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According to Wikipedia, as of November 1, 2021, 4,864 extrasolar planets have been identified. One of the closest multiple-planet solar systems to our own is around the star Gliese 876, about 15 light-years away, and it contains four planets. One takes 65.0 Earth days to revolve, at a distance of 3.17 x 107 kilometers from Gliese 876. Another planet takes 123 Earth days to revolve. How far is this second planet from Gliese 876? Include units in your answer.

User Juergen D
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In order to calculate the distance from the second planet to Gliese 876, we can use the third law of Kepler:


(D^3)/(T^2)=k

Where D is the distance and T is the period of translation.

Since k is a constant, we can write the following equation:


(D^3_1)/(T^2_1)=(D^3_2)/(T^2_2)

Using D1 = 3.17*10^7 km, T1 = 65 days and T2 = 123 days, let's calculate D2:


\begin{gathered} ((3.17\cdot10^7)^3)/(65^2)=(D^3_2)/(123^2) \\ (31.855\cdot10^(21))/(4225)=(D^3_2)/(15129) \\ D^3_2=(31.855\cdot10^(21)\cdot15129)/(4225) \\ D^3_2=114.067\cdot10^(21) \\ D_2=\text{4}.85\cdot10^7\text{ km} \end{gathered}

Therefore the wanted distance is 4.85 * 10^7 km.

User Andre Elrico
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