I'm trying to calculate the required delta-v to travel from a 200 km Earth orbit to a 200 km Mars orbit using the last equation from this answer:

$\Delta V=\sqrt{{\mu_S\over r_1}\left(\sqrt{\frac{2r_2}{r_1+r_2}}-1\right)^2+\frac{2\mu_1}{a_1}}-\sqrt{\mu_1\over a_1}+\sqrt{{\mu_S\over r_2}\left(\sqrt{\frac{2r_1}{r_1+r_2}}-1\right)^2+\frac{2\mu_2}{a_2}}-\sqrt{\mu_2\over a_2}$

I believe I have filled all the variables correctly, but I'm getting a delta-v value of 783 921 km/s. This is definitely not correct.

Here is what the filled in equation looks like:

Hohmann transfer orbit calculation

Does anyone know what I did wrong?

I want to use this equation in a space exploration game I'm working on.

  • 3
    $\begingroup$ Two quick comments: 1) It looks as if you're using km in some instances (e.g., a1), and meters for your other variables. 2) Your expression for the semi-major axis values should include the radius of the particular central body, using 200 km is only using the altitude of the orbit. $\endgroup$
    – jah138
    Apr 27, 2015 at 20:18
  • $\begingroup$ I'm pretty sure that all the distances are in km. Earth has a semi major axis of 1.496 x 10^8 km, not m right? As for the second comment: I see what I did wrong. I took the altitude above surface level. Not the actual semimajor axis. $\endgroup$
    – Avanak
    Apr 27, 2015 at 20:24
  • 1
    $\begingroup$ Yup, concur with jah138. You didn't do dimensional analysis. You're by one order of magnitude off with your distances. So instead of, say, $1.496\times10^8$, you should use $1.496\times10^{11}$. And $200 + 6378.1 km$ for radius of Earth orbit and $200 + 3396.2 km$ for radius of Mars orbit. The point about km vs m is that you used meters for your $\mu = 6.673\times10^{−11} Nmkg^{-2} * 1.98855\times10^{30} kg$. Also note that where you copied $M$ from, those last two digits that are separated by space aren't decimal places but precision. So 5.972 19 is just a different notation for 5.972±0.019 $\endgroup$
    – TildalWave
    Apr 27, 2015 at 20:25
  • $\begingroup$ I used this website for the semimajor axis: smartconversion.com/otherInfo/…. These are in km right? $\endgroup$
    – Avanak
    Apr 27, 2015 at 20:27
  • 1
    $\begingroup$ Ah I see TidalWave. I did not understand the gravitational parameter correctly. I will change km into m. And also the right altitudes. $\endgroup$
    – Avanak
    Apr 27, 2015 at 20:29


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