How long would the year be if the distince of the earth from the sun where 20% more?
To determine how long the year would be if the distance of the Earth from the Sun were 20% more, we need to consider the relationship between distance and orbital period.
The orbital period of Earth, which is equivalent to a year, is determined by its average distance from the Sun. According to Kepler's third law of planetary motion, the square of a planet's orbital period is proportional to the cube of its average distance from the Sun.
Mathematically, this can be expressed as:
(T1^2) / (T2^2) = (D1^3) / (D2^3)
Where:
T1 = initial orbital period (current year length)
T2 = new orbital period (what we want to find)
D1 = initial distance from the Sun (current average distance)
D2 = new distance from the Sun (20% more than D1)
Let's assume that the initial orbital period is 365 days, which is the current length of a year (T1 = 365 days). We can also assume that the initial distance from the Sun is X (D1 = X).
Substituting these values into the formula:
(365^2) / (T2^2) = (X^3) / ((1.2X)^3)
Simplifying:
(365^2) / (T2^2) = 1 / (1.2^3)
Rearranging the equation to solve for T2:
T2^2 = (365^2) * (1.2^3)
Taking the square root of both sides:
T2 = sqrt((365^2) * (1.2^3))
Calculating this value will give us the new orbital period (T2) or the length of the year if the distance from the Sun were 20% more.