Online Calculator: Isaac Newton's Orbits

{CalQlata © 01/01/20}

Johannes Kepler's orbits have been around for more than 450-years, yet even today, they are little understood.
A satellite's orbital dimensions are dependent entirely upon its force-centre's mass, but its performance is dependent upon its own mass.
In other words, a satellite's orbital dimensions and orbital performance are independent of each other, which means that you can swap any two satellites and their orbital dimensions will remain unaltered, but their performances will change (see Note 4).
You can demonstrate this fact in this calculator by selecting our sun as the force-centre, the earth's mass, period and perigee, and then alter the mass to Jupiter. You will see that the orbital dimensions remain constant, but the performance varies.
Each orbit is eternal and consistent, but only in a perfect vacuum, which is the case in outer-space.

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Units

This calculator is intended for metric units only. However, if you alter the green constants and blue variables to alternative units (e.g. Imperial), whilst the calculated results will be correct, they will be presented in the units entered; not the metric units indicated.

The Calculator

The primary purpose of this calculator is to provide the dimensional and performance properties of the planetary orbits in our solar system. However, you may select any combination of force-centre from the dropdown list, together with any satellite for each input value; e.g.:
Force-Centre Mass; Jupiter
Satellite Mass; Earth
Satellite Orbital Period; Venus
Satellite Perigee Distance; Neptune
or
alter the default data to anything you like,
and the calculated orbital properties will be correct for the data entered.
Then click the 'Calculate' button to calculate. Click the 'Reset' button to clear the calculated results.

π =
Newton's gravitational constant: G = m³ / s².kg
Force-Centre:
Hades sun mercury venus earth mars jupiter saturn uranus neptune pluto     mass: m₁ = kilograms
Satellite:
To calculate the orbital properties of an actual solar-system satellite, select the same satellite name for each property.

sun mercury venus earth mars jupiter saturn uranus neptune pluto moon phobos deimos    mass: m₂ = kilograms
sun mercury venus earth mars jupiter saturn uranus neptune pluto moon phobos deimos    orbital period: t = seconds
sun mercury venus earth mars jupiter saturn uranus neptune pluto moon phobos deimos    perigee radius: Rᴾ = metres
θ = °
θ is the angle through the satellite's orbit from its orbital apogee. Note; 180° is the orbital perigee.

Dimensional Properties:
constant of proportionality: K =
½ major-axis: a = metres
apogee: Rᴬ = metres
eccentricity: e =
½ minor-axis: b = metres
half parameter: p = metres
orbital length: l = metres
orbital swept area: A = metres²
orbital radius @ θ: R = metres

Dynamic Properties @ θ:
velocity: v = metres per second
potential acceleration: g = metres per second²
momentum: p = kilogram.metres per second
constant of motion: h = metres² per second
potential force: F = Newtons
potential energy: PE = Joules
kinetic energy: KE = Joules
total energy: E = Joules

The above 'potential' values ('g', 'F' & 'PE') act in a straight-line between a satellite and its force-centre.

Help

This Orbits calculator is accessible from anywhere in the website using the shortcut key; "Alt" + "o".
The "Reset" button clears all calculations on the page and reinstalls default values (this button may not respond in the FireFox browser).
Reset can also be achieved by pressing the "F5" key.

Notes:

Here are a few notes concerning the above calculations:
1) We have used NASA's data for our pre-set values for the solar-system galactic force-centre and satellite perigees and orbital periods, but they are a little out. You will notice that whilst the total energy (E) is identical at the orbital perigee and apogee, it rises (or falls) very slightly between '0°<θ<90°' and returns again between '90°<θ<180°'. You will also notice that this variation differs (slightly) for each satellite.
This is how we know that the calculation is correct (the total energies are identical at the perigee and apogee) but NASA's data is not; the total energy varies (very slightly) between the major and minor axes but unequally for each satellite.
2) You will notice a celestial body called Hades in the list of force-centres. This is the name CalQlata has adopted for our Milky Way galactic force-centre, for reasons of brevity. Its perigee and orbital period are based upon NASA's data, but its mass has been calculated (by CalQlata) using Newton's laws of orbital motion. It is not included in the satellite lists because Hades is a linear orbit satellite; it is travelling away from the last 'Big-Bang' in a straight line.
3) All of the theory used here can be studied in Laws of Motion.
4) Our own asteroid belt is compelling proof of this fact. The original planet was a very different mass before its destruction, but its orbit is still in tact. If orbital dimensions vary with a change in satellite mass, the asteroid belt would not exist. Because each piece of debris, the mass of which is different, would otherwise have regenerated an alternative orbit by now.

Downloadable Version

A full, downloadable version of this calculator is available from this website at; Newton.

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