Side elevation
Plan
Reverse plan
Thunderbird 5 elevations
Although not given a lot of exposure during an adventure, Thunderbird 5 is vital for the operation of I.R. so it's no wonder it must stay a closely guarded secret. But what do we know of this satellite from the television series, the accompanying books, records and publicity brochures? The main points to question in this day and age are:
It's clearly made in the sixties — no modern satellite would look like it. It seems to resemble the layout of the Round House that hides Thunderbird 3's launchbay. Or is it the other way around?
Most data on Thunderbird 5 have been summarized by Graham Bleathman and Sam Denham in their Haynes' Agents Thunderbirds Technical Manual published in 2012. In the process, they added some other data to explain their cutaway revelations. This article takes their efforts as a starting point.
length: 122m
diameter: 90m
orbit; claimed to be geostationary at a height of 35,786km above the Pacific Ocean in order to stay above Tracy Island at all times. True or false, at any moment in time Thunderbird 5 can only receive distress calls from the visible part of the Earth — not from the entire globe. On the other hand, the series claims Thunderbird 5 is in a low orbit like the International Space Station ISS. However, this results in Thunderbird 5 rotating around the Earth several times a day — which is no problem if helper satellites exist as we will see later
gravity: Previn coil artificial gravity generator, Earth standard (= 1g). This sounds like a rabbit out of a hat
mass: 887000 kg
performance: reception range 1,6⋅108km
power: atomic batteries, recharged by Thunderbird 3's fusion generators
Thunderbird 5 is in a stable orbit around the Earth. It is said that it was assembled from parts brought into space but, once operational, it does never land on or launch from Tracy Island.
Thunderbird 5 is a satellite that operates in the near perfect vacuum of space. Here you will find approximately 3 atoms per cubic centimeter — a factor of 1019 (19 zeroes after the digit "1") times less than we experience on Earth at ground level and what is simulated inside Thunderbird 5's living quarters (pressure of 1 atmosphere, the atmosphere being a mix of oxygen and nitrogen, just as on Earth)
Without atoms to vibrate and conduct sound, the rockets of Thunderbird 3 or any other spaceship fire in silence. It also allows Thunderbird 5 to be anything but aerodynamic in shape as there is no (air) resistance in the vacuum of space.
Due to its size, the space station is the largest of all Thunderbird craft. It is too large in size and too heavy in weight to be launched into orbit in one piece with a single rocket or reusable transporter. Just like the International Space Station (ISS), it must have been assembled in situ from prefab components brought into space individually — most likely through Jeff Tracy's Construction and Aerospace Corporation as envisioned by Alan Fennell in his long running comic story The Complete Thunderbirds Story published in the 1990's.
Thunderbird 5 moves around the Earth in a circular orbit like most satellites. It is claimed that Thunderbird 5 takes up a position above Earth and remains there. It rotates around the Earth with the same rotational speed as the planet itself. Such an orbit is always above the equator and is called a geostationary orbit and any satellite in such an orbit can be seen "hanging" above the equator at a fixed position in the sky. This claim for a geostationary orbit is false as we will see.
The reason most satellites don't fall back to Earth is because they have an orbital speed. This speed is tangent to the orbit and hence perpendicular to the gravitational pull.
Earth is a big round sphere. At the right orbital speed, the drop in height by the satellite is matched by a similar drop (bending away) of the curved Earth surface. While the satellite keeps dropping, so the Earth keeps bending away. This results in a "free fall" circular orbit of the satellite around the planet.
Isaac Newton discovered this fact in the 17th century and his reasoning is often illustrated by the shooting of several cannonballs with increasing speed from a very high mountain. The correct speed will make the cannonball move around the Earth and hit the cannon again when it completes its orbit.
Johannes Kepler determined that there is a relation between the radius of an orbit and its orbital period which is different for every planet. If the planet has a mass (in kilograms) then the relation between radius (in metres) and period (in seconds) can be described as:
Here G is the gravitational constant with a value of 6.67⋅10-11Nm2kg-2. Any satellite following such an orbit does so without spending any fuel. It is, after all, in constant free fall and just happens to be so lucky that the planet's surface bends away with just the same amount the satellite falls. The Moon runs in its Kepler orbit the way the Earth does around the Sun. They have done so for millions of years and are likely to continue doing so for millions of years more.
