CBSE Class 11 Energy of an orbiting satellite Detail and Preparation Downloads
The satellites orbit around a central massive body in either a circular or an elliptical manner. A satellite orbiting about the earth moves in a circular motion at a constant speed and at a fixed height by moving with a tangential velocity that allows it to fall at the same rate at which the earth curves. The force of gravity acts in a direction perpendicular to the direction of motion of the satellite throughout the trajectory.
As per the work-energy theorem, the initial total mechanical energy of the system plus the work done by any external force is equal to the final total mechanical energy.
Mathematically, KEi + PEi + Wext = KEf + PEf
For satellites, the force of gravity is the only external force and since gravity is considered as a conservative force, the term Wext is zero.
The equation can be simplified as KEi + PEi = KEf + PEf
In other words, the sum of the kinetic energy and the potential energy of the system is constant, while energy gets transformed between the kinetic energy and the potential energy.
The Energy of A Circularly Orbiting Satellite
Analysing circular orbits involves understanding the motion of an object (e.g., a satellite) moving in a circular path around a massive body (e.g., Earth). The key parameters for circular orbits include the gravitational force, centripetal force, and the conservation of energy. Let's break down the analysis for circular orbits:
The Energy of A Circularly Orbiting Satellite
The energy of a circularly orbiting satellite is the sum of its kinetic energy and potential energy. In a circular orbit, the gravitational force provides the centripetal force required to keep the satellite in its circular path. The total mechanical energy of the satellite remains constant throughout the orbit due to the conservation of energy. Let's break down the energy components:
Analysis For Elliptical Orbits
Analysing elliptical orbits involves understanding the motion of an object (e.g., a satellite) moving in an elliptical path around a massive body (e.g., Earth). Elliptical orbits are characterised by their eccentricity, semi-major axis, and varying distances between the satellite and the central body at different points in the orbit. The key parameters for elliptical orbits include Kepler's laws, the conservation of angular momentum, and the conservation of energy. Let's break down the analysis for elliptical orbits: