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According to Kepler's first law a planet's orbit is an ellipse with the Sun at one focus. An ellipse is a closely defined mathematical shape, while eggs have a more varied shape that cannot be defined closely.

The amount of elongation of an ellipse is measured by the eccentricity, which measures how far each focus is from the centre.

The planets have orbits with low eccentricity which means that the orbits are very nearly circular.

The Earth's orbit has a semimajor axis of a=149.6 million km and and eccentricity of e=1/60. The Sun is off-centre by a distance equal to ae which is 2.5 million km, so the distance varies from 147.1 in January to 152.1 million km in July, at the opposite ends of the major axis. The semiminor axis is only 0.014% smaller, so the amount of elongation is extremely small.

This explains why it took so long to discover that the orbits are elliptical, because the old circle/epicycle theory produced very good results until observations became accurate enough to see problems with it, which happened when Tycho Brahe came up with measurement techniques that were more accurate than ever before. That was at the end of the 16th century.

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