# Change of orbit with tangential impulse

I see a similar question: Change of orbit with a radial impulse. The answer to that question seems fine to me. In the answer, mention is made of this similar question, but it is not fully treated.

So, suppose a satellite is in a perfectly circular orbit. If you impart a brief forward impulse (in the direction of the orbit), what now happens to the orbit? (And what about a backward impulse?)

• Have you seen this one? physics.stackexchange.com/q/480904 – Gert May 24 '19 at 16:29
• @Gert, I'm familiar with the qualitative aspects of adding velocity to a circular orbit. However, I have never seen an equation for calculating the shape of the resulting elliptical orbit. Does such an equation exist? – David White May 24 '19 at 16:34
• @DavidWhite: I believe it would be very complicated. – Gert May 25 '19 at 17:19

See my answer here. Consider a satellite whose speed changes as $$\vec {v}=k\vec {v}$$ at some point of the trajectory. Figure 1 shows the trajectory before the speed has changed (blue) and after (orange). We see an elliptical trajectory that is getting farther from the central body at $$k>1$$ ant it is getting closer to the central body with decreasing $$k$$. When $$k\ge \sqrt {2}$$, the satellite leaves the central body.
• @MarkGoldfain You're welcome. I solved the problem as it is. At the beginning, the satellite moves in a circular orbit, then the satellite speed suddenly changes according to the law $\vec {v_1}=k\vec {v_0}$. As a result, the satellite moves to an elliptical orbit. – Alex Trounev May 26 '19 at 10:43