Orbit Plotting
Orbit Plotting is the process of calculating the elliptical path that celestial objects, such as satellites, follow as they move around a primary body, like a planet or star. This concept is grounded in celestial mechanics, which applies principles of physics to understand the motion of objects in space. Key historical figures, including Johannes Kepler and Isaac Newton, laid the foundation for orbital mechanics with their laws governing motion and gravitation. Kepler's three laws describe how objects move in elliptical orbits, while Newton's laws elucidate the forces that influence these movements.
In orbit plotting, essential parameters such as the lengths of the major and minor axes of the ellipse, the locations of the foci, and the eccentricity of the orbit are determined. The semimajor axis represents the average distance from the orbiting object to the primary. Detailed calculations allow scientists to predict various aspects of an object's trajectory, such as position and velocity, by plotting these factors on a Cartesian coordinate system. Understanding orbital mechanics is critical for successfully launching and maintaining artificial satellites, which provide valuable data about Earth and the wider solar system.
Orbit Plotting
FIELDS OF STUDY: Orbital Mechanics; Astrometry; Astronomy
ABSTRACT: Every object in space, whether natural or artificial, follows an orbit, or a path around another object or point in space. The study of the movement of objects in space falls under the branches of celestial and orbital mechanics. An object’s orbit may be plotted using an equation. Studying orbits has led scientists to better understand the movement of Earth and other bodies.
What Is an Orbit?
Every object in space follows an orbit, which is a regular and repeating path around another object. Objects in orbit are called satellites. Natural satellites include objects such as moons and planets, while artificial satellites include spacecraft such as space vehicles.
The study of the motions of celestial objects is called celestial mechanics, and it uses applications from physics to study objects in space. Orbital mechanics, or flight mechanics, is a branch of celestial mechanics that deals with the movement of artificial satellites. This field studies how objects such as spacecraft move while under the influence of gravitational force (attraction between two masses), atmospheric drag (resistance), and thrust (push forward).
Orbiting objects typically move in an oval pattern known as an ellipse. Orbit plotting is the process of calculating the elliptical path that a particular orbiting object will follow.
Orbital Motion
The origins of orbital mechanics date back to German astronomer Johannes Kepler (1571–1630). Kepler, using observations made by Danish astronomer Tycho Brahe (1546–1601), developed his three laws of orbital motion. Kepler’s first law says that one object (such as a planet) moves around another object (such as the sun) along an ellipse. The second law states that an imaginary line connecting the two objects sweeps out equal areas of the ellipse in equal amounts of time. This means, for example, that Earth slows its orbit as it moves farther from the sun and speeds up again as it moves closer. Kepler’s third law states that the square of an object’s orbital period (T) is proportional to the cube of the orbit’s semimajor axis (a). This relationship is written as
T2 ∝ a3
Not long after, English physicist Isaac Newton (1642–1727) proposed three laws of motion and the law of universal gravitation. His first law of motion states that if no force acts on an object, then the velocity of the object will remain constant. Thus, stable objects remain in place, and objects in motion continue to move in a straight line. According to Newton’s second law, applying force will change the velocity of an object based on the extent and direction of the force applied. The third law says that a pair of equal but opposite forces, such as push and pull, act on interacting objects. The law of universal gravitation states that two objects attract each other with a gravitational force (Fg) that is directly related to the product of their masses (m1 and m2) divided by the distance between them (r) squared:
The constant G is the gravitational constant and is equal to 6.67384 x 10−11 m3/kg∙s2.
When the gravitational pull on one object (such as a satellite) by another (such as Earth) balances precisely with that object’s inertia, the object can enter orbit. However, if the object’s momentum is greater, it will escape and continue moving in a straight line. If the gravitational force is greater, the objects will collide.
Plotting an Orbit
The body that an object orbits is called the primary. The primary is located at one of two points within the ellipse, known as foci. The foci are located on the major axis at equal distances from the center point. The major axis is the longest diameter of the ellipse, running lengthwise between its two farthest points. The minor axis is perpendicular to the major axis and is the shortest diameter of the ellipse. The sum of the distances from any point along the perimeter to each focus is constant and equal to the major axis.
The semimajor axis is one-half of the major axis, measured from the center point to the perimeter. It represents the orbiting object’s average distance from the primary. The eccentricity, which is always between 0 and 1, is the distance between the foci divided by the length of the major axis. The anomaly is the angular distance between the position of the object and its nearest point to the primary.
To plot an orbit, the major and minor axis lengths of the ellipse as well as the foci must be known. The following equation can be used to find the foci:
Here, F is the distance between one focus and the center, x is the semimajor axis (major radius), and y is the semiminor axis (minor radius).
The equation for an ellipse is given as
where a is the semimajor axis and b is the semiminor axis, for points along the x and y axes of the Cartesian coordinate system. Thus, by assigning coordinates to anomalies from different instants in time, various aspects of orbital motion, such as the position or velocity of an object traveling along an ellipse, can be plotted on a Cartesian coordinate graph.
Significance
Scientists study orbital and celestial mechanics to better understand the movement of planets and other bodies in space. This knowledge has enabled scientists to successfully launch and maintain the orbits of all manner of artificial satellites, which provide invaluable information about Earth, its neighbors, and the greater solar system.
PRINCIPAL TERMS
- anomaly: the angular distance between the position of a celestial body and its point in orbit nearest to the body it revolves around.
- eccentricity: in astronomy, a number that indicates whether an orbit is more circular or more elliptical; a circular orbit has an eccentricity of 0.
- ellipse: an oval or elongated circular shape.
- gravitational force: the attractive force or pull between objects due to their mass.
- orbital mechanics: the study of the movements of artificial satellites and spacecraft; also called flight mechanics or astrodynamics.
- semimajor axis: the distance from the center of an ellipse and the farthest point of its perimeter.
Bibliography
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