How does the tilt and orbit of a planet affect its analemma shape?

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The shape of a planet's analemma is influenced by its axial tilt and the eccentricity of its orbit. Earth's analemma is a figure eight due to its axial tilt and relatively circular orbit, while Mars, with a different tilt and more elliptical orbit, exhibits a circular analemma. The variations in analemma shapes across different planets highlight the complex relationship between axial tilt and orbital characteristics. Understanding these factors can provide insights into the solar system's dynamics. The interplay of these elements is crucial for analyzing celestial movements.
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How come the analemma for Earth is in a "figure 8" form and Mars is circular? Does it have to do with radial velocity?
 
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From wikipedia: http://en.wikipedia.org/wiki/Analemma

On Earth, the analemma appears as a figure eight, but on other solar system bodies it may be very different[3] because of the interplay between the tilt of each body's axis and the elliptical shape of its orbit.
 

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