Re: How large a meteor can fly through space without collision?

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.