Transcript Document

THIS PRESENTAION HAS BEEN RATED
TG-13
TEACHERS’ GUIDANCE STRONGLY ADVISED
Some Material May Be Unintelligible For Students Under 13.
Intense Frames of Scientific Instruction, Analysis, Comparing
and Contrasting, Description, and for Some Vocabulary.
BY THE
CLASSIFICATION AND RATING ADMINISTRATION
© 1852 All Rights Reserved
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© 1852 All Rights Reserved
VOID WHERE PROHIBITED BY LAW
ASTRONOMY
ORBITAL MECHANICS
OBJECTIVES
By the end of this presentation, students will
be able to
• Contrast the differences between the types
of orbits.
• Explain the use of these orbits to launch
rockets to inner and outer planets.
MOTION OF A SATELLITE
According to the law of gravitation,
gravity maintains all planets, rockets
and satellites in circular - near circular
motion around the planet and sun.
What, then, is the velocity of a
satellite in a low-earth,
near-circular orbit?
Fnet = Fg = mac
mg = m v2
r
g = v2
g = G mp
r
r2
v2 = G mp
r
Since the velocity of a satellite on the
surface of a planet is vo…
…then the velocity needed to launch
a rocket into orbit of radius r;
altitude of r-rp is
v2 = vo2 + vL2
vL2 = v2 - vo2
MOTION OF A PLANET
though planet orbits are nearly circular,
they really cannot be approximated
as circular…
VIS VIVA EQUATIONS - used to
determine the velocity of the planet at
any point in its orbit:
a circular orbit
an elliptical orbit
a parabolic orbit
a hyperbolic orbit
VIS VIVA EQUATIONS –
Circular orbit
(satellites and such)
semi major axis = radius
eccentricity = 0
Etot = -G2mp3T2
8p2a4
v2 = G(mo + mp) ( 1)
r
VIS VIVA EQUATIONS –
Elliptical orbit
(moons, asteroids, planets, etc)
eccentricity:
0<e<1
Etot is less
than zero
v2 = G(Mo + Mp) (2 - 1)
r a
VIS VIVA EQUATIONS –
Parabolic orbit
(some comets)
semi major axis
= infinity
eccentricity
=1
Etot = 0
v2 = G(mo + mp) (2)
r
VIS VIVA EQUATIONS Hyperbolic orbit
(Imperial Death Star)
Eccentricity is
less than
zero
Etot is more
than zero
v2 = G(Mo + Mp) (2 - 1)
r |a|
To launch a rocket from the earth
to an inner planet - Venus, for
example …
sun
Venus
Earth
…means the rocket is put into an
elliptical orbit around the sun
with the Earth located at the
aphelion and Venus located at
the perihelion.
sun
Venus
vL2 = v⊕2 - v♀2
Earth
To launch a rocket from the earth
to an outer planet - Mars, for
example …
Mars
sun
Venus
Earth
• …means the rocket is put into
an elliptical orbit around the sun
with the Earth located at the
perihelion and Mars located at
the aphelion.
Mars
sun
Venus
vL2 = v♂2 - v⊕2
Earth
A geosynchronous satellite
makes one complete orbit in the
same time that it takes for the
earth to spin once.
At what altitude must a
geosynchronous satellite be
placed?
T = 24hrs (3600 s) = 86,400 s
(1 hr)
At what altitude must a
geosynchronous satellite be
placed?
T2 = 4p2 a3
G mo
86,400s2 =
4p2 a3
(6.67x10-11)(5.979x1024 kg)
a3 = 7.54 x1022 m3
a = 4.22x107 m = 26,000 mi
At what speed must a
geosynchronous satellite be
traveling?
v2 = G mo
a
v2 = (6.67x10-11)(5.979x1024 kg)
(4.22x107 m)
v2 = 9.45 x107 m2/s2
v = 3074 m/s = 17,800 mph
ASTRONOMY
ORBITAL MECHANICS