Answer :
Answer:
Time period of second planet will be 126.40 days
Explanation:
We have given radius of first planet [tex]r_1=150\times 10^6km=150\times 10^9m[/tex]
Orbital speed of first planet [tex]T_1=240days[/tex]
Radius of second planet [tex]r_2=230\times 10^6km=230\times 10^9m[/tex]
We have to find orbital period of second planet
Period of orbital is equal to [tex]T=2\pi \sqrt{\frac{r^3}{G(M_1+M_2)}}[/tex]
From the relation we can see that [tex]T=r^{\frac{3}{2}}[/tex]
[tex]\frac{T_1}{T_2}=(\frac{r_1}{r_2})^\frac{3}{2}[/tex]
[tex]\frac{240}{T_2}=(\frac{150\times 10^9}{230\times 10^9})^\frac{3}{2}[/tex]
[tex]T_2=126.40 days[/tex]
Time period of second planet will be 126.40 days
Answer:
456 days.
Explanation:
Given,
r₁ = 150 x 10⁶ Km
r₂ = 230 x 10⁶ Km
T₁ = 240 days
T₂ = ?
Using Kepler's law
[tex]T^2\ \alpha \ r^3[/tex]
Now,
[tex]\dfrac{T_2^2}{T_1^2}=\dfrac{r_2^3}{r_1^3}[/tex]
[tex]T_2=\sqrt{T_1^2\times \dfrac{r_2^3}{r_1^3}}[/tex]
[tex]T_2=\sqrt{240^2\times \dfrac{(230\times 10^6)^3}{(150\times 10^6)^3}}[/tex]
[tex]T_2 = 455.68\ days[/tex]
Time taken by the second planer is equal to 456 days.