#### LeChamp

• • 1 ##### What is the FES’s science for satellites?
« on: March 15, 2018, 08:52:37 PM »
Science tells the more rational of us that a satellite orbits the spherical Earth. Kepler was the first to describe what orbit entails with an accurate description of the mathematical shape of planetary orbits. Planets move about the sun, the moon moves about the earth and these were initially thought to be circular until Kepler encountered the concept of elliptical orbits.

An orbiting object must have sufficient speed to retrace its path, lest it falls to earth under the influence of gravitational attraction and applies to both natural and artificial satellites. Kepler’s work gave scientists the ability to realise that the closer a satellite is to an object, the stronger the force of gravitational attraction, inferring it must travel faster to maintain orbit.

On gravity. All objects have a gravitational field, but only large objects (suns, planets, moons) have influential gravitational fields. For the earth, the gravitational attraction is 9.8 m/s² at the surface. For an object orbiting the Earth, generally between 160 to 2000km for Low Earth Orbit, above 2000km for Medium Earth Orbit up to approximately 36000km for geostationary orbit, the object is further from the gravitational influence, so the formula must include that distance from the earth.

A satellite can only have one speed when orbiting a particular body at a given distance because the force of gravity is constant. In space, gravity provides the centripetal force that causes satellites to orbit larger bodies. With knowledge of the mass and the altitude of an orbiting satellite it is possible to calculate how quickly it needs to travel to maintain that orbit.
Any particular satellite can have only one speed when orbiting a particular body at a given distance because the force of gravity doesn’t change. That speed can be calculated with the equations for centripetal force and gravitational force. For a satellite of mass m1 to orbit a body, the centripetal force (that which acts upon an object moving in a circular path and is directed towards the centre around which the object is moving) is needed. This force is that which, by the influence of gravity, prevents an object from flying off into space and is found as follows:
F_C=(m_1 v^2)/r
Where FC is the centripetal force, m1 is the mass of the orbited body, v² is the tangential speed and r is the radius of curvature.

Centripetal force is consequential to gravitational force, so:
(〖Gm〗_1 m_2)/r^2 =(m_1 v^2)/r
Which can be re-arranged to get the velocity as:
V=√(〖Gm〗_2/r)
where V is velocity of the satellite, G is the gravitational constant, m is the mass of the planet, and r is the of the orbit.

This formula shows that the velocity required for orbit is equal to the square root of the distance from the object to the centre of the planet multiplied by the acceleration due to gravity at that distance.
Therefore, a satellite maintains orbit due to a balance between two factors:
Its velocity (or the speed at which it would travel in a straight line)
The gravitational pull between the satellite and the object it orbits. Higher orbits require less velocity than a nearer orbit, ultimately reaching a geostationary orbit, the point at which the relative velocity of the satellite is equal to that at the earth’s surface.

Kepler’s first two law of planetary motion, (1) that the orbit of planet is an ellipse with the sun at one of the two foci; (2) that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time; were published in 1609. His third law, that the square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit, was published in 1619.
In 1687, Newton showed that Kepler’s laws apply to the solar system as consequence of his own laws of motion and law of universal gravitation.
These laws are the basis for any satellite placed in orbit around a spherical planet, like earth.

Please explain the science and proven laws to place a satellite above a flat earth.