Simple pendulum on Sun

SIMPLE PENDULUM ON SUN

INTRODUCTION

Sun is our star in the center of our solar system. Consider a fire resistant pendulum on the surface of Sun ready to swing. A pendulum is a weight suspended from a pivot so that it can swing freely. It has a bob [mass] suspended from a frictionless pivot via a string. The central position of the bob i.e. when the pendulum is at rest is called its Mean position. When the bob is made to swing on the application of external force, it oscillates back and forth about this mean position. The maximum distance traversed by the bob from the mean position is known as amplitude. The amplitude is measured in radians which is a unit of angle. The time taken by the pendulum to complete one full oscillation is called the Time Period. For small amplitude less than 1 radian, the time period is independent of amplitude of the pendulum. We intend to determine the time period of such a pendulum on Sun.

A Simple Pendulum

ASSUMPTIONS

1. The string has no tension or compression

2. The pendulum is indestructible and it is immune to destruction by gravity, high temperature or solar winds

3. Air and wind resistance are negligible

4. Effect of Gravitational Time dilation is negligible

CALCULATION

The time period of a simple pendulum is given by,

T = 2π*√ (l/g) (Eqn. 1)

Where,

T – Time period [s]

l – Length of the pendulum [m]

g – Acceleration due to gravity on Sun [m/s²]

g = 273.7 m/s² (Eqn. 2)

Let the length of pendulum be

l = 1 m (Eqn. 3)

Now substitute equations (2), (3) in equation (1)

T = 2π*√ (1/273.7)

T = 2π*√ (3.6536*10^-3)

T = 2π*0.0604

T = 0.3797 s (Eqn. 4) 

This is the time period of a simple pendulum on Sun. It means any pendulum performing small oscillations will always take approximately 1/3 second to complete one cycle anywhere on Sun provided the value of gravity is same everywhere and the effects of friction are neglected. Due to high gravity of Sun, the time period is extremely small, way smaller than that on Earth and Jupiter.

CONCLUSION

We thus determined the time period of a simple pendulum on Sun.