Why do objects move in a circle?
Why doesn’t the moon fall down?
• It does.
What is a satellite?
• Technically, anything that is in
orbit around Earth is technically a
satellite, but the term "satellite"
is typically used to describe a
useful object placed in orbit
purposely to perform some
specific mission or task. We
commonly hear about weather
satellites, communication
satellites and scientific satellites.
Whose Satellite Was the First to Orbit Earth?
• The Soviet
Sputnik satellite
was the first to
orbit Earth,
launched on
October 4, 1957.
• It weighed 184
pounds and was
23” in diameter.
What happened to it?
• After 92 days, gravity took over and Sputnik
burned in Earth's atmosphere. Thirty days
after the Sputnik launch, the dog Laika orbited
in a half-ton Sputnik satellite with an air
supply for the dog. It burned in the
atmosphere in April 1958.
Progress since then…
• ISS Video
How Do You Put Something In
• If the Earth were flat like some people used to believe, no
matter how fast you threw something out horizontally, it
would hit the ground. The faster you threw it, the farther
away along the ground it would hit. Plus - all of the balls will
hit the ground at the same time.
But the Earth is not flat!
• As something falls "straight" toward the center of the
Earth, it has to curve around with the Earth.
• Throw an object fast enough that its “fall”
matches the curvature of the Earth.
• The Earth’s curvature is such that it “drops”
about 5 meters every 8,000 m.
• So what speed would it have to go to orbit the
Earth at the surface?
8 km/s!
The only force on a satellite is the
force of gravity.
That’s the force pulling it in to the center.
• Space shuttle Atlantis final launch: NASA
video of last take-off
• Mars exploration rover
Let’s use equations to check how fast an
object near the Earth’s surface is orbiting?
• Fg = Fc
• Fg = mv2 / r
• m g = m v2 / r
• g = v2 / r
• v2 = g r
• If r = 6.38 x 106 m, what is v?
The orbital velocity is
• v2 = ( 9.8 m/s ) ( 6.38 x 106 m ) = 6.25 x 107
• v = 7.9 x 103 m/s
• That’s 17 000 mi/h!
What about the period? How long
does it take to make one orbit?
• v=d/T
• T=d/v
• T = 2π r / v
• T = 2 ( 3.14 ) ( 6.38 x 106 m ) / ( 7.9 x 103 m/s )
• T = 5074 s [ 1 min/60 s ] = 84 min
The Space Shuttle is an excellent example of a
satellite in a low-Earth orbit.
• The Space Shuttle orbits about 100
km to 200 km above Earth's surface.
Earth's radius is about 6 000 km so
this is an increase of only about 2%
or 3%. That means the force of
gravity is only about 4% to 6% less
than at Earth's surface.
Low Earth Orbit
• Imagine yourself in an
elevator when the cable
breaks! The only force on you
is gravity!
The Physical Aspect
• Bodily fluids are redistributed, with less in the lower
extremities, and more in the upper body. Without
the pulls of normal gravity, blood doesn't flow
downhill, but pools in the extremities including the
face, hands and feet, causing a puffy appearance.
And without that downward pressure, height
increases. Body mass often decreases with a loss of
muscular tissue from nitrogen depletion; the veins
and arteries of the legs become weaker, anemia
occurs, accompanied by a reduction in blood count.
Astronauts report an overall feeling of weakness and
loss of balance upon return to Earth, though
recovery is nearly complete after a week.
Types of Satellites
Types of Orbits
• Polar Orbits This orbit allows the satellite to
observe the entire Earth's surface as it rotates
beneath it. Most desired orbits are between
700 and 800 km altitude with orbit periods
between 98 and 102 minutes.
Uses of Polar Orbiting Satellites
• This orbit provides global daily coverage
of the Earth with higher resolution than
geostationary orbit. Even though
satellites do not pass directly over the
poles they come close enough that their
instruments can scan over the polar
region, providing truly global coverage.
• Geosynchronous Satellites Orbit around the Earth
at the same speed that the Earth rotates.
• What’s its period?
• 24 hours
• If they stay over the same place, they are called
geostationary. Where do they orbit?
• Over the equator. Because of this, it appears to
remain over a fixed point on the Earth's surface.
Uses of Geosynchronous Satellites
• Perfect for communications satellites because
always in view of the ground station providing
continuous TV and telecommunications
services to customers. Also ideal for making
uninterrupted observations of the weather or
environmental conditions in a given area.
• Geosynchronous- same period as
• Geostationary – orbits over the same
location on Earth
• Asynchronous – not once a day, like
the space station.
What is the orbital radius of a
geosynchronous satellite?
• Fg = Fc
• Fg = mv2 / r
• GMEMS/r2 = MS v2 / r
• GME/r2 = (2πr/T)2 / r
• GME/r2 = (2πr)2 / T2r
• GME/r2 = 4π2r2 / T2r
• GME/r2 = 4π2r2 / T2r
• Move r2 to top
• GME = 4π2r2r2 / T2r
• GME = 4π2r3 / T2
• Solving for r:
• r3 = GME T2 / 4π2
• This means that for a fixed period – like
24 hr – there is only ONE radius that will
• r3= (6.67 x 10-11)(6 x 1024kg)(86,400s)2 /4 π2
• r3 = 7.54 x 1022 m3
• r = 4.2 x 107 m
• If we subtract off the radius of the Earth,
which is 6.38 x 106 m (or 6380 km), then
• The orbital radius is 36,000 km above
earth, or 6 rE (6 times Earth’s radius).
