To calculate the time it takes for a planet to revolve around a star, we can use Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit. In this case, the semi-major axis is the distance between the planet and the star, which is 2.9 X 10^7 km. So, we can set up the equation as follows:
(T1)^2 / (T2)^2 = (a1)^3 / (a2)^3
Where T1 is the unknown orbital period, T2 is the known orbital period (in this case, we can use Earth's orbital period of 365.25 days), a1 is the unknown semi-major axis, and a2 is the known semi-major axis (in this case, 2.9 X 10^7 km).
Solving for T1, we get:
T1 = T2 * (a1/a2)^1.5
Substituting in the values, we get:
T1 = 365.25 days * [(2.9 X 10^7 km) / (1 AU)]^1.5
Using the conversion factor of 1 AU = 149.6 X 10^6 km, we get:
T1 = 365.25 days * (0.1939)^1.5
T1 = 365.25 days * 0.2762
T1 = 100.9 days
Therefore, it takes approximately 100.9 days for the planet to revolve around the star.
As for the ratio of a proton's gravitational field to that of an electron, it is important to note that the gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. Since the mass of a proton is approximately 1836 times greater than that of an electron, the gravitational field of a proton would also be 1836 times greater than that of an electron. However, the charge of an object also plays a role in the strength of its gravitational field. Since both a proton and an electron have the same charge, their ratio would be 1:1.
