Proteus gets plastered

I've been doing a project for Greely's planetary geology class on micrometeorite bombardment of outer planet satellites. This is a challenge because the micrometeorite dust particles are gravitational focused (same principle as a spacecraft doing a gravity assist) and speed up quite a bit, depositing kinetic energy, and crystallizing the surface amorphous ice. The results that I'm getting indicate that the closer in the sat is, the more it gets plastered by these dust particles. Proteus is very close in, so it get alot of impacts. Curiously, the spectra of Proteus shows very little water ice. This may mean the plastering has removed the surface ice, plasticizing the surface. Fun stuff!

I Like Triton

I like Triton. About the size of Earth's own moon, Triton was once a Kuiper Belt Object (KBO), peer of Pluto, Charon, and Eris. Then, one fine sidereal day, something happened to cause Neptune to capture Triton. We know that it was captured, and not formed with Neptune, because its orbit is retrograde relative to the planet's direction of rotation. How that capture happen is still a bit unclear, but most likely Triton was in a double-planet system (like Pluto-Charon) that flew too close to Neptune; one partner ran off free, and Triton got stuck in the ice-giant's pull (Nature article, more papers). Triton has been visited once, by the Voyager 2 spacecraft on its way out of the solar system. NASA has considered going back with a mission called "Triton Explorer" (powerpoint fact sheet). I hope they do; Triton is a world of mystery, right on our doorstep...

Having Fun at JPL

I've finished my first week at JPL, and already this looks to be a fun summer. We are revising the last year's design, switching instruments around, adding a Lidar here, shaving off some structure mass there, etc. to create an even better spacecraft. Also, it looks like I'll be able to go the Seventh International Mars Science Conference (which just happens to be at Caltech, while I'm here), so that should be fun.

It's Just Rocket Science: Part 1

People seem to have a conception that rocket science is very difficult; in effort to show that it really isn't, I'm going to try to explain its basic concepts and equations. I'll start with delta v. (Note that I copied this from my old blog.)

Delta v means change in velocity; velocity is basically the quantity that represents both speed of an object and the direction it is moving. Delta is the science/engineering shorthand for change, and thus delta v is the change in the speed and direction of an object.

For our purposes, that object is a spacecraft. How does a spacecraft move? Well, with a rocket, of course. A rocket is a simply a device that tosses material in one direction, causing whatever it is attached to move in the opposite direction. The reason for this is what Sir Issac Newton called "Conservation of Momentum". Momentum is the product of the velocity and the mass of an object, and for an object not affected by external forces, is a constant. Mathematically, this is expressed as:

m₁ * v₁ = -m₂ * v₂

Where m₁ and v₁ are the mass and velocity of the spacecraft and m₂ and v₂ and the mass and velocity of the exhaust. The negative means that the directions of the velocities are opposite. Let's look at an example:

Suppose a spacecraft that has a mass of 30,000 kg is at rest (not moving) fires a rocket that instantaneously shoots 10,000 kg of its mass out its back at a speed of 3000 m/s. How fast is the spacecraft moving now? Well, its mass after the burn is going to be 30,000 kg minus the 10,000 kg that was fired, leaving 20,000 kg. The equation above can thus be written as:

20,000 kg * v₁ = -10,000 kg * -3000 m/s

Solving for v₁, we get:

v₁ = 1500 m/s

Which converts to about 5400 km/hr or 3355 mph. Note that the exhaust velocity is negative, meaning it is in the opposite direction than the spacecraft is pointing.

The problem with this example,though, is the word instantanously. In reality, things never move instantanously, and so we need to take into account the time that it takes for the exhaust to get out of the rocket. To do this takes calculus, so I won't go into the details, but the end result, as found by the great Konstantin Tsiolkovsky, is called the rocket equation and can be written:

delta v = -v_e * ln( m_i / m_f )

Where v_e is the exhaust velocity, m_i is the mass of the spacecraft before the burn, m_f is its mass after the burn, and ln is the natural logarithm.

Let's return to our previous example and see what we get when apply the rocket equation to that situation:

delta v = -(-3000 m/s) * ln( 30,000 kg / 20,000 kg )

Solving, we get:

delta v = 1216.4 m/s

Or 4379 km/hr or 2721 mph, which is just 81% of our previous value.

Now, if you read the specifications of a rocket, you typicaly will not see the exhaust velocity, but you will probably see something called "specific impulse" or I_sp. Specific impulse is simply the exhaust velocity divided by the accelleration due to gravity at the Earth's surface, called one g, or 9.8 m/s².

I_sp = -v_e / g

Thus, we can write the rocket equation as:

delta v = (I_sp * g) * ln( m_i / m_f)

And there you have it. With the above equation, you can calculate the delta v of a spacecraft maneuver with just some basic information about the spacecraft. But what is delta v useful for? Well, that's what the next installment is for...

I'm going to Arizona

I've just been accepted into the Astrophysics PhD program at Arizona State University. It's a new department, less than a year old, so getting in on the ground floor should be fun... Also, I'll be at JPL this summer again, hopefully bringing MSCL to the point that we can get real funding...

New Heim Propulsion Paper

A new paper on Heim Theory for spacecraft propulsion was just posted this week by Walter Dröscher, Heim's protégé. Heim theory is one the many, many concepts for gravitational-electromagnetic force unification. However, it has the important prediction that spinning certain superconducting magnets at sufficient angular acceleration will produce an artificial gravitational field. Tajmar et al. showed last year that this effect may actually occur, though their configuration appeared (with heavy noise) to produce an azimuthal field. The new paper suggests a technique to produce a field normal to the axis of rotation, mean that you could actually propel a spacecraft with it. Needless to say, such a reactionless/propellantless propulsion would be quite revolutionary. Now somebody just has to try Dröscher's experiment...