SKY SCIENCE
Orbital Mechanics
PHYSICS AND CHEMISTRY
BY ERIC CHOI
Backgrounder: Page 1 of 3
ORBITAL MECHANICS
Why doesn’t the Moon fall out of the sky, the way the apple fell out of the tree and hit Isaac Newton on the
head? The answer is…the Moon actually is falling!
Imagine firing cannonballs off a hypothetical “extremely high” mountain. The Earth’s gravity (actually air
resistance too, but we will blithely ignore that) would bend the path of the cannonball and cause it to fall
back to Earth (1). The faster the cannonball is fired, the farther it would go before falling back to Earth (2).
If the cannonball was going fast enough, it would not hit the surface because the Earth is curving away
from the cannonball at the same rate the cannonball is falling. Like the Moon, the cannonball would be in
orbit (3).
Around 1605, the German astronomer and mathematician Johannes Kepler presented his three laws of
planetary motion. These laws form the basis of our understanding of satellite and planetary orbits.
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Copyright Let’s Talk Science ©2012
SKY SCIENCE
Orbital Mechanics
PHYSICS AND CHEMISTRY
BY ERIC CHOI
Backgrounder: Page 2 of 3
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Kepler’s First Law – The orbit of each planet is an ellipse, with the Sun at one focus.
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Kepler’s Second Law – A line that joins a planet to the Sun sweeps out equal areas in equal
times. For satellites in Earth orbit, Kepler’s Second Law could be restated as “A spacecraft orbits
such that the line joining it to the centre of the Earth sweeps over equal areas in equal time
intervals.” In other words, a satellite moves faster when it is close to the Earth and more slowly
when it is further away.
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Kepler’s Third Law – The square of the period of a planet’s orbit (P) is proportional to the cube of
its mean distance from the Sun (a). In other words, the further a planet is from the Sun (or the
higher a satellite is from the surface of the Earth), the longer it takes to complete an orbit.
While Kepler’s Laws describe orbital motion, it was the English mathematician and physicist Isaac Newton
(1642–1727) who would discover the underlying physics behind the observed motion. Newton’s most
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Copyright Let’s Talk Science ©2012
SKY SCIENCE
Orbital Mechanics
PHYSICS AND CHEMISTRY
BY ERIC CHOI
Backgrounder: Page 3 of 3
famous book was called Philosophiae Naturalis Principia Mathematica, more commonly known simply as
the Principia, which was published in 1687 and contained his Three Laws of Motion. This is the basis of
what is now known as “Newtonian” or “classical” mechanics. Newton’s Laws of Motion are as follows:
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Newton’s First Law – An object at rest will tend to stay at rest, and an object in motion will tend to
keep moving in a straight line, unless acted upon by some outside force.
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Newton’s Second Law – The acceleration of an object is proportional to the force applied and is in
the same direction as that force.
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Newton’s Third Law – For every action there is an equal and opposite reaction.
The latter is probably the best known of Newton’s three laws, and is really what makes spaceflight
possible. Rocket engines work by propelling exhaust out the back of the spacecraft, and since every
action has an equal and opposite reaction, the spacecraft is propelled forward.
According to Newton’s Law of Universal Gravitation, the force of gravitational attraction between any two
objects (such as a cannonball and the Earth) is directly proportional to the product of their masses and is
inversely proportional to the square of the distance between them. The more massive the objects and/or
the closer they are together, the greater the force of gravitational attraction between them, and vice versa.
This law is called “universal” because as far as we know the same principle applies everywhere in the
Universe. The motion resulting from this gravitational attraction is called two-body motion.
The type of orbit that a satellite is launched into depends on its mission. Low Earth orbit (LEO) is the
simplest orbit to achieve and is also the most extensively used. Over 90% of artificial objects orbiting the
Earth are in the LEO “corridor”, an area bounded on the low end by atmospheric drag factors (at about 200
km altitude) and at the high end by the lower Van Allen radiation belt (at about 1,000 km altitude).
Sun-synchronous orbit (SSO) is a type of polar LEO in which the Earth’s uneven gravitational field “twists”
the orbit at a rate of one revolution per year. The result is that the orbit plane will always maintain the
same angle with respect to the Sun, and the satellite crosses the equator at the same local time every
orbit. Keeping the orbit at the same orientation with respect to the Sun and having a fixed equator
crossing time means the spacecraft will experience the same lighting conditions every time it passes over
a particular point on the surface. This is why remote sensing, weather and reconnaissance missions use
Sun-synchronous orbits (for example, motion can be detected by a change in shadows).
At an altitude of 37,500 km is geostationary orbit (GEO), where a satellite goes around the equator at the
same rate that the Earth is rotating. Therefore, it appears “stationary” as viewed from the Earth. British
science fiction author Arthur C. Clarke first proposed that this orbit could be used by communications
satellites in a Wireless World article published in 1945. This is why GEO is sometimes called the “Clarke
orbit”. The majority of communications satellites and many weather satellites are in GEO orbits.
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