Orbital Mechanics

Maneuvering a spacecraft in orbit requires some tactics that most of us would find counter-intuitive. This morning I got to pondering exactly how a simple maneuver would be accomplished. I set my self a simple problem: suppose I was in a perfectly circular orbit, 1 kilometer (0.6 miles) further from Earth than the space station I wanted to dock with, which was orbiting in a perfectly circular orbit at 500 kilometers (311 miles) above the Earth's surface. What maneuvers would I need to make?

Orbital mechanics doesn't get much simpler than this.

First thing you'd notice is that the space station is moving ahead of you in its orbit. That's because at its slightly lower altitude, it needs to move about a half millimeter per second (1.2 miles per hour) faster than you in order to stay in orbit. That's a leisurely walking pace, so you'd see the space station moving slowly past you – and you'd be forgiven for thinking that you had to speed up to “catch up” to it. But in fact, you need to do exactly the opposite! You need to slow down very slightly so that you will fall down to its altitude. So you aim your maneuvering rocket to slow yourself down, and light it off for a short blast, just enough to put you into an elliptical orbit whose perigee (low point) is 500 kilometers.

Now you're moving more slowly, and falling behind the space station more quickly – but as you fall, you gain a little more speed (just as you would if you jumped off a stool). Not enough to catch up, though, and when you've fallen to 500 kilometers, you're still a little bit behind the space station. But no matter – because you're in an elliptical orbit, you're actually traveling ever-so-slightly faster than the space station, so you slowly approach it. At that point, you need to slow down some more, to match the space station's speed and orbit.

You started out above the space station, moving more slowly than it was. You made two maneuvers to dock with it: both of them slowing you down! It seems weird, and somehow wrong, but that's really how it works. All of the strangeness derives from a simple fact: satellites in higher orbits have more energy than those in lower orbits. We had to slow down (twice!) to dock with the space station because we were in a higher orbit, and had more energy (for our mass) than the space station did – so we had to get rid of some...

The above analysis is based on a simple formula for the velocity of a satellite in a perfectly circular orbit around the Earth. The formula, along with other information, can be found here, here, and here.

Reaper

Today's news includes a new weapons deployment: the MQ-9 “Reaper” (aka “Predator B”) is being deployed to Afghanistan and (a little later) Iraq. This weapon system is one of the best examples of the U.S. employing its technology capabilities in modern warfare. I was expecting this system to be developed and deployed much more quickly than has proved the case, but nonetheless it is now on the way to the battlefield.

From the Air Force web site:

SYSTEM COMPONENTS

A typical Predator system configuration would include four aircraft, one ground control system and one Trojan Spirit II data distribution terminal. The Predator air vehicle is 27ft in length and has a 49ft wingspan. The system operates at an altitude of 25,000ft and at a range of 400nm.

The endurance of the air vehicle is more than 40 hours and the cruise speed is over 70kt. The air vehicle is equipped with UHF and VHF radio relay links, a C-band line-of-sight data link which has a range of 150nm and UHF and Ku-band satellite data links.

PAYLOAD

The surveillance and reconnaissance payload capacity is 450lb and the vehicle carries electro-optical and infrared cameras and a synthetic aperture radar. The two-colour DLTV television is equipped with a variable zoom and 955mm Spotter. The high resolution FLIR has six fields of view, 19mm to 560mm.

The Raytheon Multi-spectral Targeting System (MTS-A) is fitted on the MQ-1/9 Predator. The MTS-A provides real-time imagery selectable between infrared and day TV as well as a laser designation capability. MQ-1 can employ two laser-guided Hellfire anti-armour missiles with the MTS.

The Northrop Grumman TESAR synthetic aperture radar, which provides all-weather surveillance capability, has a resolution of 1ft. Other payload options, which can be selected to meet mission requirements, include a laser designator and rangefinder, electronic support and countermeasures and a Moving Target Indicator (MTI).

This is not your mama's UAV. The multiple imaging systems on board, operating across a broad spectrum from radio frequencies to visible light, give the Reaper an ability to see and designate targets that is almost magical. The long loiter time, high ceiling, and relatively high top speed combine to provide a weapons platform with nearly instantaneous availability over a battlefield. And its ability to carry several different weapons systems on standard pylons means that it is as lethal and flexible as our top-end manned aircraft.

The Reaper is arguably the first generation of real robotic weapons platforms. It is most definitely not a toy or an experiment; it is a real, live weapons platform that made it all the way through a sometimes reluctant procurement process (the Air Force, in particular, has not always been eager to displace pilots). I believe it is a foretaste of the way future wars will be fought, and most especially of the way America can leverage its technological prowess to reduce the blood cost of war. Weapons systems in the air were almost inevitably the first to be robotized – but I don't think the ground-based systems will be far behind…

The Confession

Jim M. sends this along:

It started out innocently enough. I began to think at parties now and then – just to loosen up. Inevitably, though, one thought led to another, and soon I was more than just a social thinker.

I began to think alone -- "to relax," I told myself -- but I knew it wasn't true. Thinking became more and more important to me, and finally I was
thinking all the time.

That was when things began to sour at home. One evening I turned off the TV and asked my wife about the meaning of life. She spent that night at her mother's.

I began to think on the job. I knew that thinking and employment don't mix, but I couldn't help myself.

I began to avoid friends at lunchtime so I could read Thoreau, Muir, Confucius and Kafka. I would return to the office dazed and confused,
asking, "What is it exactly we are doing here?"

One day the boss called me in. He said, "Listen, I like you, and it hurts me to say this, but your thinking has become a real problem. If you don't stop thinking on the job, you'll have to find another job."

This gave me a lot to think about. I came home early after my conversation with the boss. "Honey," I confessed, "I've been thinking..."

"I know you've been thinking," she said, "and I want a divorce!"

"But honey, surely it's not that serious." It is serious," she said, lower lip aquiver. "You think as much as college professors and college professors don't make any money, so if you keep on thinking, we won't have any money!"

"That's a faulty syllogism," I said impatiently.

She exploded in tears of rage and frustration, but I was in no mood to deal with the emotional drama.

"I'm going to the library," I snarled as I stomped out the door. I headed for the library, in the mood for some Nietzsche. I roared into the parking lot with NPR on the radio and ran up to the big glass doors. They didn't open. The library was closed.

To this day, I believe that a Higher Power was looking out for me that night. Leaning on the unfeeling glass, whimpering for Zarathustra , a poster caught my eye, "Friend, is heavy thinking ruining your life?" it asked.

You probably recognize that line. It comes from the standard Thinkers Anonymous poster.

This is why I am what I am today: a recovering thinker. I never miss a TA meeting. At each meeting we watch a non-educational video; last week it was "Porky's." Then we share experiences about how we avoided thinking since the last meeting.

I still have my job, and things are a lot better at home. Life just seemed...easier, somehow, as soon as I stopped thinking.

I think the road to recovery is nearly complete for me.

Today I took the final step... I joined the Democratic Party.

That's a joke. I think.