Question

Saturn orbits the Sun at a distance of 1.43 × 1012 m. The mass of the Sun is 1.99 × 1030 kg.

Answer 1

The answer is A 29.6 Earth Years

Answer 2

Answer:

Saturn’s orbital period is 29.6 years

Step-by-step explanation:

It is given that,

The mass of the sun, m = 1.99 × 10³⁰ kg

Saturn orbits the sun at a distance of, a = 1.43 × 10¹² m

Using third law of Kepler's :

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

Where,

T is the orbital time period

G is the universal gravitational constant

M is the mass of the sun

a is the distance

So, $T^2=\dfrac{4(3.14)^2}{6.67\times 10^{-11}\times 1.99\times 10^{30}}(1.43\times 10^{12})^3$

$T=\sqrt{8.688\times 10^{17}}\ s$

$T=932094415.818\ s$

To convert seconds into year divide the time by 3.154 × 10⁷

So, T = 29.55 Years

or T = 29.6 Years

Hence, the Saturn's orbital period is 29.6 Earth years