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Look up Jerry Waxmans “Workbook for Astronomy”. When I did HSC physics there was 1 term of astronomy covering the origins of the calendar, orbital motion from Copernicus to the material in Newton’s Principia, 20th century astronomy.
The experiments were very close to those in waxmans book.
If you don’t have it, get a copy of Principia, much of it is still useful.
For the kids really into maths there are some good books on calculating astronomical phenomena by Duffet-Smith and Jan Meeus; these require no more than trig (lots of it).
If you can show them how to predict something they can confirm with their own eyes at night I suggest that’s about as good as it gets in terms of scientific method. Could he as simple as sunrise/set, moon rise/set, or an alignment of the planets. Showing them these things are real and that maths works is a huge part.
It’s feasible to determine the orbit of mars with the help of a modest digital camera, or the height of Mt Piton, or even measure the speed of light over 6 months by timing jupiters moons.
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