Apr 21

Apr 21 Spinning in Outer Space: Common Orbits and Prominent Locations around Earth

Prominent Orbits and Significant Points around the Earth | Alex S. Li

“Far above the Moon; Planet Earth is blue.”

— Space Oddity

***5/11/19 UPDATE: added the P/2 Orbit to the High Earth Orbit (HEO) section***

With the rise of the commercial launch industry, Outer Space is becoming more accessible and available than ever before. While selecting the right operator is an important consideration for anyone that is launching a payload into Outer Space, care also must be taken in deciding the destination in Outer Space for the mission. These locations are the topic of this post: the common orbits and significant points around the Earth for Outer Space payloads.

We will start by looking at the three common characteristics that define these orbits: altitude, eccentricity, and inclination. Then we will rotate our way through the three broad regions of Outer Space relative to the Earth—Low Earth Orbit (LEO), Medium Earth Orbit (MEO), and High Earth Orbit (HEO)—and describe the prominent orbits and destinations in each.

The Three Defining Characteristics for Outer Space Orbit

While all orbits are unique, each is defined by three common characteristics: altitude (height), eccentricity (shape), and inclination (angle).

Altitude: What is the Height?

For any mission, it is important to know how high up (“Altitude”) the payload should be; as a payload moves farther away from Earth, Earth’s gravitational pull will impact the payload less and less. Additionally, the time it takes a payload to complete one orbit around the Earth (“Orbital Period”) will increase in duration as the satellite moves higher. Because orbital period has an inverse relationship to orbital speed, this also means the lower the altitude, the higher the orbital speed. This leads to a counterintuitive result: in order to decrease an object’s orbital speed, thrust must be fired in, rather than against, the direction of forward motion. Such an action would push the payload to a higher orbit in Outer Space, thereby decreasing its orbital speed.

Eccentricity: What is the Shape?

An orbit is also measured by its shape, known as its “Eccentricity.” An orbit’s eccentricity can be greater than or equal to 0 but will always be less than 1. A complete circular orbit would have an eccentricity value of 0; as the orbit becomes more and more elliptical, its value will get closer and closer to 1. Additionally, an elliptical orbit will also have a different value for its apogee and its perigee. “Apogee” is the point of the orbit at which it is farthest away from Earth whereas “Perigee” is the orbital location at which the orbit is closest to Earth. As explained by Kepler’s second law of planetary motion and conservation of mechanical energy, for each orbital period, a satellite will spend more time near its apogee (where it travels slower because it has more potential energy and less kinetic energy) and less time traversing around its perigee (where it travels faster, having more kinetic energy than potential energy).

Inclination: What is the Angle?

The positioning of an orbit is characterized by its inclination. “Inclination” is a measure of the angle of the orbit relative to the Earth’s equator. An orbit that has an inclination of 0 degrees is rotating around the Earth directly above the equator; while a 90 degrees inclination means the orbit is traversing the Earth around the North and South Poles (“Polar Orbit”). Any inclination over 90 degrees means that the orbit is rotating in the direction opposite to Earth’s rotation (“Retrograde Orbit”). Anything below 90 degrees is orbiting the Earth in the direction of Earth’s spin (“Prograde Orbit”). One other inclination of interest is 63.4 degrees, which is known as the “Critical Inclination;” any orbit with such an inclination will not have any “Apogee Drift”—its apogee altitude would remain stable through each of the orbit’s successive rotations. This is a result of the interaction with the Earth’s gravitational field.

Low Earth Orbit (LEO)

Orbits located anywhere between the start of Outer Space to 2,000 km above Earth’s sea level are categorized as “Low Earth Orbits (LEOs)”. With eccentricity values close to zero, many of these orbits are very circular in shape.

At an altitude of approximately 600 km to 800 km above Earth’s sea level, one of the most well-known orbits in LEO is the “Sun-synchronous orbit (SSO).” As a polar orbit with an inclination of about 98 degrees, SSO passes above both the North and South Poles of Earth. What is unique about SSO is that a satellite in this orbit will pass over a part of the Earth at approximately the same solar time every time (e.g., always passing over a certain equatorial area at 3pm). This enables these areas to be photographed and analyzed under the same sun illumination settings over time. SSO achieves this special feature by having its orbit’s “Precession”—the change in the orbit’s axis of rotation due to the Earth’s equatorial bulge—match the rate at which the Earth rotates around the Sun (which is a change of about one degree a day).

