A Study on Orbital Mechanics

Space craft to solar system bodies must deal with multiple deviations under the in uence of gravity. The motion of satellite in one of the types of conic section strongly depends upon escape velocity. The goal of this paper is to nd the trajectory of satellite by analysing orbit's eccentricity and or-bital parameters. This paper also focuses on the derivation of general orbit equation from the base called Newton's law of motion and Newton's law of gravitation.


INTRODUCTION
Mechanics is a branch of science concerned with the relationship between force, displacements, energy and their e ects on physical bodies on their environment. The classical mechanics is one of the sub mechanics. Classical mechanics is concerned with the some physical laws describing the movement of bodies under the in uence of forces.

ORBITAL MECHANICS
Orbital mechanics is also known as astrodynamics. It is the application of celestial mechanics concerning the motion of rockets and other spacecraft. It is concerned with motion of bodies under the in uence of gravity, including both spacecraft and natural astronomical bodies such as star, planets, moons and comets. @ IJTSRD | Available Online @ www.ijtsrd.com | Volume -2 | Issue -2 | Jan-Feb 2018 Space craft to solar system bodies must deal with multiple deviations under the in uence of gravity. The motion of satellite in one of the types of conic section escape velocity. The goal of this paper is to nd the trajectory of satellite by bital parameters. This paper also focuses on the derivation of general orbit equation from the base called Newton's law of on's law of gravitation.
Mechanics is a branch of science concerned with the relationship between force, displacements, energy and on physical bodies on their environment. The classical mechanics is one of the sub-elds of mechanics. Classical mechanics is concerned with the some physical laws describing the movement of chanics is also known as astrodynamics. It is the application of celestial mechanics concerning the motion of rockets and other spacecraft. It is concerned with motion of bodies under the in uence of gravity, including both spacecraft and natural cal bodies such as star, planets, moons and

TRAJECTORIES:
Three general types of paths are possible under the gravitational in uence.
An elliptical orbit is a orbit with an eccentricity of less than 1. This includes the special case called orbit and its eccentricity is equal to 0.
This paper examines the classifications, cause; types and the possible solutions of conflict in organization. This discovered that conflict generates considerable ambivalence and leave many practitioners a scholars quite uncertain about how best to cope with it. Conflicts are inevitable in human life and also inevitable in organizations even between countries. Conflict occurs in organizations as a result of competition for supremacy, scarcity of economic resource and leadership style. The study also revealed that conflict in organization could be constructive o destructive which can lead to low production or good solution to production.
A hyperbolic trajectory is the trajectory of any body around a cen-tral mass with more enough speed to escape the central object's grav orbital eccentricity will be greater than one A parabolic trajectory is an orbit whose eccentricity will be equal to 1. A body travelling along an escape orbit will coast along a parabolic trajectory to in nity and never return. An elliptical orbit is a orbit with an eccentricity of less than 1. This includes the special case called circular orbit and its eccentricity is equal to 0.
This paper examines the classifications, cause; types and the possible solutions of conflict in organization. This discovered that conflict generates considerable ambivalence and leave many practitioners and scholars quite uncertain about how best to cope with it. Conflicts are inevitable in human life and also inevitable in organizations even between countries. Conflict occurs in organizations as a result of competition for supremacy, scarcity of economic resource and leadership style. The study also revealed that conflict in organization could be constructive or destructive which can lead to low production or good A hyperbolic trajectory is the trajectory of any body ral mass with more enough speed to escape the central object's grav-itational pull. The orbital eccentricity will be greater than one A parabolic trajectory is an orbit whose eccentricity will be equal to 1. A body travelling along an escape ast along a parabolic trajectory to in nity Escape velocity is the velocity required at a given position to establish a parabolic path. Velocities greater than escape velocity result in hyperbolic orbits. Lower velocities result in closed elliptical orbits.

ORBITAL PARAMETERS:
Apogee (q) refers to the farthest distance between satellite and the Earth.
Perigee (p) refers to the closest distance between satellite and the Earth.
Semi-Major Axis (a): The distance from the center of the orbit ellipse to satellite's apogee or perigee point.

Semi-Minor Axis (b):
The shortest distance from the true center of the orbit ellipse to the orbit path.
Period (T): The time required for the satellite to orbit the Earth once.
Pitch angle or ight path angle: The angle between the longitudi-nal axis (where the airplane is pointed) and the horizon.

ORBIT EQUATION
Two objects are located in inertial frame of reference XYZ. Each of the bod-ies is acted upon by the gravitational attraction of the other. F 12 is the force exerted on m 1 by m 2 , and F 21 is the force exerted on m 2 by m 1 . The position vector R G of the center of mass G is de ned by, Absolute acceleration, a The term absolute means that the quantities are measured relative to an inertial frame of reference.
Let r be position vector of m 2 relative to m 1 . The force exerted on m 2 by m 1 is, where uc r shows that the force vector F 21 is directed from m 2 towards m 1 .
Applying Newton's second law of motion on body m 2 is F 21 = m 2 R 2 00 , where R 2 00 is the absolute acceleration of m 2 .
By Newton's third law of motion, F 12 = F 21 , so for m 1 we have, Equations (7)and (8) are the equations of motion of two bodies in inertial space. By adding ,we get m 1 R 1 00 + m 2 R 2 00 = 0 ! (9).
According to Equation (3) , the acceleration of the center of mass G of the system of two bodies m 1 and m 2 is zero.
Multiplying Equation (7)  Since r' x h is perpendicular to both r' and h, so that (r' x h) . h= 0. Likewise, since h = r x r' is perpendicular to both r and r', it follows that r . h = 0. Therefore, we have C . h= 0, i.e., C is perpendicular to h, which is normal to the orbital plane.
Rearranging Equation ( Since e 1, it will be an ellipse. we know that r = Since e 1, it will be hyperbolic orbit. (5). The perigee of a satellite in a parabolic trajectory is 9000 km. Find the distance d between points P 1 and P 2 on orbit which are 11000km and 22000 km from the center of earth.