# 0.10 Artificial satellites

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Artificial satellites are the backbone of modern communication systems.

The motion of a satellite or space-station is a direct consequence of Earth’s gravity. Once launched in the appropriate orbit, these man-made crafts orbit around Earth without any propulsion. In this module, we shall study basics of satellite motion without going into details of the technology. Also, we shall develop analysis framework of artificial satellite, which can as well be extended to analysis of natural satellite like our moon. For the analysis here, we shall choose a simple framework of “two – body” system, one of which is Earth.

We should be aware that gravity is not the only force of gravitation working on the satellite, particularly if satellite is far off from Earth’s surface. But, Earth being the closest massive body, its gravitational attraction is dominant to the extent of excluding effect of other bodies. For this reason, our analysis of satellite motion as “isolated two body system” is good first approximation.

Mass of artificial satellite is negligible in comparison to that of Earth. The “center of mass” of the “two body system” is about same as the center of Earth. There is possibility of different orbits, which are essentially elliptical with different eccentricity. A satellite close to the surface up to 2000 km describes nearly a circular trajectory. In this module, we shall confine ourselves to the analysis of satellites having circular trajectory only.

## Speed of the satellite

Satellites have specific orbital speed to move around Earth, depending on its distance from the center of Earth. The satellite is launched from the surface with the help of a rocket, which parks it in particular orbit with a tangential speed appropriate for that orbit. Since satellite is orbiting along a circular path, there is requirement for the provision of centripetal force, which is always directed towards the center of orbit. This requirement of centripetal force is met by the force of gravity. Hence,

$\frac{GMm}{{r}^{2}}=\frac{m{v}^{2}}{r}$

$⇒v=\sqrt{\left(\frac{GM}{r}\right)}$

where “M” is Earth’s mass and “r” is linear distance of satellite from the "center of mass" of Earth.

The important thing to realize here are : (i) orbital speed of the satellite is independent of the mass of the satellite (ii) a satellite at a greater distance moves with lesser velocity. As the product “GM” appearing in the numerator of the expression is constant, we can see that

$⇒v\propto \frac{1}{\sqrt{r}}$

This conclusion is intuitive in the sense that force of gravitation is lesser as we move away from Earth’s surface and the corresponding centripetal force as provided by gravity is smaller. As such, orbital speed is lesser.

This fact has compounding effect on the time period of the satellite. In the first place, a satellite at a greater distance has to travel a longer distance in one revolution than the satellite closer to Earth’s surface. At the same time, orbital speed is lesser as we move away. It is, then, imperative that time period of revolution increases for satellite at greater distance.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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