Question

The orbital period of Jupiter is 11.86 years. What is its distance from the sun?
a. 3.7 AU
b. 5.2 AU
c. 37 AU
d. 52 AU

Answer 1

I just did the test and the answer is C.

Answer 2

Answer:

The distance between the sun and the Jupiter is 5.2 AU.

Explanation:

It is given that,

The orbital time period of Jupiter, $T=11.86\ years$

Since, $1\ year=3.15\times 10^7\ s$

$11.86\ year=3.74\times 10^8\ s$

We need to find the distance from the sun. It can be calculated using Kepler's third law. It is mathematically given by :

$T^2=\dfrac{4\pi^2}{GM}a^3$

a = distance from sun

G universal gravitational constant

M is the mass of sun

$a^3=\dfrac{T^2GM}{4\pi^2}$

$a^3= \dfrac{(3.74\times 10^8\ s)^2\times 6.67\times 10^{-11}\times 1.98\times 10^{30}}{4\pi^2}$

$a=7.763\times 10^{11}\ m$

Since, $1\ AU=1.496\times 10^{11}\ m$

So, $a=(\dfrac{7.763\cdot10^{11}}{1.496\cdot10^{11}})\ AU$

a = 5.189 AU

or

a = 5.2 AU

So, the distance from the sun is 5.2 AU. Hence, the correct option is (b).