Question

g Two planets are in circular orbits around a star of with unknown mass. One planet is orbiting at a distance r1=150×106 km and has an orbital period T1=240 days. The second planet has an orbital radius r2=230×106 km. Find the orbital period of the second planet T2.

Answer 1

Answer:

456 days.

Explanation:

Given,

r₁ = 150 x 10⁶ Km

r₂ = 230 x 10⁶ Km

T₁ = 240 days

T₂ = ?

Using Kepler's law

$T^2\ \alpha \ r^3$

Now,

$\dfrac{T_2^2}{T_1^2}=\dfrac{r_2^3}{r_1^3}$

$T_2=\sqrt{T_1^2\times \dfrac{r_2^3}{r_1^3}}$

$T_2=\sqrt{240^2\times \dfrac{(230\times 10^6)^3}{(150\times 10^6)^3}}$

$T_2 = 455.68\ days$

Time taken by the second planer is equal to 456 days.

Answer 2

Answer:

Time period of second planet will be 126.40 days

Explanation:

We have given radius of first planet $r_1=150\times 10^6km=150\times 10^9m$

Orbital speed of first planet $T_1=240days$

Radius of second planet $r_2=230\times 10^6km=230\times 10^9m$

We have to find orbital period of second planet

Period of orbital is equal to $T=2\pi \sqrt{\frac{r^3}{G(M_1+M_2)}}$

From the relation we can see that $T=r^{\frac{3}{2}}$

$\frac{T_1}{T_2}=(\frac{r_1}{r_2})^\frac{3}{2}$

$\frac{240}{T_2}=(\frac{150\times 10^9}{230\times 10^9})^\frac{3}{2}$

$T_2=126.40 days$

Time period of second planet will be 126.40 days