By the classification and rating administration

• THIS PRESENTAION HAS BEEN RATED

• BY THE
• CLASSIFICATION AND RATING ADMINISTRATION

• 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.

• © 1852 All Rights Reserved
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• © 1852 All Rights Reserved
• VOID WHERE PROHIBITED BY LAW

• PBIS ANTI-VACUITY

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

• 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 = 42 a3 G mo
• 86,400s2 = 42 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