The distance of planet Jupiter from the sun is 5.2 times that of the Earth. Find the period of revolution of Jupiter around the sun.
Answers
✧ Distance of planet Jupiter from the Sun is 5.2 times that of the earth.
✧ Period of revolution of Earth around the sun = 1 year
Period of revolution of Jupiter around the sun, = ?
Now, We know that :
By substituting values :
\large \underline{\underline{\bf{ \pink{Given : }}}}
Given:
\begin{gathered}\\\end{gathered}
✧ Distance of planet Jupiter from the Sun is 5.2 times that of the earth.
\sf : \implies r_j = 5.2 \times r_e:⟹r
j
=5.2×r
e
✧ Period of revolution of Earth around the sun = 1 year
\sf : \implies T_e = 1 \: year:⟹T
e
=1year
\begin{gathered}\\\end{gathered}
\large \underline{\underline{\bf{ \pink{To \: Find :}} }}
ToFind:
\begin{gathered}\\\end{gathered}
Period of revolution of Jupiter around the sun, \sf T_jT
j
= ?
\begin{gathered}\\\end{gathered}
\large \underline{\underline{\bf{ \pink{Solution : }}}}
Solution:
\begin{gathered}\\\end{gathered}
Now, We know that :
\dag \underline{\boxed{\pink{\bf \dfrac{T_j ^2}{T_e ^2} = \dfrac{r_j ^3}{r_e ^3}}}}†
T
e
2
T
j
2
=
r
e
3
r
j
3
\begin{gathered}\\\end{gathered}
\sf : \implies T_j = T_e\Bigg( \dfrac{r_j}{r_e}\Bigg)^{\frac{3}{2}}:⟹T
j
=T
e
(
r
e
r
j
)
2
3
\begin{gathered}\\\end{gathered}
By substituting values :
\sf : \implies T_j = 1 \times \Bigg( \dfrac{5.2 r_e}{r_e}\Bigg)^{\frac{3}{2}}:⟹T
j
=1×(
r
e
5.2r
e
)
2
3
\sf : \implies T_j = \Bigg( \cancel{\dfrac{5.2 r_e}{r_e}}\Bigg)^{\frac{3}{2}}:⟹T
j
=(
r
e
5.2r
e
)
2
3
\sf : \implies T_j = (5.2)^{\frac{3}{2}}:⟹T
j
=(5.2)
2
3
\sf : \implies T_j = 11.86 (approx.):⟹T
j
=11.86(approx.)
\begin{gathered}\\\end{gathered}
\underline{\boxed{\pink{\bf T_j = 11.86\: years \: (approx.)}}}
T
j
=11.86years(approx.)
\begin{gathered}\\\end{gathered}
\underline{\textsf{Hence, Period of revolution of Jupiter around the Sun is approximately \pink{11.86 years}}}
Hence, Period of revolution of Jupiter around the Sun is approximately 11.86 years