Question

The ratio of Sun to Earth and Mars is 3: 4. The earth revolves around the sun once in 365 days. What is the period of the Earth's orbit around the Sun?​

Answer 1

Answer:

it take about 487 days to coplete its one rovolution

Explanation:

no. of days=365/3×4

=487

Answer 2

As we know, Kepler's Law of Period states that, if R is orbital radius and T is time period then:-

$:\implies\sf\red {{T^2\propto R^3}}$

Therefore,

$:\implies\sf{\left(\dfrac{T_1}{T_2}\right)^2=\left(\dfrac{R_1}{R_2}\right)^3}$

$:\implies\sf{\dfrac{T_1}{T_2}=\left(\dfrac{R_1}{R_2}\right)^{\dfrac{3}{2}}}$

$:\implies\sf{T_1=T_2\left(\dfrac{R_1}{R_2}\right)^{\dfrac{3}{2}}}$

Here,we are given Information :-

• $\sf{R_1:R_2=4:3}$

• $\sf{T_2=355\ days}$

So time period of the Earth's orbit around the Sun will be :-

$:\implies\sf{T_1=365\left(\dfrac{4}{3}\right)^{\dfrac{3}{2}}}$

$:\implies\sf{T_2=4\times 1.54\ days}$

$:\implies\underline{\underline\red{{\sf{T_1=561.95\ days}}}}$