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How many times have you heard someone describe a difficult concept as
“it’s not rocket science” – meaning it’s not as difficult to understand
as rocket science is. Rocket science is synonymous with difficult subjects.
Wouldn’t it be nice to be able to say something like, "well,
I actually know rocket science, and I think this is more difficult than rocket science."
After watching today’s video, I think you may very well have the background
to be able to say just that, because I’m going to show you how communications satellites work,
and how they are launched into orbit.
Although there are several different types of satellites,
these types are the ones that probably have the biggest impact in our daily lives.
But to understand what these things do and how they are launched,
you’re going to have to learn something about…you got it,
rocket science. And I’m hoping you’ll find that it’s really not as hard as it’s cracked up to be.
That’s coming up right now…
If you’ve ever used a GPS app to find directions,
or if you have looked up the weather for your town, or watched a live TV broadcast from a
foreign country – you have interacted with a satellite. Satellites affect our daily lives.
There are almost 3000 operational satellites, owned by over 100 different countries, orbiting
the earth right now. And thousands more are planned for the future.
About 550 of these are in what’s called geo stationary orbits.
Communications satellites are typically in such orbits. What this means is that,
the satellite appears stationary compared to the rotation of the earth. It stays in
the same point in the sky at all times. In other words, you can leave your satellite
dish that receives your favorite TV shows in one position, and never have to change it.
So the question is how do scientists calculate where to put the satellite so that it remains
at the same point in space? Orbital mechanics is rooted in Keppler’s laws of planetary motion,
published way back in 1609. Newton’s laws of universal gravitation,
published in the Principia Mathematica around 1687 also plays a role in many calculations.
Keppler’s laws allow us to calculate the period and speed of such a satellite.
Speed is the square root of mu over r, where mu is the standard gravitational parameter, equal
to the Newtont’s gravitational constant times the mass of the planet,
r is the radius of the satellite from the center of the earth.
And the period has the following formula. Note that the speed and period
only depends on the radius of the satellite, and not on its mass.
A geo stationary orbit is circular,
and since the altitude of the satellite does not change, its speed must be constant.
If you do the calculations, you will find that the geostationary orbit is
35,786 km from the equator. The orbital period is 23.93 hours,
or 23 hours 56 minutes. You might say, why isn’t It exactly 24 hours? Well,
23 hours and 56 minutes is actually equal to one sidereal day. This is the time it actually takes
for the earth to complete one rotation with respect to a non-rotating frame of reference.
The reason we normally count 24 hours as being one day, is because 24 hours is the precise time the
sun is at the same spot in the sky every day. But you have to keep in mind that the earth moves with
respect to the sun. The earth moves 1/365th of the arc around the sun during this time. That’s about
4 minutes. In other words, the earth has to rotate just a little bit more about 4 minutes, before the
sun is directly overhead. But one full rotation around its axis is actually 4 minutes less than that.
Now the question is how is a communications satellite inserted into such an orbit? The first
step in this process is to launch the satellite on a rocket that has the payload capacity to carry
the satellite to this orbit, and can impart the speed necessary to maintain this orbit.
In the United States, one workhorse rocket for this task has been the Atlas V.
This rocket weighs about 700,000 lbs, or 317,000 kilograms at launch and can lift 28,000 lbs,
or 12,700 kilograms to geostationary orbit. 90% of its weight is fuel, which is typical for rockets.
The main engine is powered by liquid oxygen and RP-1 – which
is a highly refined form of kerosene, similar to
jet fuel.
How does a rocket work? First, a rocket does not rely on the atmosphere to oxidize the fuel like
a jet engine does. That’s because it carries its own oxidizer. This
allows it to be able to function in outer space where there is no atmosphere available.
A jet engine would not work here because there is no oxygen available to burn the fuel.
Rocket engines are an application of Newton’s third law, for every action, there is an equal
and opposite reaction. The combustion of fuel causes high pressure exhaust gases
to be expelled at supersonic speed. The rearward acceleration of the
mass of the fuel leaving the rocket nozzle causes the equal and opposite
reaction of forward thrust powering the rocket forward or upward during launch.
The shape of the nozzle of the rocket
is designed to increase the velocity of the exhaust gases further to increase its thrust.
Highest thrust is achieved when the mass flow rate of the fuel and exit velocity of the propellant
is high according to this equation.
The fuel has to be delivered at high volume and pressure to get the thrust required for lift.
This pressure is provided by fuel pumps that boost the pressure of the gases
before entering the combustion chamber. Because these pumps can boost the pressure,
the fuels do not have to be pressurized so high, and the thickness of their storage
tanks can be reduced resulting in weight savings, and increased payload capacity.
Now you might ask, how are these pumps driven? They're typically driven by using a
small amount of fuel to drive a turbine which drives the pump.
Maintaining a stable straight flight is an issue. Early rockets were stabilized by large fins.
