Question

The formula to find the period of orbit of a satellite around a planet is T^2=(4pi^2/GM)r^3 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?

Answer 1

Answer:so whats the answer????

Step-by-step explanation:

Answer 2

The answer is $r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$

$T^{2} = \frac{4 \pi^{2}}{GM} r^{3}$

Move $\frac{4 \pi^{2} }{GM}$ to the other side of the equation:
$T^{2} /\frac{4 \pi^{2} }{GM} = r^{3} \\ T^{2} *\frac{GM}{4 \pi^{2} } = r^{3}$

Rearrange:
$r^{3} = T^{2} *\frac{GM}{4 \pi^{2} } \\ r^{3}= \frac{T^{2} *GM}{4 \pi^{2} } \\ r^{3}= \frac{GMT^{2}}{4 \pi^{2} } \\ r^{3} = GMT^{2}/4 \pi^{2}$

Since $x^{3}= \sqrt[3]{x}$, then
$r^{3} = GMT^{2}/4 \pi^{2} \\ r= \sqrt[3]{GMT^{2}/4 \pi^{2}}$