The righthand side of the formula is a constant for a particular planet because all parts of the expression are constants. For any given orbital period T, only one orbit with radius r will fit if the fraction r3/T2 is to remain constant. For any larger period, the orbital radius must increase also to remain such a "Kepler orbit".
Any satellite that must function for a long period of time and with limited power supply, occupies a Kepler orbit around Earth. If it would not, it must constantly use its (expensive!) power supply to stay in the desired orbit and would quickly run dry.
If the period T equals a single day (24 hours of 60 minutes each of 60 seconds each = 86,400 seconds) and is in the equatorial plane, it is called a "Clarke orbit" (after author Arthur C. Clarke who first used this concept in a science fiction story). The other name is a "geostationary orbit" because the satellite turns as fast as the Earth and seems to stay in the same location in the sky. Since the Earth's radius is about 6,371km, the orbital height of a Clarke orbit above the Earth is 42,157 – 6,371 = 35,786km. Today, many satellites occupy this orbit at different positions — making it look like a string of pearls or a belt: the Clarke Belt.
At the advent of space travel, the Clarke Belt was almost empty. It is now occupied by over 8000 objects. All these satellites and the left-over debris can easily bump into each other. Therefore all satellites in the Belt are closely monitored from Earth to make sure they stay put and don't wander off to hit a neighbouring satellite. Course corrections are performed if they do wander off. Causes for perturbations in orbit are slight fluctuations of the gravitational pull of the Earth on various orbital positions as our planet is not a very smooth sphere. Also, other cosmic forces such as solar and stellar winds make satellites wander off course.
The geostationary orbit is popular for communication satellites as receiving dishes can be lined up to point at a fixed position in the sky.
Thunderbird 5 would benefit from hanging in the sky in a geostationary orbit, directly visible from Tracy Island. Yet this is not the case, despite what the series or publications claim.
With that many other satellites in the Clarke Belt today, Thunderbird 5 in that same belt would easily be discovered by those that monitor their own satellites. "The only good publicity is no publicity," as Scott says in Thunderbirds Are GO! so this is not really good for a secret organisation. An alternative is a low orbit inside the Clarke Belt. New problems must then be faced. Smaller Kepler orbits come with shorter orbital periods. In this case Thunderbird 5 doesn't stay at the same position above Earth but seems to be drifting forwards (westwards). In order to remain over the same position on Earth, it must compensate for the drift using steering rockets to slow down its movement. The rockets use fuel and hence cost (a lot of) money and they need to be refueled in time.
A second alternative is a variation of the first and the only sensible one. Forget about geostationary orbits (above the equator) and simply take any (low) orbit that fulfills Kepler's Law for a power free orbital ride and take an inclination of the orbit (not just above the equator) that suits the needs of Thunderbird 5.
There is still the requirement that Thunderbird 5 must remain in contact with Tracy Island as well as intercept any distress call from any part of the world. Enter the concept of surface footprint and helper satellites as there is no way Thunderbird 5 can "see" and "listen to" the entire globe at any one time.
As you can see from the (exaggerated) graphic, a satellite can only see that part of a planet that is within a cone of sight. The satellite is at the top of the cone and its base is a circle on the planet. The circumference of the base is outlined by the tangential lines we can draw from the satellite to the planet's surface. If you move further outward, the circumference becomes larger and so does the footprint but the latter never becomes larger than half the planet's surface.
It would take a minimum of 2 satellites at infinite distance to cover both halves of the planet's sphere. At that distance you cannot really see much. Three satellites or more, closer by and with overlapping footprints, seem more useful. When in a geostationary orbit, they could each cover one third of the planet's surface and have some overlap. But all three of them have a limited view of the "top" and "bottom" of the planet: its poles. Involve a fourth satellite, and redistribute the satellites around the planet in such a way that no area remains uncovered. Additional ones are needed if you move into a very low orbit. The closer to the planet, the smaller the footprint a satellite has and the more satellites are needed to cover the entire planet surface.
