Glossary

Satellite orbits are fascinating phenomena that showcase the interplay between gravity and motion. They rely on a delicate balance between Earth's gravitational pull and the satellite's velocity, creating stable paths around our planet.

Understanding satellite orbits involves exploring orbital periods, velocities, and energy conditions. These concepts help explain how satellites stay in orbit, why some escape Earth's gravity, and how we can use different orbits for various purposes.

Satellite Orbits

Principles of circular satellite orbits

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  • Circular orbits result from a balance between gravitational force and
    • Gravitational force acts as the , causing the satellite to move in a circular path
    • Magnitude of gravitational force depends on the mass of Earth (MEM_E), mass of the satellite (mm), and distance between their centers (rr) according to the equation: Fg=GMEmr2F_g = G\frac{M_Em}{r^2}, where GG is the gravitational constant (6.67×10−11 N⋅m2/kg26.67 \times 10^{-11} \text{ N} \cdot \text{m}^2/\text{kg}^2)
  • Centripetal force is provided by the gravitational force and is given by: Fc=mv2rF_c = \frac{mv^2}{r}, where vv is the of the satellite
  • For a stable circular orbit, gravitational force must equal centripetal force: Fg=FcF_g = F_c
    • Leads to the equation: GMEmr2=mv2rG\frac{M_Em}{r^2} = \frac{mv^2}{r}
    • Satellites in (LEO) (160-2,000 km) and (GEO) (35,786 km) maintain circular orbits using this principle
  • principles govern the behavior of satellites and other objects in space

Orbital periods and velocities

  • (TT) is the time for a satellite to complete one full orbit around Earth
    • Depends on the radius of the orbit (rr) and mass of Earth (MEM_E)
    • Equation for orbital period: T=2πr3GMET = 2\pi\sqrt{\frac{r^3}{GM_E}}
      • Example: For a satellite orbiting at an altitude of 400 km, T≈92.6 minT \approx 92.6 \text{ min}
  • Orbital velocity (vv) is the speed at which a satellite moves in its orbit
    • Depends on the radius of the orbit (rr) and mass of Earth (MEM_E)
    • Equation for orbital velocity: v=GMErv = \sqrt{\frac{GM_E}{r}}
      • Example: For a satellite orbiting at an altitude of 400 km, v≈7.67 km/sv \approx 7.67 \text{ km/s}
  • As altitude increases, orbital period increases and orbital velocity decreases
    • Gravitational force decreases with increasing distance from Earth, requiring slower velocity to maintain circular orbit
    • GEO satellites have an orbital period of 24 hours, matching Earth's rotation, making them appear stationary from the ground
  • can occur when the orbital periods of two objects have a simple integer ratio

Energy conditions for orbit vs escape

  • Total energy of a satellite is the sum of its (KEKE) and gravitational potential energy (PEPE)
    • Kinetic energy: KE=12mv2KE = \frac{1}{2}mv^2
    • Gravitational potential energy: PE=−GMEmrPE = -\frac{GM_Em}{r}
    • Total energy: E=KE+PE=12mv2−GMEmrE = KE + PE = \frac{1}{2}mv^2 - \frac{GM_Em}{r}
  • For a stable circular orbit, total energy must be negative (E<0E < 0)
    • Gravitational potential energy is greater in magnitude than kinetic energy
    • Satellites in LEO and GEO have negative total energy
  • If total energy is greater than or equal to zero (E≥0E \geq 0), satellite will escape Earth's gravitational field
    • Kinetic energy is greater than or equal to the magnitude of gravitational potential energy
    • Spacecraft leaving Earth for interplanetary missions must achieve
  • (vev_e) is the minimum velocity required to escape Earth's gravitational field
    • Depends on the mass of Earth (MEM_E) and distance from the center of Earth (rr)
    • Equation for escape velocity: ve=2GMErv_e = \sqrt{\frac{2GM_E}{r}}
      • Example: At Earth's surface, ve≈11.2 km/sv_e \approx 11.2 \text{ km/s}
  • systems are used to adjust orbits and maintain desired trajectories

Advanced Orbital Considerations

  • are locations in space where the gravitational forces of two large bodies create equilibrium points for a smaller object
  • poses a significant challenge for satellite operations and requires careful tracking and avoidance strategies
  • Non-circular orbits, such as elliptical orbits, can be used for specific mission requirements

Key Terms to Review (30)

