Answer:
Tp/Te = 2
Therefore, the orbital period of the planet is twice that of the earth's orbital period.
Explanation:
The orbital period of a planet around a star can be expressed mathematically as;
T = 2Ļā(r^3)/(Gm)
Where;
r = radius of orbit
G = gravitational constant
m = mass of the star
Given;
Let R represent radius of earth orbit and r the radius of planet orbit,
Let M represent the mass of sun and m the mass of the star.
r = 4R
m = 16M
For earth;
Te = 2Ļā(R^3)/(GM)
For planet;
Tp = 2Ļā(r^3)/(Gm)
Substituting the given values;
Tp = 2Ļā((4R)^3)/(16GM) = 2Ļā(64R^3)/(16GM)
Tp = 2Ļā(4R^3)/(GM)
Tp = 2 Ć 2Ļā(R^3)/(GM)
So,
Tp/Te = (2 Ć 2Ļā(R^3)/(GM))/( 2Ļā(R^3)/(GM))
Tp/Te = 2
Therefore, the orbital period of the planet is twice that of the earth's orbital period.
