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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
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
To launch a rocket from the earth to an inner planet - Venus, for example …
sun
Venus
Earth
vL2 = v⊕2 - v♀2
To launch a rocket from the earth to an outer planet - Mars, for example …
sun
Venus
Earth
Mars
To launch a rocket from the earth to an outer planet - Mars, for example …
sun
Venus
Earth
Mars
vL2 = v♂2 - v⊕2
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 = 42 a3 G mo
86,400s2 = 42 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?
