According to this expression, if our Sun was replaced by a star twice the mass, how many days would our year be?
To determine how many days our year would be if our Sun was replaced by a star twice the mass, we need to understand the concept of orbital period.
The orbital period is the time it takes for an object to complete one orbit around another object. In the case of our Earth, it takes approximately 365.25 days to complete one orbit around the Sun, which we define as a year.
The orbital period is determined by two factors: the mass of the central object and the distance between the two objects. According to Newton's version of Kepler's Third Law of Planetary Motion, the orbital period is proportional to the square root of the cube of the semi-major axis (average distance) of the orbit.
In this case, if the Sun is replaced by a star twice the mass, the mass of the central object (the star) would change, but the distance between the Earth and the new star is not mentioned. Therefore, we cannot determine the exact number of days our year would be without knowing the new distance.
However, if we assume that the distance remains constant, we can use Kepler's Third Law to estimate the new orbital period. Since the mass of the central object is doubled, the orbital period would increase. By plugging the new mass into the equation and solving for the new orbital period, we can find an estimation.
Keep in mind that this is a simplified explanation, and there are additional factors and complexities involved in determining the exact orbital period.