Expert: Philip Stahl - 9/9/2007

Question
QUESTION: I read the following in Science:
At approximately 170 kilometers in diameter and having characteristics similar to carbonaceous chondrite meteorites, the Baptistina parent body resided in the innermost region of the asteroid belt when it was hit by another asteroid estimated to be 60 kilometers in diameter. This catastrophic impact produced what is now known as the Baptistina asteroid family, a cluster of asteroid fragments with similar orbits. According to the team's modeling work, this family originally included approximately 300 bodies larger than 10 kilometers and 140,000 bodies larger than 1 kilometer.

Question: How could there be a huge impact between asteroids iln the asteroid belt? Are they traveling in different directions, which would result in a head on collision. Or, do they all travel in the same direction and approximately the same speed, which would result in a nudge?

ANSWER: Hello,

The key point to bear in mind in terms of the asteroids in the "asteroid belt"  - is that they all have very elliptical orbits, as opposed to circular ones. This means there are likely to be many intersections of the respective orbits over time, and hence collisions. This will occur even in the case of all traveling in the same direction.

Such collisions indeed, can also form "binary asteroids" - such as the pair Ida, which is orbited by Dactyl. These orbit around a common center of gravity and were plausibly formed in the course of frequent collisions, as well as fragmentation from earlier collisions.

Collisions can also occur by virtue of a gravitational "nudge" which will either be from another )perhaps larger, more massive) asteroid, or even Jupiter (many asteroids display "orbital resonances" or integral ratios of their own orbital periods with respect to Jupiter's)

Hope this helps.

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QUESTION: The asteroids must be all going the same approximate direction, that is following fairly similar orbits, else it would not be called a belt. Please correct or explain. also:

Why does not "gravitational nudge" result in the earth pulling in the moon for a collision? Or why doesn't the planets get closer to the sun over time. This seems like a dumb question but I don't get it. I have heard that the gravity from one galaxy can suck in another for a merger etc. and this is light years away. Our closer moon should have been doomed long ago. thanks for your help.

Answer
Hello again,

First, the difference is that the mass of the typical asteroid in the asteroid belt is far less than the planet Jupiter which (gravitationally) dominates the asteroids. By contrast, the Moon is barely 1/80 the mass of the Earth, so there is far less scope for the Moon to be "nudged" by Earth than asteroids to be "nudged" by Jupiter.

There are also other complexities that factor in. For example, the Earth rotates faster than the Moon moves in its orbit. Because the tides are linked to the more slowly moving Moon, they act by friction as a *brake on Earth's rotation*, gradually slowing it down. (It is estimated by 0.0007 seconds per century).

The angular momentum *lost by the rotating Earth* in this process is transferred to the Moon's angular momentum. Thus, the Moon is accelerated in its orbit, causing it to slowly spiral outwards...AWAY FROM the Earth. The
day and month are thus lengthening at different rates.

Calculations have actually been retro-worked to show how the length of month differed when the Moon was much closer to Earth in the past. For example, when the Moon was only 16,000 km away (10,000 miles) the month was approximately seven mean solar days long. (As opposed to the current value nearly four times more)

Planets don't get closer to the Sun over time because the Sun's gravitational attraction for them (F = GMm/r^2, where M is the Sun's mass, m the planet's, r the distance, and G the Newtonian gravitational constant) is balanced by the planet's centripetial force:  mv^2/ r.

So long as this balance is sustained:

GMm/r^2  =    mv^2/ r

or


GM/r^2  =  v^2/ r

any given planet will continue in its defined orbit (with specified orbital parameters) without getting closer to the Sun over time.

Now, IF one re-arranges the last of the two equations above, to solve for r, the distance:

GM/ v^2  = r

We can see that if the planet's orbital velocity were to somehow *increase*  for any reason, than r would *decrease* and the planet would get closer to the Sun.

For example, since r ~  1/v^2

then if the planet's velocity doubled its distance to the Sun would be 1/4 closer (inverse square law).

"Merged" galaxies may happen for any of a number of reasons, and not necessarily because a smaller one has been gravitationally "sucked" into another from a large distance. It is more likely the two galaxies were on a collision course - say within the same cluster of galaxies- and as they intersected in their motions the cores had sufficient mass (perhaps because of black holes accumulated in their centers - like the Milky Way) to "merge" into a single "colliding galaxy".

A more likely process is what is called "galactic cannibalism". In this case a monster massive galaxy - say a supergiant elliptical galaxy, exerts tidal forces (see my Earth-Moon example invoking tides earlier) on a much smaller galaxy, a dwarf ellptical say, and disrupts it over time. The smaller one, usually ten million times or more less massive, then breaks up into fragments, which are pulled into the larger one.

Also be aware that such tidal forces can manifest without galaxies actually "merging'. Even a relatively close encounter might pull material off, via tidal forces, to the other. An example would be the galaxies designated NGC 4676a and NGC 4676b, which you can google to learn more about.

Unfortunately, a detailed understanding of these processes requires a lot of physics. There is only one popular book I know of that can really be of help - and that is Isaac Asimov's 'The Collapsing Universe'. While the book is really about black holes and how they're formed, the first two chapters ('Particles and Forces', and 'The Planets') give one of the best introductions ever to the nature of gravity and the forces acting on the planets, moons, etc.

It would be well worth your time and effort to get this book to see Asimov's at-length explanations and illustrations - which go far beyond what I can give in a forum such as this.