|MadSci Network: Astronomy|
I probably will not answer your question, but will give some information that will help you form your question more specifically. First, it is important as to whether your object is an asteroid or comet (something that big would probably not be referred to as a "meteoroid." (note on terminology: meteoroid=object still in space, meteor= object burning in Earth's atmosphere, meteorite=object that makes it to the ground). An asteroid traveling through space would not "erode", it does not contain volatile material. It would only change its size/shape by a collisions. It could travel through space without major collisions. Comets do lose mass, but unless close to the Sun, would not lose a significant amount to reduce in size. However, if a comet/asteroid the size of the Earth were to impact the Earth, there is no way with the thickness of our atmosphere that it would be reduced to the size of a pebble. "Armageddon" took place with objects 100 km in size. I am not sure if that was what you were asking. Something to think about which might help you is that the current theory on how the Moon was formed was by a giant collision between a Mars size object with the Earth. The debris blown out from the Earth formed what is now our Moon. I hope this information helps. However, if you resubmit your question, be specific on where this erosion takes place (during the entire lifetime of the object or just in the Earth's atmosphere). Also, where is this object coming from? Is the erosion by small collisions with dust/debris on its journey? Is it a comet or an asteroid? Good luck.
Try the links in the MadSci Library for more information on Astronomy.