# How can I calculate the delta-v correctly, this way does not seem to be correct?

I'm learning about Astrodynamics, and I would like to ask how can I calculate the $$\Delta V$$ for an interplanetary mission.

I used a website for the porkchop plots (http://sdg.aero.upm.es/index.php/online-apps/porkchop-plot), which gives me the $$\Delta V$$ of the mission, and I am comparing my calculations with the $$\Delta V$$ that the site gives me, but they aren't alike at all, so I was thinking that maybe you could help me to calculate it correctly.

The calculations I did are following the site http://www.braeunig.us/space/interpl.htm

Solving the Kepler equation, I get the position and velocity of each planet at departure and arrival ($$\vec{V_{p1}}$$ and $$\vec{V_{p2}}$$). In my case, the planets are Earth and Jupiter and the date of departure is 21/01/2030, with a time of flight of 869 days (I used the porkchop plots in the first site I linked for choosing a departure date). After that, I solve the Lambert problem given the two positions and the time of flight, getting two velocities ($$\vec{V_1}$$ and $$\vec{V_2}$$).

With those values, I obtain the difference between the spacecraft heliocentric velocity and the planet orbital velocity. That is, $$\vec{V_1}-\vec{V_{p1}}$$. Taking that value as $$\vec{V_\infty}$$, I calculate the injection velocity as $$V_o=\sqrt{V_\infty^2+\frac{2\mu}{r_o}}$$. Being $$\mu$$ and $$r_o$$ the values respect to the Earth. As I have a parking orbit with a radius of 200 km, $$r_o$$ is the sum of the Earth radius plus 200 km. At last, I calculate the $$\Delta V$$ as the difference between the injection velocity and the orbital velocity

$$\Delta V=V_o-\sqrt{\mu/r_o}$$

Qeustion: With these calculations, I have a $$\Delta V=19$$ km/s approximately, but the $$\Delta V$$ I have according to the porkchop plot is about 8.8 km/s. I am new with Astrodynamics, so I am trying to learn how to calculate this properly, but I don't find the mistake and I don't know what's wrong.

• I wasn't the downvoter, but usually Stack Exchange doesn't like "how do I do X" questions without good research effort. Can you tell us why the existing questions about delta V don't help you, or show the calculations that aren't comparing to the website? – Bear Jun 4 '18 at 18:37
• Hello, sorry for the way I asked the question. I added the calculations I made with the explanation according to what I searched. I didn't find any books that explains this properly, so I don't know what to do to calculate this properly. – Alberto De Celis Romero Jun 4 '18 at 19:20
• Why was this downvoted when nonsense like "Why do not we fly to space with helicopters?" sits at +12? – Hobbes Jun 4 '18 at 19:23
• @Hobbes How disrespectful of helicopters! It's all about reusability today. – Everyday Astronaut Jun 4 '18 at 20:26
• @Hobbes I've added something to the title of that question. The body of the question does try to address the problem from a quantitative perspective, it was just an unfortunate choice of titles. The post itself was not "nonsense". – uhoh Jun 5 '18 at 1:36