With some calculations and the aid of surface footprint calculation graph, we can derive the following formula for the footprint of a satellite at orbit h (for its orbital height above the Earth surface you must subtract the Earth radius R).
The angle φ (half the angle of the top the cone):
The area of the surface of the sphere above circumference AC (the footprint for any satellite at point T):
If we are at ground level h = R and therefore R/h = 1 so the footprint is zero, at infinity R/h = 0: the footprint is half the globe. For any other height the footprint is easily calculated.
Given the Earth's surface area (sphere with radius R) is given by SEarth = 4πR2Earth with R = 6,371km, the surface area of the Earth is SEarth = 510,064,472km2.
You can compute the minimum number of satellites needed to cover Earth's entire surface once you calculated the footprint of a single one. Some results are shown in the table below. The same data data is illustrated in the graph at left.
It is clear that the number of satellites initially decreases rapidly with the increasing height. The larger the distance from Earth, the more complete (but the less detailed) the view. The reduction of the amount of satellites turns out to have an asymptotic behaviour, approaching but never quite reaching 2. Therefore, the minimum number of complete satellites must be 3.
| height above Earth (km) | half angle (degrees) | footprint (km2) | minimum number of satellites |
|---|---|---|---|
| 100 | 79.95 | 3,939,158 | 130 |
| 200 | 75.87 | 7,758,422 | 66 |
| 300 | 72.79 | 11,463,181 | 45 |
| 400 | 70.24 | 15,058,511 | 34 |
| 1,000 | 59.84 | 34,581,868 | 15 |
| 2,000 | 49.58 | 60,901,432 | 9 |
| 3,000 | 42.85 | 81,603,760 | 7 |
| 4,000 | 37.92 | 98,313,738 | 6 |
| 7,000 | 28.47 | 133,447,058 | 4 |
| 10,000 | 22.91 | 155,703,955 | 4 |
| geostationary 35,786 | 8.7 | 216,380,597 | 3 |
| lunar orbit 378,029 | 0.95 | 250,678,214 | 3 |
| infinity | 0.00 | 255,032,236 (= half the Earth's surface) | 2 |
There is an additional danger: the Van Allen Belts. These belts were discovered in 1958 by professor Van Allen after the early satellites, Explorer 1 and 3, demonstrated their existence. They consist of high energy charged particles such as electrons and protons that originate from solar and interstellar winds. Due to their electric charge, these particles are deflected by the Earth's magnetic field and move collectively into particular areas known as the Van Allen Belts. There appear to be two belts: an inner and an outer belt, both equally dangerous. These charged particles are hazardous to human life and equipment if exposed to them for any longer period of time. The first belt is found between 1,000km and 6,000km above Earth, the second much further away, at 13,000km to 16,000km.
A compromise solution that avoids the Van Allen belts seems to be an orbit at a height of 7,000km, requiring 4 satellites to cover all corners of the Earth. These four satellites form a three sided pyramid (a tetrahedron) with equal triangular sides. Each of the satellites can directly see the other three: they are all in direct lines of vision and hence of communication. They all have the same orbital period and radius and being in a Kepler orbit, do not require energy to keep circling the Earth. And since all sides of the tetrahedron are equal, their distances are equal. For this construction it can be shown that:
where R is the orbital radius and a the length of the sides of the tetrahedron. In our case a is the distance between the satellites. For a height of 7,000km, the orbital radius includes the Earth radius and is therefore equal to 7,000 + 6,371 = 13,371km. This results in a distance between satellites equal to a = 13,371/0.61237 = 21,835km. One of these four satellites is of course the "main" satellite, Thunderbird 5. The others could have been named "Thunderbird 5A", "Thunderbird 5B" and "Thunderbird 5C". Even the name "Thunderbird 6" would be more deserved than it was for the biplane nicknamed "Thunderbird 6" in the movie of that name.
Because their Kepler orbits are not in the equatorial plane and are not geostationary, none of them "hang" above Tracy Island or can even see the island at all times. The island falls into one of the satellite's footprints at any particular moment, however, and that satellite will function as relay station for Thunderbird 5 to communicate with Tracy Island.
Space is a dangerous place and full of small and large moving objects that may affect Thunderbird 5 or one of its satellites. Currently there is no such thing as a deflector shield — that is a popular excuse for science fiction writers. What would incoming objects deflect off?
