?

i = 1/(1/1 - 1/(1.5 * 10^11)) = 1.0000000000067 meters

The difference is something like 6.7 * 10^-12 meters. It's smaller than an atom.