Trajectory Equation, Flight Path Elevation Angle, Zenith Angle and more...
Orbital Elements and Orbital Mechanics
The understanding and know-how of orbital elements and orbital mechanics is essential to understanding the secrets of space-flight.
The topics covered in orbital mechanics section are,
Newton’s Law of Gravitation
The Newton’s Law of Gravitation states that, Any two bodies attract each other with a force that is directly proportional to the product of their masses and the force is inversely proportional to the square of the distance between them (between there centers).
1st Law of Motion: Every body continues or remains in the state of rest or of uniform motion in a straight line unless it is acted upon by an external force.
2nd Law of Motion: The time rate of change of momentum is proportional to the force applied on the body and it acts in the same direction as that of the force or When a force is applied on a body it produces acceleration in it.
3rd Law of Motion: To every action, there is always an equal and opposite reaction.
1st Law (Law of Orbit): The orbit of the planet about the Sun is an ellipse with the Sun at one focus.
2nd Law (Law of Area): The line joining the planet to the Sun sweeps out equal areas in equal intervals of time.
3rd Law (Law of Period): The square of the period of a planet is proportional to the cube of the semi-major axis of its elliptical orbit about the Sun.
The bodies are assumed to be spherical and symmetric. This enables us to treat the bodies as point masses with their masses concentrated at their centers.
There are no forces acting on the system (absence of both external and internal forces) other than the gravitational forces which acts along the line joining the centers of the two bodies.
E, Conservation of Mechanical Energy
Specific Mechanical Energy which is the sum of the kinetic and potential energies per unit mass and denoted by E remains constant in an orbit. This means that the value of E doesn’t change during motion in an orbit.
h, Conservation of Angular Momentum
The specific angular momentum of a body remains constant along its orbit or during its motion in an orbit.
Since h the specific angular momentum is conserved in an orbit and since h is a vector quantity. So this means that both r and V must always remain in the same plane referred to as the orbital plane. That is why it is the orbit of the planet about the sun lies in a plane.
Local Vertical, The local vertical is obtained when the location of the satellite or body coincides with the direction of the vector r.
Local Horizontal is perpendicular to the local vertical and lines in the plane.
The angle between the local horizontal and the local velocity vector is called as the flight path angle or flight path elevation angle and is denoted by the symbol phi.
The angle between the local vertical and the local velocity vector and that shows the direction of the velocity vector is given by the symbol gamma and is called as the Zenith angle.
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