Question

the ratio of orbital radii of two satellites of a planet is 1:2.what is the ratio of their time period?

Answer 1

Answer:

Explanation:

Given The ratio of orbital radii of two satellites of a planet is 1:2.what is the ratio of their time period?

We know that from Kepler’s law we get

    T^2 is proportional to a^3 where a is the length of semi major axis.

T1^2 / T2^2 = a1^3 / a2^3

T1/T2 = √(a1 / a2)^3

T1 / T2 = (a1 / a2)^3/2

T1 / T2 = (1 / 2)^3/2

          = 1 / (√2)^3

         = 1 / 2√2

Answer 2

Answer:

$\frac{1}{2 \sqrt{2} }$

Explanation:

According to the question,

The ratio of orbital radii of two satellites of a planet is 1:2.

That is

$\frac{r_{1}}{r_{2}} = \frac{1}{2}$

From Kepler's law, we know that

Square of time period is Proportional to the cube of the length of semi major axis that is radius. That is

T² ∝ r³

Now,

$\frac{t_{1}^{2}}{t_{2}^{2}} = \frac{r_{1}^{3}}{r_{2}^{3}}\\\frac{t_{1}^{2}}{t_{2}^{2}} =(\frac{1}{2})^{3}\\\frac{t_{1}}{t_{2}} = (\frac{1}{2})^{\frac{3}{2}}\\\frac{t_{1}}{t_{2}} = \frac{1}{2\sqrt{2}}$

Hence, the ratio of their time period $\frac{1}{2 \sqrt{2} }$.