### Orbitology

#### Orbital Theories

Orbital Mechanics is the study of planetary motion and its applications to satellite programs. The theories governing Orbital Mechanics originated from three famous scientists and astronomers: Nicolaus Copernicus, 1473-1543, Johannes Kepler 1571-1530, and Sir Isaac Newton, 1643-1727.

(The images on the opposite page of this text are of Copernicus, Kepler and Newton)

In the 1500s, Copernicus originated the Heliocentric Theory. It states that the Earth revolves around the sun as it rotates on its axis. This theory became the impetus for studying planetary motion and orbital mechanics.

(The image on the opposite side of this text is of Copernicus surrounded by his books and equipment looking up into the heavens.)

In the 1600s, Johannes Kepler wrote Three laws of planetary motion:

1. All planets move in elliptical orbits.
2. Satellites closer to the Earth travel faster in their orbits than satellites in orbits farther away from the Earth.
3. The time required for a planet to make one rotation around the Sun is related to its distance from the Sun. The farther a satellite is from the Sun, the longer it will take to complete its orbit.

(The image on the opposite page of this text is of Kepler with his scientific notes in the background.)

Sir Isaac Newton’s Three Laws of Motion:

1. A body in motion will keep moving in the same direction and at the same speed unless acted upon by an external force. Satellites move in a curved path around the Earth because gravity acts as an external force upon them.
2. Objects in elliptical orbits slow down as they get further from the Earth and accelerate as they get closer to the Earth.
3. For every action, there is an equal and opposite reaction. The thrust required to put a satellite in to orbit is based upon gravitational pull.

(The picture on the opposite side of this text is of Newton with a depiction of how the universe was thought to look in his time in the background.)

#### Orbital Characteristics

Satellite orbits are either elliptical or circular. An elliptical orbit is any orbit having a path that varies in altitude as the satellite orbits the earth. A circular orbit is very close to being a circle. The satellites distance from the Earth’s surface remains relatively constant throughout the orbit.

(The image on the opposite side of this text is of two Earths with red circles around them. The one Earth is tilted to the right depicting Elliptical orbit. The other Earth is upright depicting Circular orbit.)

Apogee is the point in an orbit where a satellite is farthest from the Earth’s surface. Perigee is the point in an orbit where the satellite is closest to the Earth’s surface. The apogee of an elliptical orbit is farther away from the Earth’s surface than the perigee, but the apogee and perigee of a circular orbit are the same.

(The image on the opposite side of this text shows the Earth on its right side with a red circle around it. The top half of the circle is the word Apogee with an arrow pointing to that section of the circle. The bottom half of the circle is the word Perigee with an arrow pointing to the bottom half of the circle.)

Nadir is a point on the Earth directly below the satellite at any given moment. Ground track is the connection of all nadir points of a particular satellite.

(The image on the opposite page depicts the Earth with the banner “Nadir” at the top of the Earth. A broken red line cuts across the Earth in an upward swing to the right, with a yellow and green ball on it and the words “Ground Track” next to the line. The yellow ball moves towards the green ball.)

A polar orbit causes the satellite to pass over the North and South Poles. An equatorial orbit is aligned with the equator.

(The images for this text depict the Earth with a red circle going vertically around it, Polar Orbit, and a red circle going horizontally around it, Equatorial Orbit.)

#### Orbital Types

A Low Earth Orbit, or LEO, can view only a narrow swath along the ground trace due to its close distance to the Earth. However, it allows for many repeat visits per day.

Orbit Characteristics:

• Circular or Elliptical Altitude: 100-800 miles
• Orbital Period: 90-120 minutes
• Speed: approx. 17,000 mph
• Orbits per Day: 14-16

(The image on the opposite side of this text depicts the Earth with a diagonal red circle around it and a blue ball racing around that circle. The banner “Low Earth Orbit (LEO)” is above the image.)

A Highly Elliptical Orbit, or HEO, provides its best coverage in the northern hemisphere. It has the ability to dwell on a particular target due to relatively slow movement at apogee. However, the size of the sensor’s footprint changes with altitude.

Orbit Characteristics:

• Elliptical Altitude: 200-22,000 miles
• Orbital Period: 12 hours
• Orbit Speed: 7,500 mph at apogee
• 17,000mph at perigee
• Orbits Per Day: 2

(The image opposite this text depicts the Earth on the lower left-hand corner of the page with a very high and wide diagonal red circle around it with a racing blue ball on it. The banner at the top of the page says “Highly Elliptical Orbit (HEO).”)

A Geosynchronous or GEO is synchronized with the rotation of the Earth, making it appear stationary. The ground track is near the equator. A GEO is good for constant view of one geographic area.

Orbit Characteristics:

• Circular Altitude: 22,300 miles
• Orbital Period: 24 hours
• Speed: approx 7,500 mph
• Orbits per Day: 1

(The image on opposite page from this text shows the Earth with a red circle evenly wide around it and the blue ball racing around it. The banner at the top of the page says “Geosynchronous Orbit (GEO).)

#### Factors Affecting Satellites

Satellites remain in orbit through the equal, counteracting forces of gravity and velocity. Earth’s gravity pulls the satellite toward the Earth, while the satellite’s velocity moves it away.

(The graphic on the opposite side of this text show the Earth with half a red circle around it. The blue ball is part way round the circle with the word “Gravity” near it and three green arrows pointing towards the Earth. At the pointed end of the semi-circle on the opposite side is the word “Velocity.”)

Altitude also affects a satellite’s motion. The higher the altitude, the slower the satellite moves in its orbit. This is an example of Kepler’s third law. Satellites in elliptical orbits move slower at apogee than at perigee.

(The image on the opposite side of this text is depicting the Earth at the bottom left-hand corner with a wide arching red circle around it and two blue balls rotating around on the circle. At the top of the page is the word “Apogee” and at the bottom left is the word “Perigee.”)

The location of the launch site and direction of the launch, in relation to the eastward rotation of the Earth, will affect the performance of any launch vehicle.

(The image on the opposite side of this text depicts a green map of the United States. On the left side of the map is a silver and red rocket launching on a purple line trajectory with the words “launch veers to the west.” On the right side of the map is a silver and red rocket launching on a purple line trajectory with the words “launch veers to the east.” When the user runs the cursor on the bottom right hand side of the page, the rockets move back and forth on their purple line trajectory.)

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