E aí, Ismael
Aplicando-se a
3ª Lei de Kepler para os dois satélites, temos:
[tex3]\frac{ \text{r}^3 }{ \text{T}^2 } = \text{K}[/tex3]
Assim,
[tex3]\begin{cases}
\text{Satélite X}: \quad {\Large\frac{ \text{r}^3 }{ \text{T}^2 }} = \text{K} \,\,\,\, \Rightarrow \,\,\,\, {\Large\frac{ (7\text{r})^3 }{ 1 }} = \text{K} \quad {\color{RawSienna}\text{(I)}} \\\\
\text{Satélite Y}: \quad {\Large\frac{ \text{r}^3 }{ \text{T}^2 }} = \text{K} \,\,\,\, \Rightarrow \,\,\,\, {\Large\frac{ \text{r}_{\text{Y}}^3 }{ (8)^2 } } = \text{K} \quad {\color{RawSienna}\text{(II)}}
\end{cases}[/tex3]
Dividindo-se [tex3]{\color{RawSienna}\text{(II)}}[/tex3]
por [tex3]{\color{RawSienna}\text{(I)}}, \,[/tex3]
vem:
[tex3]343\text{r}^3 = \frac{\text{r}_{\text{Y}}^3}{64} \,\,\,\, \Rightarrow \,\,\,\, \boxed{\text{r}_{\text{Y}} = 28\text{r}}[/tex3]