Electrically charged objects rushing towards Thunderbird 5 can be deflected by intense electrical fields. These fields would require large currents to generate them and these would interfere with the subtle communication signals Thunderbird 5 was designed to intercept.
But there are solutions to protect the satellite from debris and particles that are quite well known and universally applied in space technology today. Thunderbird 5 has a constant monitoring system that detects the small objects when they are still at a large distance. This allows the computer systems ample time to respond. The main monitoring is performed by the twin gate antennas positioned on Thunderbird 5's docking bay.
If large objects are en route to Thunderbird 5, it can use its selective retro-rockets normally used for docking procedures with Thunderbird 3 to temporarily slightly move into another orbit. The oncoming object can pass undisturbed. Once passed, the original orbital position of Thunderbird 5 is reclaimed. During this maneuver, all laser-communication with the other satellites is adjusted to keep the station fully operational.
Small objects can be diverted by small intense laser cannon that are accurately pointed at the incoming object. A short laser blast produces sufficient radiation pressure on the object to divert it from the course that would cause it to impact Thunderbird 5.
Micro-sized and smaller objects are too small to be registered by the antennas but, despite their speed, their impact on Thunderbird 5 is minimal. The outer hull of the satellite is thick and made of a sturdy yet flexible alloy that can disperse the momentum of the hit and halts the objects almost without a scratch to the hull.
The star-fix sensors housed in the transparent domes on top of Thunderbird 5 calculate its precise position in relation to the stars and are used to return the satellite to its normal orbit if evasive action was needed. This precision is needed to keep the configuration of the four satellites intact as well as to compensate for any pulling or pushing force exercised on the satellites because of the gravitational fluctuations of Earth.
As we made clear, the island is not somewhere "beneath" Thunderbird 5 all the time. That does make the position of the island more intriguing. If not on the equator somewhere in the Pacific, where is this closely guarded secret island?
Jeff gives two, contradictory, clues about it. In Thunderbirds Are GO! he claims the island is 5 hours ahead of England ("11 o'clock – that makes it about 4pm in England"). Yet in Security Hazard, Chip is taken back to his home in England and Jeff states "We're almost at the other side of the Earth." Indicating the time zones on a map, it would seem that Security Hazard has more likelihood of being on target than Thunderbirds Are GO!. The latter would position the island near the Chilean coast whereas the former has a much larger Pacific Ocean region. A geostationary orbit also requires the island to be positioned along the equator. At least it narrows down The Hood's search for the island.
The vacuum of space and the required normal atmospheric pressure for human beings inside the living quarters of Thunderbird 5 impose special conditions on its walls. They must be sturdy enough to withstand incoming micro-particles that cross the orbit of Thunderbird 5 but must also hold up to the pressure difference of 1 atmosphere between the outside and inside of the satellite. This is a relatively small difference that most materials can easily overcome. The ISS space station certainly does. The walls must also contain good insulating material to avoid the comfortable warmth of room temperature inside the living quarters to radiate away into space where the temperature is at almost absolute zero (0K (0 kelvin) or –273°C).
The insulating material inside the outer hull of Thunderbird 5 may well consist of Radiant R, a NASA development produced by Buckeye Radiant Barrier in Ohio. Insulation is provided by 2 layers of 99% pure aluminum separated by a single layer of insulating polypropylene and given ruggedness by a nylon grid. The construction is capable of regulating all three manners of heat transfer: radiation, convection and conduction, and is claimed to be 95% efficient. Some of the power generated by Thunderbird 5 will be used to compensate for any heat loss through the hull into outer space.
Like any vehicle in a hazardous environment, Thunderbird 5 must be subdivided into compartments to spread the risk of danger — especially in the living quarters. Each can be sealed off to localize and contain any disaster in case one part of the satellite is damaged and leaks air or warmth into space or explodes by decompressing.
Thunderbird 5 is in constant free fall to Earth. This means that anything inside Thunderbird 5 is weightless. Things keep having mass as the Earth is pulling them down by its gravity but since everything (including the floor) is falling at the same rate in the same direction, nothing weighs anything as there is nothing that pushes against them to give them weight.
