Do astrological bodies travel at consistent speeds?

Generally not when objects are subject to the force of some other massive object. For example, our earth travels around the sun in an ellipse. When the earth is closest to the sun we tend to increase speed. Kepler was the first person to formulate this. His third law I think.

If an object is not subject to the influence of any mass then it would travel at a constant speed in a vacuum.

Tut