Two special subtypes of the SSO are the “Noon-Midnight Orbit” (passing the equator at noon and midnight) and the “Dawn-Dusk Orbit” (passing any part of the Earth at sunrise or sunset). The dawn-dusk orbit has an additional trait such that the solar panels on any payload in this orbit will always see the Sun (as the satellite is never shadowed by the Earth) with its sensitive instruments being able to always point toward the night-side of the Earth without needing any manual adjustments.

LEO is the common destination for many satellites providing data communications because of this sector’s high bandwidth and low communication latency. The International Space Station also resides in LEO, navigating at an altitude between 330 km to 420 km above Earth’s sea level. But, there are also several disadvantages for objects orbiting in LEO. Payloads that are at the bottom segment of LEO will experience significant orbital decay as atmospheric drag pulls these objects toward Earth. Therefore, frequent boosting maneuvers are needed to keep them in their original orbits (“Orbital Station-Keeping”). Additionally, due to the relative short distance to the Earth, satellites in LEO have limited fields of view and can only communicate with small areas of the Earth. Hence, a group of satellites (“Constellation”) is generally needed for missions that require continuous coverage, thereby contributing to the space junk issue in the increasingly crowded LEO sector.

Medium Earth Orbit (MEO)

Orbits between 2,000 km to 35,780 km above Earth’s sea level are known as “Medium Earth Orbits (MEOs).” These orbits are commonly used for navigation and communication services; the MEO region is home to several well-known satellite constellations such as the Global Positioning System (located at a height of 20,180 km). There are three well-known orbits in MEO: the Semi-Synchronous Orbit, the Molniya Orbit, and the Tundra Orbit.

The “Semi-Synchronous Orbit” is a prograde orbit located at approximately 20,200 km above Earth’s surface and has a very low eccentricity value. The most important feature of the SSO is its 12-hour orbital period: it will pass over the same spot on Earth twice a day. Due to its consistency and predictability, this orbit is used for navigation services, such as the GPS constellation.

The “Molniya Orbit” is a highly elliptical orbit with an eccentricity value of 0.74, and is primarily used for communications purposes. This orbit has an inclination of 63.4 degrees with each orbital period lasting around 12 hours. Near its apogee (around 39,700 km above sea level), a satellite in the Molniya Orbit would have visibility over a broad stretch of the Polar region and Northern Hemisphere (alternating between Russia and North America). The orbit takes its name from the Russian word for “Lightning,” describing the rapidness a satellite in this orbit will move through its perigee (600 km above sea level) phase. Additionally, because the orbit has a relatively small perigee when compared to its apogee, a communications satellite in this orbit will move very slowly around its apogee segment (as explained by Kepler’s Second Law above and known as “Apogee Dwelling”) while it is above the Northern Hemisphere, enabling long-durational uninterrupted communications services with the ground below.

With an inclination also around 63.4 degrees, the “Tundra Orbit” shares many similarities with the Molniya Orbit. However, Tundra has a much longer orbital period at one “Sidereal Day”—23 hours, 56 minutes and 4 seconds, or about 4 minutes less than a “Mean Solar Day” (our common 24-hour cycle based on the positioning of the Sun). This is due to Tundra Orbit’s eccentricity value being much lower, at around 0.2 to 0.3. Essentially a highly elliptical Geosynchronous Orbit (covered in the upcoming High Earth Orbit section), Tundra orbits have an apogee of 46,990 km above sea level and a perigee of 23,980 km above sea level. Sirius Satellite Radio used to operate a constellation of three satellites in the Tundra Orbit as, due to its high inclination, each satellite had wide coverage over North America for an extensive amount of time due to apogee dwelling. However, Sirius has since deorbited these satellites and now operates exclusively in the Geostationary Orbit (will be covered momentarily).

High Earth Orbit (HEO)

Finally, all orbits that are more than 35,780 km above Earth’s sea level are in the “High Earth Orbit (HEO)” zone. HEO includes the orbit of Earth’s satellite, the Moon, which is rotating at an altitude of approximately 384,000 km (“Lunar Orbit”). Several other significant orbits and locations in this region include the circular Geosynchronous Orbits (of which the Geostationary Orbit is a unique case) and the five Lagrange Points.

