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I don't have any knowledge in physics, but in a world building related question, I need to know how can I calculate the orbit or the distance in each point of the orbit around a spherical object in space.

This would be the values of the orbiter 'planet' (A):

Radius:               1645.8294922995256
Diameter:             3291.658984599051
Circumference:        10341.051684139216
Circle area:          8509803.921575
Sphere surface area:  34039215.6863
Sphere volume:        18674248357.085728

And this, the values of the mass that the other would orbit around (B):

Radius:               179665.31384583088
Diameter:             359330.62769166176
Circumference:        1128870.4601659337
Circle area:          101409432758.5
Spere surface area:   405637731034
Sphere volume:        24293010084644784

So my question is, if I want to calculate the longest distance from A to B in the orbit, or the shortest, or basically any point on it, is there an easy formula to do so?

I've researched a little bit and learned about why planets orbit in microgravity. I sourced from a Quora answer:

The earth is constantly trying to fall into the sun, but it keeps missing. That is essentially what an orbit is. The sun exerts an attractive force on the earth, accelerating the earth directly towards the sun. This acceleration is constantly taking place. However, the earth also has some sideways momentum (perpendicular to the direction towards the sun). So as it falls towards the sun, it also moves to the side. As long as that sideways motion is enough to "side-step" the sun, the earth will orbit instead of crashing. You can see this more clearly in a more elliptical orbit:

Is it right to say so?

Also, if I had different values for A and B, how can I calculate the orbit and distances on them? Is there a specific formula?

Thanks in advance.

Edit: Specifying how elliptical would the orbit be and the average distance: As said before it is more on World Building, but it's supposed to simulate Earth's condition but in a smaller area. Using a rule of three I've calculated the 'Sun' size and the orbiter planet area comes from a pixel measure standard (in a map). It should be somehow like Earth, but smaller, what I don't know is if it would be the same orbit or same speed since they are smaller. Also, I'm interested in knowing the factors and formula so I can calculate it myself. The average distance would be an Astronomical Unit reduced to the current scale, which I do not surely know how can I calculate it. The scale is relative to the planet data.

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  • $\begingroup$ given two planets there are an infinite number of possible orbits, you need to be more specific, such as the average distance between planets and the ellipticity of the orbit $\endgroup$ – Wolphram jonny Jun 21 '16 at 19:20
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The Quora quote is not useful because it does not tell you how to do any calculations. You need websites which explain how to calculate radius and period of orbit. eg

http://www.physicsclassroom.com/calcpad/circgrav http://www.physicsclassroom.com/class/circles/Lesson-4/Mathematics-of-Satellite-Motion

A more advanced webpage for calculating general (non-circular) orbits is :

https://en.wikipedia.org/wiki/Orbital_mechanics

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