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The apex of the Earth's way is the point on the celestial sphere towards which the Earth appears to be moving due to its motion around the Sun. As the ecliptic is defined as the mean plane of the earth's orbit around the Sun, the apex will lie on, or very close to, the ecliptic. 

If we make the approximation that  the Earth's orbit is circular, then the Apex of the Earth's way is the point on the ecliptic 90 ahead of the Sun. We can also calculate the approximate speed of the Earth by dividing the circumference of a circle, with radius 1 AU, by the time taken to complete one revolution.

2 x pi x 149,597,870

365.25636 x 24 x 60 x 60

29.7847 km/s

The above calculations are an approximation based on the Earth's orbit being circular. A more rigorous analysis should take account of the eccentricity of Earth's orbit.

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