At 35,786 km above Earth’s surface, a satellite in a circular “Geosynchronous Orbit (GSO)” will have the same orbital period as that of Earth’s rotation on its axis. The most well-known GSO, the “Geostationary Orbit (GEO)”, has an inclination of 0 degrees (right above the equator). What makes GEO unique is that an object in GEO will always appear to stay in a fixed position relative to a spot on Earth. This trait makes the GEO a highly sought after orbit and satellite launches to this orbit are carefully regulated by the International Telecommunications Union (for more information, please see my orbital parking spot post). For these payloads, satellite receivers on the ground do not need to rotate and track these satellites once they arrive at a “locked-in” position in the GEO. As a side note, because GSO’s primary characteristic is having an orbital period of one sidereal day, depending on eccentricity, GSO orbits can also exist outside of HEO as well; for instance, the aforementioned elliptical Tundra Orbit is technically categorized as a GSO.

Other unique HEO orbits include the lunar-resonant orbits such as the P/2 orbit. Named for having an orbital period half that of the Moon, the P/2 orbit is a highly elliptical (eccentricity value of 0.55) but stable orbit. Objects in P/2 experience gravitational forces from the Earth and the Moon that cancel each other out (“orbital resonance”), enabling long durational missions. The P/2 orbit has an apogee of 375,000 km above Earth’s sea level and a perigee of 108,000 km. Due to the orbit’s high altitude, the orbit is completely outside of the Van Allen Belts, minimizing effects of radiation on objects in the P/2 orbit. Due to these characteristics, the P/2 orbit is being used by the Transiting Exoplanet Survey Satellite (TESS) as part of the NASA’s Explorers program for a 2-year mission as the space telescope search and identify exoplanets, planets outside of the solar system.

In the Sun-Earth system, there are also five points in HEO where various Outer Space forces—such as the Earth’s and Sun’s gravitational pulls, forces from Coriolis acceleration, and orbital centripetal force—cause the objects located at these locations to stay stationary relative to the Earth as both rotate around the Sun. These points are named after the astronomer Joseph-Louis Lagrange and are known as the five Sun-Earth “Lagrange Points" (L1 to L5). Of the five Lagrange Points, L1, L2, and L3 are characterized by their unstable equilibrium; like a ball at the top of a hill, any slight perturbation will cause the object at these points to move irreversibly toward some other location. Meanwhile, L4 and L5 are stable equilibrium points; hence, objects at these locations will act like a ball at the bottom of a valley, eagerly returning to these points after being nudged slightly away.

“L1” is located on the straight line right in between the Earth and the Sun and is about 1.5 million km from Earth. Any object in L1 will have a constant view of the Sun and the daylight side of the Earth. Several satellites are currently occupying L1 including: the Solar and Heliospheric Observatory, the Deep Space Climate Observatory, the International Sun Earth Explorer 3, and the LISA Pathfinder.

“L2” is also on the straight line containing the Earth and the Sun but sits 1.5 million km past the Earth from the Sun. Due to this position, a satellite in this orbit only needs a unidirectional heat shield to block the Sun’s radiation. Currently, European Space Agency’s Gaia probe is stationed here but there are several payloads planned for L2 including the James Webb Space Telescope, Wide Field Infrared Survey Telescope, and Advanced Technology Large-Aperture Space Telescope.

With the Sun being the focal point, “L3” is the point directly opposite (180 degrees) of Earth on Earth’s orbit around the Sun. As L3 is also on the straight line between the Earth and the Sun but, from the perspective of the Earth, directly behind the Sun, it is very difficult for a payload at L3 to communicate with Earth due to the Sun’s interference. Currently, there are no known satellites at L3.

Finally, “L4” and “L5” are points on Earth’s orbit around the Sun with L4 being 60 degrees ahead of Earth’s rotation (with the Sun serving as the focal point) and L5 being 60 degrees behind Earth’s rotation. With this angle, the Earth, the Sun, and L4/L5 would form the three vertices of an equilateral triangle. Because of the stable nature of these two points, dust and asteroids tend to gather at these locations. Scientists have given these objects the name “Earth Trojans.”