# Why is the velocity of a satellite the result of a sum of two velocities? (clarifying img included)

I am a newbie when it comes to orbital mechanics. The velocity of a spacecraft is given by a sum of two types of velocities. But I don't understand the difference between both velocities:

$V = V_{кр}+\Delta V$ Could somebody help me understand?

• Hi and welcome to Space Exploration. This process will be easier is going to be quite slow or peppered with misunderstanding if you leave it to respondents to choose their own guessed translations from cyrillic. Could you provide your own translation please, specifically that of Vkp. It looks also as if the circled meaning of the lower case omega in the diagram is significant too. That said, the delta-V symbol is conventionally used to represent the velocity increment imparted by the vehicle and often, perhaps in this case, who knows, it is assumed to be imparted impulsively. – Puffin Apr 7 '17 at 10:05
• The next puzzle is the meaning of the solid and dotted lines. Their relationship either shows a rotation of the line of apsides, which seems plausible given the "little omega", or perhaps is not intended to show a simple single manoeuvre at all. – Puffin Apr 7 '17 at 10:12
• @Puffin The translanswer below does a good job. Solid line is the real elliptical orbit, dashed line is a circular orbit passing through a given point along the real orbit. You are right; ideally, OP should have also included some helpful English summary or at least approximation for the image. It looks like a translanswer came so quickly that they didn't have time to add it. – uhoh Apr 7 '17 at 11:45
• I'd propose a transl-answer tag, but the moderators might put me on a hyperbolic trajectory out of SXSE :) ...unless... unless it's a good idea, in which case I'll take full credit! – uhoh Apr 7 '17 at 11:47
• @uhoh Your eccentricity just increased. – a CVn Apr 8 '17 at 11:39

My translation:

In some cases, one needs to express semi-major axis and eccentricity of an elliptic orbit in terms of parameters (speed and radius) of the circular orbit passing through a certain point of the elliptic orbit (Fig 1.3). Let's represent the spacecraft's velocity as a sum

$V = V_{circ} + \Delta V$,

where $V_{circ}$ is the velocity of movement along the circular orbit of radius $r$, determined by formula (1.4);

$\Delta V$ is the velocity relative to the circular, required to attain the actual velocity.

So, as the text says, for a given point of a given elliptic orbit, $V_{circ}$ or $V_{кр}$ is the velocity that a circular orbit that passes through this point (and lies in the same plane as the elliptic orbit, presumably) has at this point. And $\Delta V$ is the difference between $V$, which is the velocity of the elliptic orbit at this point, and $V_{circ}$.

It's probably explained later in the book what they need to represent $V$ as such a sum for.

• That's interesting and makes a lot more sense now. +1. It's not a convention for expressing an orbit I'm familiar with. I'd be interested to hear more about how its used too. Given the explanation here, it seems the useful number is the delta V, either as a vector or as a scalar in conjunction with the flight path angle from circular to elliptical, which is perhaps what lower case omega represents. – Puffin Apr 7 '17 at 12:47