Respuesta :
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 :
[tex]T^2=\dfrac{4\pi^2}{GM}a^3[/tex]
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, [tex]T^2=\dfrac{4(3.14)^2}{6.67\times 10^{-11}\times 1.99\times 10^{30}}(1.43\times 10^{12})^3[/tex]
[tex]T=\sqrt{8.688\times 10^{17}}\ s[/tex]
[tex]T=932094415.818\ s[/tex]
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
