To find the time taken by a planet to describe a given arc of its elliptic orbit starting from the nearer and of the major axis.
To find the time taken by a planet to traverse a given arc of its elliptical orbit starting from the nearer end of the major axis, you need to calculate the planet's mean motion.
The mean motion, also known as the average angular velocity, is the angular distance travelled by the planet in a certain amount of time. It is related to the orbital period of the planet, which is the time it takes to complete one full revolution around its orbit.
To calculate the mean motion, you can use the following formula:
Mean Motion = 2π / Orbital Period
The orbital period is usually given in units of time (e.g., days, years), and the mean motion is given in units of radians per unit of time.
Once you have the mean motion, you can use it to calculate the time taken to traverse a given arc of the orbit by using the following formula:
Time = Arc Length / Mean Motion
The arc length is usually given in units of distance, such as kilometers or astronomical units (AU), and the time is given in units of time (e.g., seconds, minutes, hours).
So, to find the time taken by a planet to traverse a given arc of its elliptical orbit starting from the nearer end of the major axis, you need to know the orbital period of the planet and the length of the arc. With these values, you can use the formulas mentioned above to calculate the mean motion and the time taken.