Re: why are mountains on the moon smoother than mountain peaks on earth?

Hello, Angela...

Let's start with some general stuff and get to the specific question a bit
later on.

How the moon was formed is something still debated. The best current theory
is one in which a Mars-sized object hit the proto-Earth very early on in the
history of the solar system.  This collision ended up merging most of the
Mars-sized collider into the Earth, but with a substantial part of the 
collider's mostly silicate mantle being flung off to form the moon. This 
theory is the most successful at explaining 

	a. why the moon is so low in volatile species (like water as found in 
hydrated minerals)
	b. why the moon has a significantly lower density and far less iron 
than the Earth	
	c. the angular momentum of the Earth-moon system.

Early on in the solar system, there were lots of collisions. For the first
few hundred million years they were probably the major force shaping the
surface of planetary bodies. We still see the evidence of this on the less
geologically active rocky planets (Mercury, the moon, and to some extent,
Mars) as craters.

Since that time (ending perhaps 3.8 billion years ago), the moon has been
subject to very little change. There is no water or air, so erosion does
not occur there. Also, the very small size of the moon did not allow any
major geologial activity such as is evident on the Earth (moving plates,
volcanos, mantle convection, subduction zones, etc).  A extremely slow 
process of "sandblasting" by smaller meteors does take place on the moon, 
and is responsible for the production of the lunar "soil" (powdered rock, 
actually) called "regolith."

On the Earth, however, the radioactivity of certain elements in the body of
the planet provided enough heat to keep the engine of geological processing
going right up to the present day with no signs of stopping any time soon.
This causes the mantle to well up at ridges (hidden under the ocean and 
called...no surprise...mid-ocean ridges), push the plates of the Earth's 
surface around, and eventually cause them to be swallowed in subduction
zones.  All this pushing and shoving builds mountains, and the largest
mountains we have, the Himalayas and the Andes, are due to these forces.
The Earth also has water and an atmosphere, however, so that the forces of
erosion are constantly wearing down the mountains. 

Now, with all that said, just how rough is the moon and how rough is the
Earth?  Answer, in both cases, is not very much at all relative to the size 
of the body involved. The crust of the Earth can be considered to be
the skin on an apple, meaning the tallest mountains are thinner, in 
proportion, than the skin of an apple is to the whole apple. 

Let's leave the whole planet/moon out of it and take a more human scale of 
things; how much climbing will we have to do to reach the top?
The tallest mountains on the Earth are 29,000 to 30,000 feet tall (Mt. 
Everest in the Himalayas, Mauna Kea in the Pacific...measured from its
base at the floor of the ocean). The tallest mountains on the moon are
around 16,000 to 20,000 feet tall, from the references I could dig up:

	Rukl, "Atlas of the Moon"
 http://library.thinkquest.org/C004044/moon.htm
 http://pi.isu.edu/Geo_Pgt/Mod06_Moon_a_b/moon_pages/mod6Part1.htm

OK, the Earth wins. Why?

The mountains on the moon were formed by collisions. This is a pretty
"bad" way to make mountains. The incoming mass tends to splatter stuff
all over the place (look at the moon, especially around the fairly recent
crater Tycho, and observe the "rays" spreading out from it. These are
trails of ejected material scattered by the body that caused the crater
to form) instead of piling it up. Some of the ejecta does come down together 
and make mountains of pretty good size around crater edges, however, and 
this is what forms the tallest mountains on the moon.  On the Earth, 
however, the geologic forces are very capable of shoving whole continents 
around (at the rate of an inch or two a year) and jamming them into each 
other. This is how the Himalayas have formed, starting quite a few millions 
of years ago when India began colliding with Tibet. That process is what 
pushed Mt. Everest up 29,000 feet and is still making it grow taller.  The 
geological forces of the Earth are huge, and in spite of the Earth's greater 
gravity, capable of shoving rocks up higher than the collisional processes 
on the moon piled up rubble from collisions.

But, in another sense, you might call the moon the "winner." Compare the
age of the mountains. Those on the moon are some 4 billion years old. The
mountains on the Earth that existed 4 billion years ago are all long gone,
worn down by erosion to nothing.  This is sort of like comparing a sprinter 
to a marathon runner; the former may go faster, but can't run as long a 
race. Similarly, the mountains of the moon may not be as tall, but they sure 
do last a long time. Wait a billion years; Mt. Everest will be long gone,
but the moon's mountains will be almost as they are today.

To better understand the formation of the solar system, and the Earth in 
particular, I suggest you read "From Stone to Star" by Claude Allegre. 
A good recent introductory textbook on geology will also be useful.