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# if I have the velocity of the planetary orbit and the mass of the sun, how do I get the radius of the orbit?

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if I have the velocity of the planetary orbit and the mass of the sun, how do I get the radius of the orbit? I have v=root GM/r or

velocity of 2x10^4 m/s = root of 6.67x10^-11 x 2 x 10^30 kg over the radius. I am learning math all over since I retired so I can enjoy astrophysics

Aug 20, 2015

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You know jwveverka you probably not have to learn maths all over. The maths on Earth is the same as the maths in outer space.

Maybe maths is different in Brazil though

Aug 20, 2015

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v = √(G*M/r) can be rewritten as v2 = G*M/r, which can then be rearranged as r = G*M/v2

$${\mathtt{r}} = {\frac{{\mathtt{6.67}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left(-{\mathtt{11}}\right)}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{\left({\mathtt{30}}\right)}}{{\left({\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{4}}}\right)}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{r}} = {\mathtt{333\,500\,000\,000}}$$

r = 3.335*1011 m

.

Aug 20, 2015
#2
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