Answer:
Time period of the planet is
[tex]T_2 = 278.7 years[/tex]
Explanation:
As we know by Kepler's law of time period
square of time period of planet is proportional to the cube of its orbital radius
[tex]\frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3}[/tex]
here we know for Earth
[tex]T_1 = 1 year[/tex]
[tex]R_1 = 1.5 \times 10^{11} m[/tex]
now we have
[tex]\frac{1^2}{T_2^2} = \frac{(1.5 \times 10^{11})^3}{(6.4 \times 10^{12})^3}[/tex]
[tex]T_2^2 = 7.77 \times 10^4[/tex]
[tex]T_2 = 278.7 years[/tex]
The time period of the planet will be "278.7 years".
We know,
By using the Kepler's law, we get
→ [tex]\frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3}[/tex]
By substituting the values, we get
→ [tex]\frac{1^2}{T_2^2} = \frac{(1.5\times 10^{11})^3}{(6.4\times 10^{12})^3}[/tex]
By applying cross-multiplication, we get
→ [tex]T_2^2 = 7.77\times 10^4[/tex]
→ [tex]T_2 = 278.7 \ years[/tex]
Thus the above approach is correct.
Learn more:
https://brainly.com/question/14539831
