Basic Astronomy

[bertibott]

Hi,

I have been playing KSP for a while now and recently started playing around with the kOS mod wich made me realize, that while I have a general understanding of orbital mechanics I am having trouble getting my head around how things work specifically. The stuff I learned at school all those years ago, or in basic engineering (not quite so many years ago) helped somewhat... but I was limited to rather basic and/or special cases. There is not much spaceflight to be done when you are limited to to circular, zero-inclination orbits. Why does everything alwasy have to have nasty properties such as eccentricties or directions (and why don't they behave like decent academic examples and follow one of the karthesic axis? Having been a good student to this day I always buy at least 17 melons at once!)?

For example I have been trying to calculate my own circularization burns... A rather simple method I would say would be to calculate the actual velocity at Apoapsis and the velocity a circular orbit would have at that Altitude. The difference would be the required dV. Relatively easy... also only scalars involved so far. But now comes the tricky part.. when do I start and where do I point? Far a start I would like to be able to calculate when and where my rocket will be... not too hard on a circular orbit but on an elipse?

 

Long story short does anyone know a good place to read up on things like orbital mechnics? I asked google... but I guess I searched for the wrong keywords.

[PB666]

3 hours ago, bertibott said:

Hi,

I have been playing KSP for a while now and recently started playing around with the kOS mod wich made me realize, that while I have a general understanding of orbital mechanics I am having trouble getting my head around how things work specifically. The stuff I learned at school all those years ago, or in basic engineering (not quite so many years ago) helped somewhat... but I was limited to rather basic and/or special cases. There is not much spaceflight to be done when you are limited to to circular, zero-inclination orbits. Why does everything alwasy have to have nasty properties such as eccentricties or directions (and why don't they behave like decent academic examples and follow one of the karthesic axis? Having been a good student to this day I always buy at least 17 melons at once!)?

For example I have been trying to calculate my own circularization burns... A rather simple method I would say would be to calculate the actual velocity at Apoapsis and the velocity a circular orbit would have at that Altitude. The difference would be the required dV. Relatively easy... also only scalars involved so far. But now comes the tricky part.. when do I start and where do I point? Far a start I would like to be able to calculate when and where my rocket will be... not too hard on a circular orbit but on an elipse?

 

Long story short does anyone know a good place to read up on things like orbital mechnics? I asked google... but I guess I searched for the wrong keywords.

Position follows the areea rule (the area swept by an orbiting object per unit time does not change). The period is determined by u and a.  You need an engineering addon like MechJeb to know the period.

For transfers the time required for the transferring ship is about 1/2 the period, since dividing ellipse along the low and high points in an orbit creates two equal halves, and given the area rule, thus the area is swept in one period, half the area amounts to half the period. Once you know the transfer time, all you need is the period of the target orbit angle its angular velocity its going to cross 360 per period. Since you know the transfer time, you can calculate the number of degrees the target orbit sweeps in the transfer time. Since the ship transfers 180 degrees the target sweeps x degrees. There for the targets positions relative to the transfer ship should be 180-x degrees, in front of the ship if it is positive and behind the ship if it is negative. 

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

Many of the equations are here in the link above. 

https://en.m.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

The are other pages that link to this page.

u (greek mu) = celestials gravitation constant = universal gravitational constant * central bodies mass

(for a small satellite)

In the game the semi-major axis (a) is equal half the major axis, which is sum of the altitudes of the periapsis, apoapsis and central bodies diameter. 

e is the difference of the Apo and Pe divided by the major axis.

 

 

Edited April 13, 2016 by PB666
Fixed typo

[YNM]

2 hours ago, bertibott said:

... But now comes the tricky part.. when do I start and where do I point? Far a start I would like to be able to calculate when and where my rocket will be... not too hard on a circular orbit but on an ellipse?

Long story short does anyone know a good place to read up on things like orbital mechanics? I asked google... but I guess I searched for the wrong keywords.

You'll need some books. Although I suppose some chaps on Wiki probably already nailed it.

DeltaV for weird trajectory change : you just need to look for the vector version of the usual equation. One that's very helpful is angular momentum equation.

Position : lookup anomalies. True and Mean anomaly are often used - to change between the two, you'll need eccentric anomaly.

Length of burn : there's this.

Edited April 13, 2016 by YNM