Question

According to the given formula for orbital time period t ^2 = 4π ^2/gm a^3 , which physical quantity does 'a' represent?

a. Acceleration
b. Distance from the sun
c. Time
d. Gravitational constant

Answer 1

In the given orbital time period formula, 'a' represents the semimajor axis of the orbit or the average distance from the body to the object it is orbiting.

Step-by-step explanation:

In the formula t^2 = (4π^2)/(gm) a^3, the variable 'a' represents the semimajor axis of the elliptical orbit of a body around a larger celestial body, usually the distance from the body to the center of the object it is orbiting. This formula is a rearrangement of Kepler's Third Law of Planetary Motion which states that the square of the orbital period (T) of a planet is directly proportional to the cube of the semimajor axis of its orbit (a). When 'a' is expressed in astronomical units (AU) and T is measured in years, for objects orbiting the Sun, this relationship is not only proportional but also equal, given that 1 AU is the average distance between Earth and the Sun.