The occupants of Thunderbird 5 and everything not attached to the walls would float around — much as you see happening in the International Space Station (ISS). John or Alan may walk on the floor if they wear magnetic shoes or something else that glues them to the floor. But everything else around them would still float around: pens, books, microphones, food, drinks — everything. Weightless situations are difficult to film on Earth so all sci-fi series sin against this situation. Also, the astronauts inside Thunderbird 3 seem to be under the influence of gravity giving them weight where often no weight can exist.
To avoid or explain away the lack of weightlessness, Star Trek came up with artificial gravity and inertia dampers. According to the Haynes Technical Manual, Thunderbird 5 has some "Previn Coil Artificial Gravity Generators". That chapter in physics on anti-gravity has not been written yet.
Atomic power is released based on chemical reactions. This chemical or atomic power involves the gluing together of atoms into new molecules by exchanging the outer shell electrons, releasing binding energy in the process. Chemistry is full of examples of atomic power release (exothermic reactions) such as exploding dynamite. Although it sounds futuristic, atomic power is not used in Thunderbird 5 to satisfy its energy needs. Whenever "atomic power" is mentioned, it should almost always be read as "nuclear power".
Being high in space, the solar energy flux is a lot more intense than on Earth. All energy carried by all wavelengths of electromagnetic radiation can be captured. On Earth only wavelengths of visible light and radio waves penetrate the atmosphere and only that energy can be absorbed by solar panels. Solar energy seems a viable option, yet it is not.
Solar panels can be mounted on top and at the sides of Thunderbird 5 to generate electricity that is stored in batteries for later use. When Thunderbird 5 is in the shadow of the Earth or Moon the panels are ineffective and the energy consumption of all equipment would rely on battery stored power. Due to the many additional functions of Thunderbird 5 and equipment attached to the hull of the space monitor, only a small part of the satellite could be fitted with solar panels and additional sources of energy provision are needed. The option of special wings for solar panels as used by many satellites that travel the solar system is not practical. Their size and reflection in visual light would make Thunderbird 5 conspicuously bright and clearly visible from Earth.
Far more efficient is nuclear fusion power. In the 21st century we can convert hydrogen nuclei into helium nuclei through nuclear fusion. The starting product of hydrogen weighs slightly more than the helium end product and this "mass defect" is released as an enormous amount of nuclear energy according to Einstein's famous E = mc2 formula.
All equipment inside Thunderbird 5 is run by electricity generated from nuclear fusion engines that are aboard the satellite. The fusion engine of Thunderbird 5 is a much improved version of the Tokamak fusion reactor developed by the Russians in the 20th century. The name Tokamak stands for the Russian equivalent of "toroidal chamber with magnetic coils" — a torus shaped chamber surrounded by magnets. Guess what the copper coloured ring around Thunderbird 5 is used for?
To give you an idea of how much energy can be released by fusing two "flavours" of hydrogen (deuterium and tritium): fusing 600 grams of deuterium and 900 grams of tritium – 1.5kg of fuel in all – equals the total energy consumption of the city of New York during the entire year of 2005.
Using nuclear fusion, Thunderbird 5 is capable of generating enough power on very little fuel. The helium end product is stored in helium tanks for other usage while the neutrons created in the process can be combined with deuterium to create a fresh supply of tritium. This is very useful since the half-life of tritium is short and therefore its "best before" period is very short. But it can be made "on demand" just before it is needed by Thunderbird 5's equipment itself.
The way to fuse the deuterium and tritium nuclei is to give them a high speed so they can overcome their positive charge repulsion through what is known as the quantum mechanical tunnel-effect. Using strong electric and magnetic fields, the charged particles can be sped up to almost light speed. Then they are allowed to collide and fuse and release the "mass defect" as pure energy. Charged particles in magnetic fields induce a lorentz-force on them that is perpendicular to the direction of movement. This forces the nuclei to move in a circular path around the circumference of Thunderbird 5. The nuclear energy released by the fusion reaction is transferred to thermal energy by a water system where liquid water turns to steam. This in turn operates a turbine that converts the thermal energy into electrical energy that is either used directly or stored in batteries for later use by Thunderbird 5's equipment.