What’s the velocity of a
geosynchronous satellite?
• Fg = Fc
• Fg = mv2 / r
• GMEMS/r2 = MS v2 / r
• GME/r2 = v2 / r
• GME/r = v2
• v= square root of (GME/r)
• V = 3070 m/s
So all the geosynchronous satellites
orbit at this radius!
Geosynchronous orbits are
1/10 the distance to the moon!
Space Junk at Tipping Point
• Debris – green dots
What happens when satellites
plunge back toward Earth?
• This happened on Sept. 22, 2011.
• Watch Out! NASA UARS satellite to hit
Earth... Anywhere!
• (Upper Atmosphere Research Satellite)
Comparing velocity, radius and period:
6.38 x
83 min.
8 km/s
Geostationary 4.23 x
24 hr.
3 km/s
27.3 days
1 km/s
Surface/ LEO
3.84 x
Does this make sense?
Doesn’t v = 2πr/T?
Then doesn’t that mean
that as r ↑, v ↑?
But v depends on T, so to eliminate v:
Fc = Fg⇒ mSv2/r = GmSmE/ r2⇒ v = √GmE/r
v2 = GmE/r = 4π2r2/T2
r3/T2 = Gm/4π2= constant
• r3 ∝ T2
• So as r increases, T increases.
Summary - 2 ways to find velocity:
• V = 2πr / T
• V = √ (GME/r) (This means square root!)
• Where r is the orbital radius, not the
height above the surface.
Problem Solving
• What is the speed of a space shuttle in a
circular orbit 1000km above Earth’s surface?
• The mass of Earth is 6 x 1024 kg and the radius
of Earth is 6.38 x 106 m. G = 6.67 x 10-11.
R = 7.38 x 106 m
Fc = Fg
V2 = GMe/R
V = 7.35 x 103 m/s or 16,500 mph
NASA GOES - P Mission Overview
• Cup of coffee
• Going to the bathroom
Space Junk Video
• 4 min.
Real Time Satellite Tracking
• Click and drag applet
Tracking ISS
• Another ISS tracking site.
Satellite Tracking
• Position of ISS and other satellites
History of ISS
Attitudes of ISS
• Adjusting the angle for solar
Interactive Reference Guide
• Videos of how the crew eats,
sleeps and exercises.
Upcoming Launches
NASA in motion
• Link to NASA Drawing Video
Cup of Joe
• Link to Cup of Joe Video
Atlantis leaves ISS
• Link to Undocking Video
Takeoff and Landing of Discovery
Apollo Guys – Co Ops
• Link Apollo Guys (Apologize)
Watching on the screen
Saturn V lifts off the ground
After many sims,
Flight control has got it down
You say that its not easy, but
Astronauts are all moonbound and wait
Were watching them on TV
Walking on the lunar ground and say
We did it Apollo Guys!
How GPS Works
•The dashed lines
show the actual
intersection point,
and the gray bands
indicate the area of
The solid lines indicate
where the GPS receiver
"thinks" the spheres
are located. Because of
errors in the
receiver's internal clock,
these spheres do
not intersect at one point.
Three spheres are necessary
to find position in two
dimensions, four are needed
in three dimensions.
Problem Solving #1
• A satellite over Jupiter is placed 6 x 105m
above surface, given mass of Jupiter, find v.
• Mass of Jupiter = 2 x 1027 kg,
• Radius of Jupiter = 71,492 kilometers
So r = radius of Jupiter + height over surface
r = 7.2 x 107 m
V2 = GMJ/r
v2 = 1.76 x 109 m/s
v = 4.195 x 104 m/s
Problem Solving #2
• A satellite wishes to orbit the earth at a height
of 100 km (approximately 60 miles) above the
surface of the earth. Determine the speed,
acceleration and orbital period of the satellite.
(Given: Mearth = 5.98 x 1024 kg, Rearth = 6.37 x
106 m)
• Speed = = 7.85 x 103m/s
• Acceleration = a = 9.53 m/s2
• Orbital period = T = 5176 s = 1.44 hrs
• One of Saturn's moons is named Mimas. The mean
orbital distance of Mimas is 1.87 x 108 m. The mean
orbital period of Mimas is approximately 23 hours
(8.28x104 s). Use this information to estimate a mass
for the planet Saturn.
• Using the T and R values given, the T2/ R3ratio is 1.05
x 10-15. This ratio is equal to 4*pi2/ G * Mcentral.
• Mass of Saturn can be found to be 5.64 x 1026kg.
• Satellites circling unknown planet. Sat1 has v1
= 1.7 x 104 m/s, and r = 5.25 x 106 m. Sat2 has
r = 8.6 x 106 m. Find v for Sat2.
So MPLANETG = constant = v2r
V12r1 = v22r2
V2 = 1.33 x 104 m/s
Which of following statements is accurate
regarding man-made satellites?
• A. It is possible to have a satellite traveling at either a
high speed or at a low speed in a given circular orbit.
• B. Only circular orbits (and not elliptical ones) are
possible for artificial satellites.
• C. A satellite in a large diameter circular orbit will
always have a longer period of revolution about the
earth than will a satellite in a smaller circular orbit.
• D. The velocity required to keep a satellite in a given
orbit depends on the mass of the satellite.
Next Genertion Car Navigation
Practice Questions Giancoli
Satellites orbiting earth
Launching Satellites

similar documents