Mass is trivially conserved in this system, since neither body is changing mass. In this section, we will prove that the two-body equation of motion satisfies conservation of energy.

Orbiting spacecraft are subject to a variety of environments. Knowledge of the orbit is required to quantify the solar, albedo and planetary (also called outgoing longwave radiation, or OLR) fluxes. …

For an elliptic orbit the specific orbital energy is the negative of the additional energy required to accelerate a mass of one kilogram to escape velocity (parabolic orbit). For a hyperbolic orbit, it is …

Total energy remains constant and the law of conservation of mechanical energy applies due to the absence of any non-conservative forces. If the propeller or thrust of a spacecraft or satellite is turned …

Like the case of circular motion, the total amount of mechanical energy of a satellite in elliptical motion also remains constant. Since the only force doing work upon the satellite is an internal (conservative) …

While the satellite is moving from point A to point B in the elliptic orbit (that is, during the transfer, after the first burn and before the second), both mechanical energy and angular momentum are conserved.

As we said, total mechanical energy in a conservative field (such as a gravitational field) stays constant. But, a spacecraft in orbit may get close to Earth during part of its orbit and be far away in another part.

That is, the mechanical energy of an object in orbit, whether that orbit is circular or elliptical, stays the same. Note that we’re not saying that all orbiting objects have the same mechanical energy, only that …

In this video, we’ll explain the fundamental principles behind the conservation of orbital energy in celestial mechanics. We’ll start by discussing how energy is transferred in space...

To satisfy the minimum energy requirements of this problem the satellite should be launched from someplace on the equator where the speed of rotation (and thus the kinetic energy) is a maximum.