- The orbit of every planet is an ellipse with the sun at a focus
- A line joining the planet and the sun sweeps out equal areas during equal intervals of time
- The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

These three laws were consistent with the Copernican idea that the Earth is not the center of the universe and earned Kepler a lot of scorn from the various Churches. 100 years or so later, Newton was able to derive Kepler's laws from his own, more fundamental laws of motion:

- There exists a set of inertial reference frames relative to which all particles with no net force acting on them will move without change to their velocity. That is, a body in motion stays in motion and a body at rest stays at rest if no external force acts on the body.
- Observed from an inertial reference frame, the net force on a particle of constant mass is proportional to the time rate of change of its linear momentum. That is, force is mass times acceleration. The net force acting on a body is the body's mass multiplied by its acceleration.
- Whenever a body, A exerts a force on another body, B, B simultaneously exerts a force on A with the same magnitude in the opposite direction. These two forces act along the same line. That is, for every action there is an equal and opposite reaction.

- Every point mass attracts every other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between the point masses:

- F = G m1*m2/r^2

Together, you can derive Kepler's three laws of planetary motion (until you get too precise and then you need General Relativity). I won't bore you with any more details by doing so.

What you can also derive is the motion of any object passing by the Earth, for example.

Way back in October, a near-earth asteroid a few meters across with a trajectory very likely to bring it into contact with the Earth was detected. Very shortly after the detection, observers realized that the object would hit the earth, and the knowledge of physics allowed the observers to predict that it would impact somewhere over Sudan. The prediction was that it would break up in the atmosphere.

It did. The atmospheric impact was detected and the energy release was measured.

Pieces of that asteroid-turned-meteor-turned-meteorite have been recovered.

I posted a blurb where I did the math to estimate the density, and therefore the properties of the asteroid. Let's see if I was right... :)

Before we do that, I just want to point out how wonderfully strong science is in doing what it's meant to do: explain how things in our universe work.

The typical scientific method is something like this:

We make some observations: Planetary motion observed by Brahe and Kepler.

We make a prediction: Kepler's laws of planetary motion and Newton's laws of motion.

We test that prediction: Discover new planets by observing their gravitational influence on the known planets, and then accurately predicting the new planets' orbits and looking in the right place.

We make adjustments to the prediction based on new data: Mercury's orbit, light curves, Einstein's General Relativity.

We repeat.

Observation: There is a rock out there that has a certain trajectory.

Prediction: this rock will impact Earth's atmosphere somewhere over Sudan.

Test: We observed that rock impacted Earth's atmosphere somewhere over Sudan.

And yet again:

Observation: The energy released was about 4*10^12 joules.

Prediction: The asteroid would have a density of 1800 kg/m^3.

Prediction: The asteroid was mostly rock and emptiness between the rocks.

Test: Pick up pieces of the rocks that fell to Earth and measure density.

Well, here's the paper discussing the work of the meteorite hunters.

They reported a density of between 2100 and 2500 kg/m^3. That's higher than my prediction, but the energy released from the air blast has been updated to be about 6.7*10^12 joules, the asteroid diameter was increased to be about 4.1 m in diameter instead of the 3 meters I used, and the least dense parts of the rock burned up in the atmosphere while the most dense survived.

Here are some pictures. Much of what you see is the ablation crust, but you can also see into the interior of the rock in (d). It's not solid throughout. In fact, the measured porosity is on the order of 10% to 25%. A rubble pile. The recovered bits only account for about 0.005% of the initial mass of the impactor (the rest burned up in the atmosphere).

This is the first time the meteorites from an object first seen in space have been recovered. This is a big deal because usually we have to rely on reflected light to tell us about the rocks in space. That is fraught with problems and having a rock on the earth that came from a known object in space is going to help immensely.

It is also fortunate that we detected the asteroid and made the prediction of where it would explode in the atmosphere; the kind of material this is made of does not survive the weather on the Earth for very long and we have never found this kind of meteorite on the ground.

The authors of the recovery paper have backtraced the orbit of the object and have found a likely candidate asteroid for the source of this rock.

## 1 comment:

Hmmm.....amazing...

It looks mighty small .....in a very big world...hungh..they found a piece....

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