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ANTONII [103]
3 years ago
12

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?
Mathematics
2 answers:
Bess [88]3 years ago
5 0

Answer:so whats the answer????

Step-by-step explanation:

Natalija [7]3 years ago
3 0
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}}
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