Angular momentum: Angular momentum is a measure of the quantity of rotation of an object and is a vector quantity. It is given by the product of the moment of inertia and angular velocity.
Angular Momentum: Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is the measure of an object's rotational inertia and its tendency to continue rotating around a specific axis. Angular momentum is a vector quantity, meaning it has both magnitude and direction, and it plays a crucial role in understanding the behavior of rotating systems across various topics in physics.
Apogee: Apogee refers to the point in a satellite's or celestial body's orbit where it is farthest from the Earth or the body it is orbiting. It is the opposite of perigee, which is the point of closest approach.
Centripetal force: Centripetal force is the force that keeps an object moving in a circular path, directed towards the center of the circle. It is necessary for maintaining circular motion and depends on mass, velocity, and radius of the path.
Centripetal Force: Centripetal force is the force that causes an object to move in a circular path, constantly changing the direction of the object's motion. It is the force that acts perpendicular to the object's velocity and points towards the center of the circular path.
Elliptical Orbit: An elliptical orbit is a type of orbital path followed by a celestial body, such as a satellite or a planet, around another body. It is an elongated, oval-shaped trajectory that is defined by the gravitational forces between the two objects.
Escape velocity: Escape velocity is the minimum speed an object must have to break free from a celestial body's gravitational influence without further propulsion. It depends on the mass and radius of the celestial body.
Escape Velocity: Escape velocity is the minimum speed required for an object to break free of a planet or moon's gravitational pull and enter into space without being pulled back down. This concept is crucial in understanding the motion of objects under the influence of gravity.
Geostationary Orbit: A geostationary orbit is a specific type of Earth's orbit where a satellite revolves around the planet at the same rate as the Earth's rotation, allowing the satellite to remain stationary relative to a fixed point on the Earth's surface. This unique orbital path is crucial for various satellite-based applications and technologies.
Geosynchronous Orbit: A geosynchronous orbit is a type of satellite orbit where the satellite's period of revolution matches the Earth's rotation period, causing the satellite to remain stationary relative to a fixed point on the Earth's surface. This unique orbit has important applications in the fields of satellite communications, weather monitoring, and navigation.
Hohmann Transfer: A Hohmann transfer is a type of orbital maneuver used to change a spacecraft's orbit, typically between two circular orbits of different radii around a central body, such as a planet or the Sun. It is named after the German engineer and astronautical pioneer Walter Hohmann, who first proposed this orbital transfer method.
International Space Station: The International Space Station (ISS) is a large spacecraft in low Earth orbit, serving as a microgravity and space environment research laboratory. It orbits Earth at an average altitude of approximately 400 km.
Ion Thruster: An ion thruster is a type of electric propulsion system used for spacecraft propulsion. It generates thrust by accelerating charged particles, known as ions, to high exhaust velocities using electrical or magnetic fields.
Kepler: Kepler was a German astronomer and mathematician who is best known for his laws of planetary motion, which describe the orbits of planets around the Sun. His work laid the foundation for our understanding of satellite orbits and the energy associated with them.
Kepler's Laws: Kepler's laws are a set of three fundamental principles that describe the motion of planets around the Sun. These laws, formulated by the German astronomer Johannes Kepler in the early 17th century, provide a mathematical foundation for understanding the dynamics of celestial bodies and their orbits.
Kinetic energy: Kinetic energy is the energy possessed by an object due to its motion. It depends on the mass and velocity of the object.
Lagrange Points: Lagrange points are five positions in the orbital plane of a two-body system where a small object can be in a stable orbit relative to the two larger bodies. These points are named after the Italian-French mathematician Joseph-Louis Lagrange, who discovered them in 1772.
Low Earth Orbit: Low Earth Orbit (LEO) refers to the region of space surrounding the Earth at an altitude of approximately 2,000 kilometers (1,200 miles) or less. Satellites and spacecraft that operate in this region are subjected to the Earth's gravity and atmospheric effects, which influence their orbital dynamics and energy requirements.
Newton: Newton is the standard unit of force in the International System of Units (SI), named after the renowned English physicist and mathematician, Sir Isaac Newton. It is a fundamental unit that is essential in understanding and describing the behavior of objects under the influence of various forces, as well as in the study of mechanics, dynamics, and other related areas of physics.
Newton's Law of Gravitation: Newton's Law of Gravitation is a fundamental principle in physics that describes the attractive force between any two objects with mass. It establishes that the force of gravity between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them.
Orbital Decay: Orbital decay is the gradual reduction in the altitude of a satellite's orbit around a planet or other celestial body, typically due to the effects of atmospheric drag or other external forces. This process can eventually lead to the satellite's reentry and destruction as it falls back to the surface.
Orbital Mechanics: Orbital mechanics, also known as astrodynamics, is the study of the motion of objects around celestial bodies, such as planets, moons, and stars. It encompasses the principles and laws governing the motion of these objects, including their trajectories, velocities, and the forces acting upon them.
Orbital Period: The orbital period is the time it takes for a satellite or other object to complete one full revolution around a larger body, such as a planet or star, under the influence of gravity. It is a fundamental property of an object's orbit and is closely related to the object's distance from the central body.
Orbital Resonance: Orbital resonance is a phenomenon in which two or more celestial bodies, such as planets, moons, or asteroids, exhibit a periodic interaction due to their gravitational influence on each other. This interaction results in a synchronized motion where the orbital periods of the bodies are related by a ratio of small integers.
Orbital speed: Orbital speed is the minimum velocity an object must have to maintain a stable orbit around a celestial body. It depends on the mass of the central body and the radius of the orbit.
Orbital Velocity: Orbital velocity is the speed at which an object, such as a satellite or planet, moves in its orbit around another object. It is a crucial parameter that determines the stability and characteristics of an object's orbital path.
Perigee: Perigee is the point in a satellite's elliptical orbit around the Earth where it is closest to the planet's surface. This term is particularly relevant in the context of satellite orbits and energy, as the perigee of a satellite's orbit directly impacts the satellite's velocity, potential energy, and overall orbital dynamics.
Rocket Engine: A rocket engine is a type of reaction engine that generates thrust by expelling a high-speed propellant. It is the primary propulsion system used in spacecraft and missiles, providing the force necessary to overcome Earth's gravity and achieve escape velocity.
Satellite Propulsion: Satellite propulsion refers to the various methods and technologies used to power and maneuver satellites in space. It is a crucial aspect of satellite operations, enabling the placement, maintenance, and control of satellites in their desired orbits.
Space Debris: Space debris refers to the collection of defunct man-made objects, such as old satellites, rocket parts, and fragments from collisions or explosions, that orbit the Earth and pose a threat to active spacecraft and astronauts. This debris can range in size from tiny paint flecks to large abandoned equipment, and its presence in Earth's orbit has become an increasing concern for the space industry and scientific community.
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