(a) Earth can be thought of as a sphere of radius ` 64 00 km`. Any object (or a person ) is performing circula motion around the axis os earth due to earth`s rotation (period 1 day ). What is acceleration o object on the surface of th earth 9at equator ) towards its centre ? What is its latitude ` theta` ? How does these accelerations compare with `g=9.8 m//s^2 `?
(b) Earth also moves in circular orbit around sum every year withon orbital radius of ` 1.5 xx 10 ^(11) m`. What is the acceleration of earth ( or any object on the surface of the earth ) towards the centre of the sum ? How dies thsi acceleration comparte with ` g=9.8 ms^2 `?

Explanation

To solve the problem step by step, we will break it down into two parts as given in the question.

### Part (a)

1. **Given Data**:
- Radius of the Earth, \( R = 6400 \, \text{km} = 6.4 \times 10^6 \, \text{m} \)
- Period of rotation of the Earth, \( T = 1 \, \text{day} = 24 \times 60 \times 60 \, \text{s} = 86400 \, \text{s} \)

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