Mathematical Pendulum on Earth's Equator · IZhO 2020 #1.1

Physics · mechanics

Problem

A mathematical pendulum is located on the equator of the Earth. Denote the period of its oscillations at midday T1T_1, and at midnight T2T_2. Find the relative difference of these periods ε=T2−T1T1\varepsilon = \frac{T_2-T_1}{T_1}. Use the following approximations and numerical values: Earth is an ideal ball of radius r1=6.4⋅106r_1 = 6.4 \cdot 10^6 km; the Earth's orbit is a circle of radius r2=1.5⋅108r_2 = 1.5 \cdot 10^8 km with the center located in the center of the Sun; the axis of rotation of the Earth is perpendicular to the plane of the Earth's orbit; the influence of the Moon and other planets is neglected; acceleration of gravity at the Earth's pole is g0=9.8g_0 = 9.8 m/s²; the period of revolution of the Earth around its axis is 1 day; the period of revolution of the Earth around the Sun is 1 year.

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