Good reference. The orbits in two body systems are conic sections: circle, ellipse, parabola, hyperbola. Within earth's neighborhood a Mars transfer orbit would be a hyperbola with regard to the earth with a focus at earth's center. But once outside the earth's neighborhood, this path would be modeled as an ellipse with the sun at a focus.


Well then, it was your hugely off topic post I was replying to.



Indeed. I Google for Why Not Space or Stranded Resources. When I see someone repeating Murphy's misinformation, I challenge it.


Right. It's a complicated and important topic. There are zealots on both sides. And I admit I am not dispassionate.

I offer my math and a critique of Murphy's math. I ask people to take the time and effort to study what's going on so they can have an informed opinion.

In the case of patched conics, the speed of a hyperbola is sqrt(Vesc^2 + Vinf^2)
where Vesc is escape velocity and Vinf is the difference between earth's velocity (about 30 km/s) and perihelion velocity of a heliocentric transfer orbit. For a Mars Hohmann transfer orbit, Vinf is about 3 km/s.

When I see sqrt(a^2 + b^2) it's my habit to think of the pythagorean theorem. And that's how I visualize the speed of a hyperbola: as the hypotenuse of a right triangle with Vesc and Vinf as legs.

Thus the speed for Trans Mars Injection hyperbola would be sort(11^2 + 3^2) km/s which is about 11.4 km/s. Murphy commits a very common mistake, he just adds 11 and 3 to get 14 km/s. He also neglects aerobraking and delta V savings that can be had from 3 body mechanics. From a high school student these would be forgivable errors. From someone with Murphy's credentials, they are inexcusable.

There are many serious flaws in Murphy's arguments. I talk about them at Murphy's Mangled Math

And with that I will bow out. Out of respect for other readers I will no longer participate in the hugely off topic sub-thread Kramble has started on this forum.

Tom Murphy isn't dispassionate -- he has an ax to grind. He fancies himself a Paul Revere shouting an urgent message "Peak Oil is Coming! Peak Oil is Coming!" He is correct to urge us to conserve our resources. However he fears the prospect of space resources will lull us into complacency. Thus he starts with a preconceived conclusion and sets about to gather evidence to support what he's already decided is true.

And this leads to some horribly wrong math. A freshman aerospace student would recognize the way he patches conics is ridiculous. The only people who take Murphy's Why Not Space or Stranded Resources seriously are those who haven't done the math.