Question

if the distance of the planet Jupiter from the sun is 5.2 times that of the earth calculate the period of Jupiter Revolution around the sun

Answer 1

The period of Jupiter Revolution around the sun is 11.85 years.

Explanation:

Let r is the radius of earth and r' is the radius of Jupiter. If the distance of the planet Jupiter from the sun is 5.2 times that of the earth such that,

$r'=5.2\times r$

We need to find the period of Jupiter Revolution around the sun. Using the Kepler's third law of motion to find it.

Time of earth,

$T=kr^{3/2}$............(1)

For Jupiter

$T'=kr'^{3/2}$...........(2)

Dividing equation (1) and (2) as:

$\dfrac{T}{T'}=(\dfrac{r}{r'})^{3/2}$

$\dfrac{T}{T'}=(\dfrac{r}{5.2r'})^{3/2}$

$T'=11.85\times T$

The time of revolution for earth is 1 year

So, $T'=11.85\ years$

So, the period of Jupiter Revolution around the sun is 11.85 years. Hernce, this is the required solution.

Learn more :

Kepler's third law of motion.

https://brainly.in/question/4970187

Answer 2

The period of Jupiter Revolution around the sun is 11.86 years.

Given:

$r_{J}=5.2 r_{e}$

To find:

$T_{J}=?$

Solution:

The time taken by the earth to complete one revolution around sun is one year.

$\mathrm{T}_{e}=1 \text { year }$

Now, the orbital period is given by the formula,

$\frac{\mathrm{T}_{J}^{2}}{\mathrm{T}_{e}^{2}}=\frac{r_{J}^{3}}{r_{e}^{3}}$

On taking square root on both sides, w get,

$\mathrm{T}_{\mathrm{J}}=\mathrm{T}_{e}\left(\frac{r_{\mathrm{J}}}{r_{\mathrm{e}}}\right)^{3 / 2}$

On substituting the value of the radius of earth, we get,

$\mathrm{T}_{\mathrm{J}}=1 \times\left(\frac{5.2 r_{e}}{r_{e}}\right)^{3 / 2}$

Thus, the time takes by the Jupiter to revolve around the sun is:

$\therefore \mathrm{T}_{\mathrm{J}}=11.86 years$