For stable flight the center of pressure where the net aerodynamic force acts,
must be lower than the center of gravity. This is because if its
angle of attack changes relative to its flight path, the net force acting below the
center gravity cam restore the stability that realigns the nose of the rocket.
Modern rockets don’t use fins though, because of the extra weight and aerodynamic drag they cause.
Stability comes from swiveling the thrust nozzle to keep it stable. This is called gimbaled thrust.
A geosynchronous orbit is achieved in stages. Typically, the rocket will take the satellite
on its orbital altitude, but the initial orbit is elliptical.
This elliptical orbit has to be changed to a circular orbit to become geostationary.
So for example, An elliptical orbit may take the satellite to an altitude of 150 km, at its
at its lowest point, called the perigee, and to the geo stationary orbit of
35,786 km at its highest altitude, the apogee. We can use Keppler’s laws to calculate the speeds
it will have at these points – about 36,500 km/hr at perigee, and 5800 km/hr at apogee.
The laws of physics are such that the satellite continues on an elliptical orbit
until something changes its orbit. This change is done by accelerating the rocket
at precisely the right time during its trajectory so that it forms a more and more circular orbit
with every pass around the earth.
The thrusters have to be turned on precisely at the apogee to accelerate the craft from 5800 km/hr
to 11,000 km/hr – which is the speed it needs to have to maintain a circular geostationary orbit.
As you can probably surmise, there is only one geostationary orbit and it is at 35,786 km
above the earth’s equator. There is no other geostationary orbit.
And there are 500 satellites at that altitude. This real estate, even in space is limited. The
total perimeter available is about 265,000 km. This wouldn’t be a problem if each of the 500
satellites were placed equal distance apart, there would be 500 km of space between them.
But that’s not the way the world works. There are many more satellites above
the most developed regions of the earth. They are sometimes less than 10 km apart.
And the speed with which they have to move is 11,000 km per hour,
or 3 km per second, there is not much space. They are less than 4 seconds apart. The real
estate here has is a prized commodity, as you might imagine, and is tightly controlled by an organization called, the
international telecommunications union (ITU) which assigns each satellite a slot at this perimeter.
On addition, unless the rocket is launched from somewhere in the equator, it will have an orbit that is
not quite geo stationary because it will not be in line or in the same plane relative to the equator.
So for example, when satellites are launched from Cape Canaveral, Florida, which is located at about
28.5 degrees north latitude, the orbit will be inclined 28.5 degrees from the equator. This has
to be adjusted. And this requires more fuel.
It is beneficial, therefore, for countries to launch their rockets
as close to the equator as possible so that less rocket fuel is needed to make this adjustment.
In addition, launching from close to the equator gives the rocket
added inertia because of the earth’s greater speed of spin near the equator, so that the launched
rocket will already be moving at the speed of the earth's spin at the equator before the launch.
Note that not all communications satellites are placed in geostationary orbits. Some are placed
in low earth orbit too. Low earth orbit satellites can serve the same function, but you have to use
many of them as they are moving at such high speeds. And there has to be constant
hand off of transmissions from one satellite to another. But the advantage is that these
satellites are cheaper to launch and cheaper to make because they don’t have to be as powerful,
since transmission distances are a lot shorter.
So what happens now, that we finally have our satellite in orbit around the earth.
We have adjusted to make it a circular geostationary orbit.
We have placed it in a correct slot assigned by the ITU. And we
have adjusted its angle of orbit so that it is in the same plane as the equator?
The first thing that happens is that solar panels are deployed so that the satellite
can have power to function.
The main function of the satellite
is to receive signals from earth mainly in the form of radio transmissions,
amplify them, and relay them back at a different frequency back to the surface of the earth. The
shift in frequency is used to prevent interference of incoming signals with outgoing signals.
Since radio waves are a form of electromagnetic radiation, same as visible light,
they do not bend much around the curvature of earth – photons are too fast after all.
The job of the satellite is to transmit radio waves over long distances. Otherwise,
this would require a string of thousands of relay stations on earth to do the same task.
These satellites usually have at least two antennas which may be aimed at two
different points on the ground. Each is used for both incoming and outgoing transmissions.
These antennas are generally made as large as possible for greater sensitivity in receiving
signals from earth which can become quite faint by the time they reach the satellite. But
the size is limited to about 10 feet diameter, or 3 meters, due to space restrictions inside the rocket.
Interestingly, a geostationary orbit is sometimes called the "Clarke orbit," named
for science fiction writer Arthur C. Clarke, who wrote "2001-A space odyssey." Believe it or not,
he was the first person to detail the usefulness of such an orbit in a story he wrote back
in 1945. That tells you that science fiction can sometimes foretell future science fact.
The next time you watch satellite TV, or use your GPS app, listen to SiriusXM radio,
or check the weather, think about the rocket science and the incredible technology
that goes into allowing us the privilege to enjoy these fantastical technologies.
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And if you have a question, post it in the comments below because I try to answer all of them.
I will see you in the next video my friend!