How did he get the fraction with fraction power? So we have a simple equation that is from Kepler.

Joshua Foley 2022-07-05 Answered
How did he get the fraction with fraction power?
So we have a simple equation that is from Kepler.
( r ¯ 1 r ¯ 2 ) 3 = ( T 1 T 2 ) 2
In an explanation of a physics book, you can resolve for r 2 like this:
r 2 = r 1 ( T 1 T 2 ) 2 / 3
And I found
r 1 = T 1 2 T 2 2 r 2 3 3
First question, is my approach correct? My second and main question is how did he get the r 2 equation that I stated first. The physics book doesn't explain how to get from the main equation to r 2 = r 1 ( T 1 T 2 ) 2 / 3 . Can someone explain me, please? (By the way, of course the equation for r 1 and r 2 should be different).
Thank you!
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Answers (1)

Karla Hull
Answered 2022-07-06 Author has 20 answers
Your equation looks good. Check this out:
r 1 = T 1 2 T 2 2 r 2 3 3 = r 2 3 3 ( T 1 T 2 ) 2 3 = r 2 ( T 1 T 2 ) 2 3
Now all you need to know is that x a b is defined as x a b
Does that help?

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