Transcript Understanding Orbits

Orbital Mechanics 101, Part I
 Understand basic orbital
mechanics and how orbits
work
 Understand the different
types of orbits used for
different purposes
 Understand basic principles
of Interplanetary Travel
mechanics
Newton’s Laws: Gravity
 Newton’s Law of Universal Gravitation:
The force of gravity between two bodies
is directly proportional to the product of
their two masses and inversely
proportional to the square of the
distance between them.
 F = G M1M2
R2
 If we double the distance between the
two masses (R) in the upper part of the
figure to (2R) in the lower figure, the
gravity force (Fg) is decreased by four
(Fg/4).
Spheres of Influence
 A body’s sphere of influence (SOI) is
the surrounding volume in which its
gravity dominates a spacecraft.
 In theory, SOI is infinite.
 In practice, as a spacecraft gets
farther away, another body’s
gravity dominates.
 The size of a planet’s SOI depends on:
 The planet’s mass
 How close the planet is to the Sun
(Sun’s gravity overpowers that of
closer planets)
Escape Velocity
 Because a body’s size and mass
determine its gravitational pull, escape
velocity differs for each object as
explained by our pal Newton
F = G M1M2
R2
….Or just think of a baseball
Orbital Motion: Baseballs in Orbit
8 Km
5m
 If a baseball player throws a baseball
horizontally from a mountain top:
 Gravity pulls the ball toward the ground.
 The faster a ball is thrown horizontally, the
farther it will go before gravity pulls it to the
ground.
 When an object moves fast enough, it will
go far enough as it falls to “miss” the Earth
and stay in orbit.
Orbital Motion: Baseballs in Orbit
12 Km/sec
D
8 Km/sec
5 Km/sec
12 Km/sec
G
8 Km/sec
5m
5 Km/sec
5m
5m
For that second of travel, gravity will pull the baseball approximately 5 meters towards
the earth
For every 8Km traveled the earth’s surface given that it is curved, drops 5 meters from
under the object in motion
So if my baseball is traveling 8Km/sec the distance downward caused by gravity is offset
by the curvature drop-off of the earth, hence…. An orbit is sustained
Orbital Motion: Baseballs in Orbit
 Therefore, a baseball thrown fast
enough to cover exactly 8
kilometers in the time it takes the
ball to fall 5 meters will be in a
circular orbit.
 Increasing velocity (adding more
energy) will make it an elliptical
orbit, unless escape velocity is
reached
Orbital Velocity
 Orbital velocity – the speed an object must maintain to stay in orbit
 The closer an object is to Earth, the faster it needs to travel to remain in orbit
 The higher a spacecraft climbs from Earth, the slower it can travel and still resist
gravity
At an altitude of 124 miles the required orbital velocity is just over 17,000 mph (about 27,400 kph). To maintain
an orbit that is 22,223 miles above Earth, the satellite must orbit at a speed of about 7,000 mph . That orbital speed
and distance permits the satellite to make one revolution in 24 hours.
Orbiting Around a Soda Can
 On top we have an orbit around a soda can.
 If we draw a line on the soda can directly below
the orbit we’d get a ground track.
 If we cut the soda can in half and laid it flat, the
shape of the ground track is as shown in the
lower figure.
10
Non-Rotating Earth
 Here’s what a ground track would look like for a non-
rotating Earth if we stretch the Earth onto a flat-map
projection.
 Notice that the ground track is made by a spacecraft in
orbit around Earth—this orbit is a great circle.
Add Earth’s Rotation
Non-Rotating Earth
 This is a typical
low Earth orbit.
 The “map” moves
eastward so the
second orbit
ground track looks
like it moved to the
west.
Rotating Earth
Types of Orbits
 Low-Earth orbit – an orbit up to about 1,240 miles above the Earth
 Medium-Earth orbit – one with an altitude of about 12,400 miles
 High-Earth orbit – an orbit at an altitude of about 22,300 miles
Types of Orbits
Low Earth Orbit (LEO)
• Lowest altitude a spacecraft must achieve to in
order to orbit the Earth (520 km altitude )
• Spacecraft in these orbits circle the Earth
approximately every 90 minutes or so.
• Used for things that we want to visit often like the
Hubble Space Telescope and the International Space
Station
• A significant disadvantage is the speed of the
satellite which at 18,000 miles per hour in LEO does
not spend very long over any one part of the Earth at
a given time.
Apogee
Perigee
Types of Orbits
Polar Orbits
• These orbits have an inclination near 90 degrees.
• This allows the satellite to see virtually every part
of the Earth as the Earth rotates underneath it.
• It takes approximately 90 minutes for the satellite
to complete one orbit.
90 deg
Types of Orbits
Geosynchronous (Geostationary) Orbits (GEO)
• Orbits with a period of about 24 hours.
• Since it matches the revolution cycle of the earth, it holds stationary over a given
point of the earth’s surface
• Disadvantage is the expense in putting a satellite into high orbit nor is it possible to
repair it via the space shuttle.
• Geosynchronous orbit is over Earth’s equator and is called a Geostationary orbit
Types of Orbits
Orbital Mechanics 101, Part I
 Understand basic orbital
mechanics and how orbits
work
 Understand the different types
of orbits used for different
purposes