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No, a "simple calculator" is the four-function beast I bought in 1973 for $100. Today's calculators and PDAs have huge memory sizes and sophisticated programming, but again we're talking about apples and oranges.
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Oh, man, you're taking me back! 1973, a TI calculator, with a Square Root function! I was in heaven!
I used it to simulate orbits, using the very, very simplest model of duplicating the previous velocity vector and adding a gravity vector. I drew the niftiest little ellipses and occasional hyperbolas.
Our cosmic correspondent could do better with a four-banger with square root, and an honest approach to the facts, than with the entire resources of the internet and a closed mind.
BTW, I think I know most of the answers to your quiz on orbits, but there were a couple of questions that I might have gotten wrong. Post the answers, please!
Silas