“PHLYZICS”
Satellites
 Anything that orbits something else is called a SATELLITE of that “something else”.
 When a satellite orbits something, it travels in a circular path (well…..not exactly, but we
will be assuming so to make the calculations do-able)
 But wait!!!! Things don’t want to move in circular paths. They want to move
___________________________________________________. Therefore, something
must be providing a _____________________.
 What provides the centripetal force to keep a satellite in orbit? ____________________
 An important equation: h = R – r (or altitude = R - r)
 Some mathematical relationships:

 Some thoughts on satellites
v  ________
Since T = ____________,
T  ________

- Satellites do NOT need to use their rocket boosters to stay in orbit, only to get into orbit.
- Satellites move REALLY fast (~20,000 m/s, for example).
- Satellites are used for communications, defense, GPS, etc.
- Satellite “crowding” or “traffic” will be a major world issue in the future.
- The lower (altitude) a satellite orbits, the faster it moves AND the shorter its period.
- Satellites that orbit at the equator with a period of 24 hours are called “GEOSYNCHRONOUS” satellites.
- Earth is known as a “natural” satellite of the sun. The moon is a “natural” satellite of the
earth.
Some Deep(–space) questions.
1) Sir Isaac Newton postulated that if you took a
cannon to the top of a tall mountain, and fired it
fast enough, you could get the cannonball to orbit
the earth. Assuming that we took the cannon to
the top of Mount Everest (8,848 m tall), how fast
would the cannonball need to be fired (horizontal
to the earth’s surface) to get it to orbit the earth?
2) There are satellites in orbit right now above the earth. Some move (relative to us, here in
Holland, PA) and some stay at a fixed point relative to certain locations (like the equator).
The satellites that have a fixed position relative to us are called “GEO-SYNCHONOUS
SATELLITES”. Find the altitude of one of Verizon’s geo-synchronous satellites.
3) Explain why synchronous satellites could not orbit DIRECTLY ABOVE Holland, PA.
4) Why is one synchronous satellite not enough to communicate with all places on the earth?
Facts about numbers of satellites in orbit
Information from
http://www.radio-electronics.com
There are over 2,500 satellites in orbit around the Earth
There are also over 10,000 man made
objects orbiting around the Earth. These include a variety of pieces of satellite debris ranging from
panels to disused equipment.
Facts about satellite firsts
The first satellite named Sputnik 1 was launched by the Soviet Union on 4th October 1957. It was a
football sized globe that transmitted a "beep beep" sound as it orbited the Earth. The word Sputnik
means satellite. It continued transmitting for about 21 days. It was followed four months later by the
US satellite Explorer 1 which was launched on 31st January 1958.
Possibly one of the best known satellites was Telstar 1. Built by AT&T it was launched on July 10, 1962,
and on the same day live television pictures originating in the United States were received in France.
Facts about satellite orbits
Most communications satellites use what is termed a geostationary orbit. These are at an altitude of,
around 22,000 miles and as a result of their speed and the circumference of the orbit they travel
round the Earth above the equator in 24 hours. As they travel at the same rate that the Earth
rotates, they stay above the same point on the Earth's surface all the time.
In contrast, Low Earth Orbits are just above the Earth's atmosphere and are typically between 100
and 800 miles in altitude. Orbiting at this altitude, an object may only take about 90 minutes to
completely circle the Earth, travelling at around 17,000 miles per hour. Low Earth Orbit (LEO) is used
by manned vehicles such as the space shuttle and the International Space Station. It is also used for
weather and remote sensing satellites. On a clear night it is usually possible to see with the naked eye
several satellites in low earth orbit passing overhear.
Facts about the Global Positioning System (GPS)
The GPS system is run by the US Department of Defense. It consists of 24 operational satellites
although there are some extra in orbit as spares in case of catastrophic failure even though each
satellite is built to last for ten years. The satellites are named Navstar satellites and each one weighs
around 1860 pounds. They are about 17 feet across with the solar panels extended, and they transmit
about 50 watts, although the solar panels generate around 700 watts.
The satellites are in one of six orbits. These are in planes that are inclined at approximately 55
degrees to the equatorial plane and there are four satellites in each orbit. The orbits that are roughly
20200 km above the surface of the earth and the satellites travel at a speed of around 14000 km /
hour (i.e. about 8500 mph) which means they complete each orbit in roughly 12 hours.
Satellite Mechanics
mEarth = 6 x 1024 kg
K
R3
T2
rEarth= 6.4 x106 m
K orbits  1.01E13 ms 2
3
Earth
aC 
K orbits  3.35E18 ms 2
3
Sun
0. Derive the Satellite Equation, v 
v2
R
Fg 
FC 
GmM
R2
2R
v
f 
1
T
G  6.67 E  11 Nm
kg 2
g
GM
R2
mv 2
R
T
2
v
GM
R
GM
. Make sure to fully understand where it comes from.
R
1. What is the orbiting speed of a satellite moving uniformly in a circular path with an orbital
radius (distance from the center of the satellite to the center of the earth) of 7.4 x106 meters.
2. What is the orbiting speed of a satellite moving uniformly in a circular path at a height above
the earth of ….
a) 5000 km
b) 10,000 km
c) 20,000 km
3. A 5000 kg satellite is orbiting at a speed of 2000 m/s around Mars, which has a mass of
6.37 x 1023 kg. Find:
a.
b.
c.
d.
The orbital radius at which it is orbiting.
The period of this satellites motion.
The frequency of this satellite’s motion.
The magnitude and direction of the centripetal force.
4. A man-made satellite takes 28 days to orbit the earth.
Answers:
1) 7,353.98 m/s
2) 5,925 m/s; 4,940 m/s; 3,893 m/s
3) 1.062E7 m; 9.27 h; 3E-5 Hz;
1,883.2 N
4) 3.896E8 m; 3.831E8m; ____
4
5) 2.98 x 10 m/s, ______
6) R = 4.016E8 m; 9,704.2 m/s
7) 465.4 m/s
8) .577 v1, 5.2 T1
a. Using Kepler’s 3rd Law, find the satellite’s orbital radius.
b. Find the satellites altitude above the earth’s surface, using the radius of the earth given
above.
c. Explain why this satellite needs to orbit in space, instead of in the earth’s atmosphere.
In other words, why would an atmospheric orbit be undesirable?
5. With what speed does the earth orbit the sun? The mass of the sun is 2 x 1030 kg, and the radius
of the earth’s orbit is 1.5 x 1011 m. Why don’t you “feel” like the earth is moving this fast?
6. Space Explorer!!! You are looking through your telescope when you find a new moon of
Saturn. You watch, day after day after day, and you find that it orbits the planet once every 3
days. Using this information, and the facts that the Kepler constant for Saturn’s moons is
9.64E14 m3/s2 and Saturn’s mass is 5.67 x 1026, find (if possible) this new moon’s mass,
velocity, and orbital radius. If one of these numbers is impossible to find, please explain why.
7. When a satellite is launched from Cape Canaveral, FL, it needs to attain a speed of 3,075 m/s in
order to become a GEO-SYNCHRONOUS satellite. That is REALLY fast. Launching from
close to the equator allows the launched satellite to steal some of this velocity from the rotating
earth (whereas the earth has no rotational velocity to give at the poles). How much velocity
does the satellite “gain” if it is launched AT the equator instead of at the North Pole?
8.
A satellite has its orbital radius tripled. What effect does this have on its velocity? On its
period?