# Propulsion-Free Satellites {© 01/05/19}

This page describes a propulsion-free satellite, which has been provided by Keith Dixon-Roche based upon his many discoveries concerning Isaac Newton's laws of orbital motion.

A propulsion-free satellite is any orbiting body that relies on Newton's constant of motion (h) to generate the energy required to keep it in orbit around its force-centre. I.e. a satellite that does not need an artificial means of propulsion.

All natural satellites, such as our sun, the planets and their moons are propulsion-free because they follow 'non-circular' elliptical orbital paths.

Satellites following circular orbits must provide their own kinetic energy, which is the reason they require a dedicated artificial propulsion system of their own to remain in orbit.

Whilst spy-satellites need to follow circular orbits because their orbital paths must be altered from time to time, communication satellites and space-stations will benefit from this orbital system because their obits can remain fixed. Propulsion-free satellites are smaller, cheaper to design, build & launch, and therefore more reliable. Moreover, they will remain in orbit forever unless physically removed

The only requirement for a propulsion-free satellite is that it is launched into a non-circular elliptical orbit, which means you need to know the [velocity] vector at any point in the required orbit. This is, however, very simple to calculate using Newton's laws of orbital motion.

Once in orbit, each satellite in the same orbital path should be line-of-sight with neighbouring satellites and ground stations, providing accurate positioning for receiving and transmission purposes (Fig 1).

The orbit best suited to your requirements will be based upon on your satellite performance preferences.

For example;

**A**) If the shortest elapsed time between signal transmission and reception is important, this will mean that you need to keep the apogee radius as small as possible

**B**) If the orbital period is important, you may need make the perigee quite large, but signal transit time will be greater

**C**) Our moon's orbital eccentricty

A calculation example for each of the above options is provided below (see Table below):

Before calculating, we must define the immoveable constants:

We already know that the constant of proportionality for the earth is;

K = 9.91826542816423E-14 s²/m³

The earth's equatorial radius is; r = 6378137 m

Moreover, we know that perpetuality can only be achieved in a perfect vacuum, therefore the satellite's perigee radius must be greater than the earth's theoretical atmospheric ceiling at its equator, which we know is; H = 8103507.73 {m} plus a suitable safely margin (say; 1.2 x H)

This gives us a minimum perigee radius of: R = r + 1.2 x H = 16102346 m

The mass of the satellite is unimportant; as stated before, satellite mass does not affect orbital shape and satellite velocity.

The three controlling variables for Options A to C are as defined below:

**A**) e = 0.016 (similar to our sun's orbit in the Milky Way)

**B**) 24-hour orbital period

**C**) e = 0.06135

A few useful start-up formulas are provided below:

K = t²/a³ = (2.π)² / G.m₁ {s²/m³}

a = 3√[ t²/K ] = (Rᴾ + Rᴬ)/2 = Rᴾ.(1+e) / (1-e²) {m}

e = √[ 1 - (b/a)² ]

Symbol | A | B | C | units | ||

θ | 45 | 45 | 45 | ° | ||

θ | 0.785398163 | 0.785398163 | 0.785398163 | ° | ||

T | 20845.88707 | 86400 | 22376.7558 | s | ||

Rᴾ | 16102346 | 16102346 | 16102346 | m | ||

R | 16545555.5 | 46329469.44 | 17865282.42 | m | ||

Rᴬ | 16624062.01 | 68340056.64 | 18207294.58 | m | ||

Orbital Shape: | ||||||

a | 16363204.01 | 42221201.32 | 17154820.29 | m | ||

e | 0.015941743751 | 0.618619425886 | 0.061351519297 | |||

b | 16361124.61 | 33172808.71 | 17122504.40 | m | ||

p | 16359045.47373 | 26063570.03793 | 17090249.39135 | m | ||

ƒ | 16102346 | 16102346 | 16102346 | m | ||

x' | 260858 | 26118855 | 1052474 | m | ||

A | 8.41068504E+14 | 4.40010159E+15 | 9.22790961E+14 | m² | ||

L | 1.02806510E+08 | 2.37785879E+08 | 1.07685418E+08 | m | ||

K | 9.91826543E-14 | 9.91826543E-14 | 9.91826543E-14 | s²/m³ | ||

vᴾ | 5011.316479447 | 6325.426330783 | 5122.088180596 | m/s | ||

v | 4877.077223360 | 2198.475497586 | 4616.643285663 | m/s | ||

vᴬ | 4854.045408221 | 1490.402677103 | 4529.922651757 | m/s | ||

gᴾ | -1.53513191815 | -1.53513191815 | -1.53513191815 | m/s² | ||

g | -1.45398961576 | -0.18544253556 | -1.24710849672 | m/s² | ||

gᴬ | -1.44028921876 | -0.08522624248 | -1.20069630121 | m/s² | ||

EL | 81.81165564 | 7.712847708 | 71.25069177 | kW.hr | ||

po | 5.7905 | 24 | 6.2158 | hr | ||

ps | 0.05545190185 | 0.22795789084 | 0.06073299721 | s | ||

m₂ | 25 | 25 | 25 | kg | ||

KE | 2.9452196E+08 | 2.7766252E+07 | 2.5650249E+08 | J | ||

Orbital Options (refer to Laws of Motion for
symbol descriptions and formulas)EL = satellite launch energy po = orbital period ps = maximum signal period (at satellite apogee) m₂ = satellite mass KE = satellite kinetic energy |

You can see above that the kinetic energy needed to launch a 25kg (an arbitrary value) satellite can be as low 7.7 kW (i.e. little more than a pair of domestic kettles) for 1 hour.

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