The fuel ingredients needed for the fusion reactions, mostly deuterium, are stored in fuel tanks located in the docking bay area of Thunderbird 5 behind the big "5" number shield. These tanks can be ejected in case of trouble. This idea is also used in the design of the Skythrust airplane in Alias Mr. Hackenbacker — and the concept was proven right. The tanks are isolated in much the same way as the Space shuttle fuel tanks were isolated against atmospheric or orbital heat. They are in effect huge thermos flasks isolated by SOFI (spray-on foam insulation) that consists of polyisocyanurate with a higher temperature stability than urethane foam.
Although the fusion engines are very efficient, the deuterium fuel needs to be replenished once in a while. The new fuel is transported by Thunderbird 3 in tanks in its nose cone. Once docked, the nose cone is conveniently near the tanks and some pumps in the docking bay will transfer it from Thunderbird 3 to Thunderbird 5.
The Haynes' manual suggests that Thunderbird 3 brings fuel for itself to tanks in Thunderbird 5. I think that is highly unlikely: Thunderbird 3's fuel consumption is far too high to use the satellite as a gas station.
Communications are of vital importance for a communication satellite. For this reason the communication systems on Thunderbird 5 as well as the assisting satellites have been installed in multiple failover configurations. The main antennas connecting the satellites are sticking out of Thunderbird 5 to limit the influence and shadow-effects of Thunderbird 5 itself. Because the satellites are in a fixed position relative to each other, the communication is focused as a beam and targeted to each of the three other satellites. The audio-signals are encoded and superimposed on a laser beam directed at the satellites. This way minimum spillover is achieved, limiting the chance of discovery during transmission. Further reduction of the possibility of discovery is that broadcasts are only made when there is something to transmit. A final method to avoid discovery is obtained by using laser frequencies for communications that are well into the ultra-violet end of the spectrum. This way, no normal radio telescope or receiver will ever tune into these frequencies by accident.
Each of the three satellites assisting Thunderbird 5 has a big main monitor antenna on a long pylon underneath the satellite, just like Thunderbird 5 itself. This antenna is always pointed at Earth and receives the distress calls as part of all the communication signals broadcast from Earth and intercepted by International Rescue. For this reason the antenna is designed for ordinary radio wave frequency reception and transmission. Because of the height of their orbit, the sensitivity of the equipment is very high to receive the very faint signals from Earth.
The use of a directed ultraviolet laser between satellites does not apply to communication with Tracy Island. The Earth's atmosphere absorbs most electromagnetic frequencies except for visible light and radio waves. In itself, this is a fortunate thing as it thereby protects life on Earth from exposure to potentially harmful radiation such as ultraviolet, X-ray and gamma rays originating from the Sun or interstellar space.
For communication between the satellites and Tracy Island normal radio frequencies are used. Eavesdropping by other parties can still be limited by narrowing the width of the radio beam as much as possible and by scrambling the message.
This focused transmission to base is made possible by using the 8 parabolic antennas that are mounted underneath Thunderbird 5 (as well as the satellites). The 8 parabolas can adjust their orientation to focus the beam on Tracy Island. They focus on the antenna on Tracy Island that is regularly serviced by Alan who is brought there by Thunderbird 2 as seen in Attack of the Alligators!. Given a distance between satellites of 21,835km and a distance from Tracy Island to the nearest satellite of at least 13,371km, instantaneous response seems possible since the signal takes a minimum of 0.04 seconds one-way if Thunderbird 5 can communicate directly. Relayed via another satellite, the signal distance would be at least 35,206km which takes electromagnetic radiation 0.1 seconds to traverse. This communications delay is way shorter than the 1.3 seconds the Apollo mission crews on the Moon needed to receive or transmit a message to or from Earth. The 0.1 second delay allows for near normal conversation.
Time is known to be flexible in view of Albert Einstein's general (or special) relativity theory. It only comes into play at speeds above 0.3 times the speed of light or when a big mass (such as a planet or star) is nearby. Although the orbital speed is nowhere near light speed and the Earth has a large mass but is nowhere near stellar mass, the time delays do affect communication. This is not only the case for Thunderbird 5 and helper satellites but also for the general GPS (global positioning system) satellites.
