The distance between the perihelion and aphelion of the sun is 10A.U. What is its orbital period in term of years?

Question

Alexander Acosta · Accepted Answer

The period will be 11.18 years.

The distance between perihelion and aphelion is twice the semi major axis distance. So the semi major axis #a=5 AU#. Kepler's third law relates the period #T# to the semi-major axis by the formula #T^2=a^3#. So #T^2=5^3=125#. Taking the square root gives #T=11.18# years.

Asher Cohen · Answer

As of now, AU = 149597871 km, nearly, and the distance referred is 2 AU. If AU becomes 5 AU, for the same orbital speed, the period might become 5 years.

In general, the time frame is (distance traveled) /(average orbital velocity) = (29.78 km/s)/(2 pi AU km) = 31563169 seconds = 365.3 d, almost = a year... When AU grows to 5 AU, the orbital speed and period remain the same. becomes five years. This is a virtual occurrence. For an a = 5 AU, we could theoretically have an infinite number of orbits. Jupiter additionally notes that the orbit's parameter eccentricity, e, is arbitrary. has a period of 11.87 years and an a = 5.20 AU. When the distance is in time in Earth-year units and AU units, the proportionality dimensional constant According to Kepler's third law (normalized version), (Semi-major axis 1 AU)^3 = (Period in year unit)^2 = 1 (year) / (AU.AU.AU). In fact, the mean Sun-Earth distance for this (orbit period) near- The exactitude relation is very useful. The period of dimension T (time) can be determined through dimensional analysis. by incorporating a constant of dimension L that is connected to any distance a of For dimensional homogeneity, proportionality is required.

John Alexander · Answer

undefined Kepler's Third Law states that the square of a planet's orbital period is directly proportional to the cube of its semi-major axis. The formula is $ T^2 = k \times a^3 $, where $ T $ is the orbital period in years, $ a $ is the semi-major axis in astronomical units (A.U.), and $ k $ is a constant. Given the information, you can't determine the orbital period without the constant $ k $.