Mathematics

Question

The formula to find the period of orbit of a satellite around a planet is where r is the orbit’s mean radius, M is the mass of the planet, and G is the universal gravitational constant. If you are given all the values except r, how do you rewrite the formula to solve for r?

2 Answer

  • From my website, I have an online Kepler's Third Law calculator. 
    The formula is G · m · t² = 4 · π² · r³
    I had to solve I have the formula solved for 'r', 't' and 'm' and I made a graphic of all three formulas. (see attached).
    Anyway, since the formula is G · m · t² = 4 · π² · r³ then we can solve for 'r'

    r³ = (G · m · t²) / (4 · π²) and therefore
    r = 
    cube root [(G · m · t²) / (4 · π²)]

  • Answer:

    r=

    Step-by-step explanation:

    4 PIE SQUARED[tex]\sqrt[3]{\frac{GMT^{2} }{4\pix^\pi {2}  } }[/tex]

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