For exact communication to take place, all clocks in all satellites as well the clock down on Earth need to be kept synchronized. The high orbital speed results in satellite clocks running slower than the clock on Earth. When overhead, Thunderbird 5 has a maximum speed in relation to an Earthbound receiver and its time delay is given by the Lorentz time dilation:
which produces the "famous" conclusion that all moving clocks tick slower (although Jeff will think John's clock is slow, John will think the opposite – it's almost zero), the time difference per day is almost but not quite negligable.
At the same time, Earth has a mass of 5,972⋅1024kg and the presence of this mass makes clocks run slower too. The stronger the gravitational potential θ (the more negative its value, the closer to the mass), the slower time passes. In comparison with someone on Earth, the clock inside a satellite moves faster. The relative difference in interval measured in two positions at different distance to Earth is given by:
where θ1 and θ2 are the gravitational potentials at ground level and 7000km high (a more negative potential the closer you are to the mass: θ = —G⋅MEarth/r where r is the orbital radius).
For Earth values this equates to
In t = 24 hours the difference is 3.1 ⋅ 10–5s (or 31 microseconds) that clocks run faster in satellites than on Earth.
The result of the two effects is that the satellite clocks run slightly less than 31 microseconds faster than a clock on Earth. Enough for Brains to ensure that each of the three helper satellites regularly synchronizes with Thunderbird 5 and all four synchronize with Tracy Island at ground level to agree on "true" time on Tracy Island. Since clocks go faster in a satellite, the "easy" correction mechanism is to ensure all satellite clocks deliberately go somewhat slower which reduces their "tick" frequency which is sped up by relativity to be in line with the normal "tick" frequency of Earth.
Thunderbird 5 and its satellites constantly run the risk of being seen by astronauts that happen to be "nearby" to service their own satellites. Visual sightings are impossible to avoid and therefore Thunderbird 5 cannot be totally invisible. It's likely that Jeff Tracy registered all his satellites with the World Space Administration as part of his Tracy Construction and Aerospace Corporation. This way, the satellites are known, can be seen and do not raise any suspicion.
Still, it helps to remain invisible as much as possible. Invisible means that whatever radiation is thrown on an object is not returned to its source. The object remains "black" in the blackness of space and is not seen. A reflected radar beam is not received at its source. The idea put forward in the Haynes Technical Manual to send back a negative image is physical nonsense. A negative image (negative of what?) is still an image and its return would positively affirm there is something there that sent it.
Something is totally invisible if it absorbs all radiation that is thrown at it in any frequency: radio, visible light, X-ray. Such an object is called the perfect absorbing body. But no such object can exist. Absorbing all incoming radiation means the object absorbs all the energy involved. Doing so will heat up the object. It will start to be warmer than its surroundings (0K in space) and will start to radiate itself. This is known as "black body radiation". Depending on its temperature, the black body radiates mostly at a wavelength that depends on its temperature (according to Wien's Law). Had Thunderbird 5 been a black body, it would have warmed up the satellite to a temperature of a few kelvin and therefore most of the radiation would have been in the very long radio wavelengths of 1 meter. Not many detectors and receivers are tuned to such long radio waves, but if they did, they would detect Thunderbird 5.
Another technique to reduce visibility is to use stealth techniques. Stealth means that any radiation that is thrown at the object is deflected in a different direction. This way the sender does not receive anything and will assume there is nothing there.
Detection or visible sighting always remains a possibility but can be reduced and defused when the satellites are properly registered. Come to think of it… it may not be a good idea to advertise the name of the satellite on the fusion ring outside Thunderbird 5. Or the name of the organization mirror reversed on the window of the main control room.
I am pleased to say that Thunderbird 5 has even triggered some academic science interest and a fun paper is devoted to it, written by J.C. Coxon, J.F. Barker and T.M. Conlon in the Journal of Physics Special Topics. They start from the assumption that Thunderbird 5 follows a low stationary orbit at 390km, the same as the International Space Station (ISS), rather than the 7,000km we mentioned earlier as a possibility. Given that Thunderbird 5 is clearly visible in the episodes, it must be clearly visible on Earth.
