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This diagram has been discussed quite a lot, but my issues is with the Delta v requirement for a Hohmann transfer to Mars.

The diagram states that the Delta v for change from Earth intercept to Mars intercept is 1060 m/s. I get the required Delta v for raising the aphelion to Mars' orbit to 2944 m/s. What did I overlook?

Solar System Subway map

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    $\begingroup$ Assuming you're orbiting the sun in a solar system with no planets, and you want to raise your apoapsis to Mars' distance, then it is around 2.9 km/s. But in reality, you have to get into LEO, and escape Earth's gravity well. This costs more delta-v. So from lift-off to Hohmann injection burn it's about 13 km/s total. (You have to add up the numbers on the path you want to take). $\endgroup$
    – Star Man
    Commented Jun 7, 2020 at 17:23
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    $\begingroup$ Because you only took the vis-viva equation and neglected the fact that he burn to leave the earth already counts against that. $\endgroup$
    – Polygnome
    Commented Jun 7, 2020 at 19:05
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    $\begingroup$ That value isn't actually for earth intercept to mars intercept. That is the additional required delta-V to go from LEO to mars intercept. The values don't sum in series, because when you burn to eject from LEO you benefit from the Oberth effect. The map should have some kind of clarification added to it. It is much more expensive to burn to raise your apoapsis, then coast to the apoapsis and then eject to mars than it is to eject to mars directly from a LEO parking orbit (although multiple apoapsis raising burns at the LEO periapsis + ejection would be the same). $\endgroup$
    – lamont
    Commented Jun 7, 2020 at 20:32
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    $\begingroup$ @lamont The way charts like that work is you do add the numbers in series, the Oberth effect has already been considered. Note that this means you can't use it to find routes between other bodies because of this. $\endgroup$
    – Loren Pechtel
    Commented Mar 15, 2021 at 3:40
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    $\begingroup$ Yeah that's what I said the 1060 includes the Oberth effect from burning from LEO. If you're not burning from LEO the 1060 number can't be applied. $\endgroup$
    – lamont
    Commented Mar 15, 2021 at 7:00

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Thank you all. Of course, I forgot about the Oberth effect. The $\Delta v_{esc}$ required to escape Earth from LEO and the $\Delta v_2$ required to raise aphelion to Mars' orbit isn't just the sum of those two, but $$ \Delta v_0=\sqrt{v_{esc}^2+v_2^2} $$ Thanks again.

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