4.16.3 EARTH SATELITE MOVEMENT

Background and actual explanation

Every cosmic body has a gravitational field that extends out indefinitely, and theoretically, any observer is always under the simultaneous gravitational effect of all cosmic bodies. From these influences, an Earth observer, notice only the gravitational effect of closed cosmic body, Earth, Moon, Sun, other planets of Solar System.

For an observer which distances from Earth, a decreasing of its attractive force will be measuread, simultaneously with the increasing effect of other heavenly bodies. There is a point where the equilibrium of these forces is attaint.

This point is the most unsecure place in a real word, because the distance between the cosmical body does not remain constant in time. Due to the continuos modification of distance between the celestial bodies, the equilibrium of force for a body situated in the free gravitational efect point is perturbed and the observer will fall in the direction of one celestial body.

In order to attain a secure, stable state of weightlessness, it is accepted that it is possible to escape the effect of gravity in the second way: with the aid of inertial forces. In case of a circular free orbiting of an object around the Earth, the object's weight is offset by the centrifugal force generated during the orbiting. The object is, therefore, in a stable state of free suspension in relation to the Earth.

Von Braun explained, quite long time ago, using the mental experiment of Newton, why a satellite is able to stay up arround Earth. An object thrown horizontally, but at faster and faster speeds, will folow a more and more extending curve. For a certain speed the curvature of the trajectory would become equal to the curvature of the Earth. As a result, the object never gets closer to the ground and it's considered an satelite.

Acting on the satellite, according to his description, are two forces: gravity, pulling the satellite toward Earth, and centrifugal force, pushing the satellite away.

Von Braun quotations: as the object is moving faster speed its trajectory will be less deflected because the centrifugal force is increased by its higher speed, and more effectively counteracts the Earth's gravitational pull”; and "A circular orbit occurs whenever a small mass, travelling through the gravitational field of a big one, happens to have a speed at which the centrifugal force is precisely strong enough to balance the large body's gravitational pull." [...] If the balance between gravitational and centrifugal force is not perfect, [...] the small body will describe an elliptical path around the large one."

Proposed explanation

If a gravitational field is equivalent with a accelerated field, in order to put a satelite on the orbit a very simple problem should be solved; at a certain distance d from Earth, as example, the satelite should have a opposite acceleration, able to compensate the attraction of Earth like in fig 1 . Because, the gravitational acceleration is directed to the center of Earth considered like a sphere, it is very simple to determine the direction of compensating accelerated field.

Figure 1. Acceleration compensation

In practice, in order to place a body on a Earth orbit, the body is accelerated tangential to the direction of gravitational acceleration. As consequence, related to the center of force (Earth) a centripetal acceleration is counted. This means, over satelite act two forces, one is gravitational acceleration and second is a centripete forces generated using propelant during satelite placement on the orbit or after that with the occasion of periodic corrections of satellite position.

The centripetal component can be very easy put under another form

, but there is so:

The form of centripetal force is similar with the field of a vortex (dependence related to the cube of distance), and practically the satelite is moving under the field of a gravitovortex force as was already presented in gravitation book and the total force acting over him is:

It is important to emphasize that both forces are real and every of them produce distinct effects. It is not possible to identify the newtonian atraction force as being equal with centripetal (or centrifugal ) force.

Figure 2. Total force acting over a sattelite

How is repected the third Newton low in this case?

The newtonian component makes the satelite to fall in the gravitational field of Earth and also the Earth to fall in gravitational field of sattelite. Due to the mass differences, anyone counts only the falling of sattelite in Earth gravitational field.

The centripetal component is generated using propelant and aplying the momentum conservation low there is a dependence between rotational motion of satelite and quantity and direction of ejected gases.

For every observer both forces are real and in real word the pseudoforces are inexistents.

In order to count the real movement of an object, an accelerated observer (like an Earth observer), as was described in chapter II, should remove first the proper movements on order to get the real motion of studied object.

As example, for a stationary satellite related to an Earth observer, it is wrong to consider the satellite acted only by gravitational force. Because the Earth observer is rotating with the same centripetal acceleration like stationary sattelite, for him it is impposible to see the effects of this accelerations. The equality of gravitational force with a centripet or ,,centrifugal force” is out of question. If two forces are equal and opposite, the movement of a body is a linear one with constant speed. Nothing is more absurd in actual physics that considering the equilibrium of two forces lead to a stable rotational motion.

If the Earth observer firstly removes its proper motion, he will count the real movement of satellite and besides the newtonian atracation also a centripetal force will be observed.

It is wrong to consider a satellite falling, just as an apple does when pulled down by gravity. If the satellite wouldn’t be tangentially accelerated using propelant, in this case there it will be a similitude between falling apple and falling satelite and both movements are linear.

The low of physics must represent the reality of phenomena and not the subjective perception of a subject. It is impposible to be admited the fact that an observer who does not count a force, it means that force does not exist.