The path traced by Gyroscope is elliptical in nature and is finally settled towards the meridian. Lets find out how.
Path traced by north end of Gyroscope
The north end of the Gyro spin axis initially points at some point X, which is above the Earth’s horizontal and a bit east of the actual meridian. Due to the Earth’s gravitational pull, A torque TH is applied across the Gyro’s horizontal axis and at the same time this torque TH is applied across the Gyro’s vertical axis also.
Due to the direction of rotation of Gyro, , this torque TH causes the Gyro to precess towards the wet. As the north end of the Gyro is towards the east of the actual meridian, Earth rotation results in an upward tilt of the Gyro. However, this movement is damped by the downward precession. It is why, the resultant path traced by the Gyro is towards the meridian. This downward precession becomes more and more strong as the Gyro spin axis comes near the meridian.
As the north end of the Gyro passes west of the meridian, Gyro tilts a bit downwards due to the Earth’s rotation. However, the torque TH continues to precess the Gyro towards the west till the Gyro spin axis passes through the Earth’s horizontal. At this point, The vertical and horizontal torque ceases to act. However, due to earth’s rotation, the Gyro continues to tilt downwards. Once the Gyro spin axis is below the earth’s horizontal, the vertical and horizontal torque generated by the Earth’s rotation again implies on Gyro. But this time it is in opposite direction. This process results in the damping of Gyro towards the meridian. This resultant movement of Gyro finally settles it to the meridian following an ecliptic path.
Path traced by Gyroscope in 24 hrs
- Angle of Tilt=o
- Angle of Drift=0
- Rate of Tilt=0
- Rate of Drift= max
After 6 Hours
- Angle of Drift = max
- Rate of Drift = 0
- Rate of Tilt = max
- Angle of Tilt = ½ MAX