How Much Delta-V is Needed for a Hohmann Transfer to Mars?

[hhhmortal]

Homework Statement

Estimate the total delta-V required to perform a Hohmann transfer between the Earth and Mars, ignoring the gravitational influences of the two planets. The planetary orbits may be assumed to be circular and in the same plane.

Why will there be a minimum wait time at Mars before a return journey to Earth, via a second Hohmann transfer, becomes possible?

Homework Equations

v = [GM(2/r - 1/a)]^1/2

The Attempt at a Solution

Is this more simple than I think it is, Do I need to link conic sections instead?


Thanks.

 

[hhhmortal]

^Bump

 

[aerospaceut10]

So by ignoring the gravitational influences of the two planets, you're concerned strictly with the interplanetary orbit transfer, I assume.

Well, both planets are still in their orbit, so you have to account for their motions. The Hohmann transfer is efficient for use of delta v but not the transfer time...what do you know, or what equations do you know, that can be used to account for the synodic period of the two planets?

 

[hhhmortal]

So by ignoring the gravitational influences of the two planets, you're concerned strictly with the interplanetary orbit transfer, I assume.

Well, both planets are still in their orbit, so you have to account for their motions. The Hohmann transfer is efficient for use of delta v but not the transfer time...what do you know, or what equations do you know, that can be used to account for the synodic period of the two planets?

Well I have used equations from the following webpage:

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

and then just added delta-v1 and delta-v2:

But apparently there's another way of doing it, which is escaping from Earth using equation:

V(excess velocity)² = v(initial velocity)² - v(escape velocity)²


When do I use which?

Thanks.

 

[aerospaceut10]

Well I have used equations from the following webpage:

http://en.wikipedia.org/wiki/Hohmann_transfer_orbit

and then just added delta-v1 and delta-v2:

But apparently there's another way of doing it, which is escaping from Earth using equation:

V(excess velocity)² = v(initial velocity)² - v(escape velocity)²


When do I use which?

Thanks.

Just to clarify, the original question you asked was about the minimum wait time. Did you figure out what you needed to account for?


And for the

"V(excess velocity)² = v(initial velocity)² - v(escape velocity)²"


I'm assuming v(escapevelocity) is vfinal velocity, and V(excess velocity) is Vdelta. That's just the pythagorean theorem for the triangle formed with the three vectors...you still need to use the equations from the Hohmann transfer to calculate the actual values for the delta V required for each burn. So you need both, basically.

 

[Janus]

Let's put it this way. You are traveling from one object moving in a circle with one period to another moving in a different circle and at at different speed. The time it takes for you to move from one circle to the next is fixed. What conditions have to be met in order for the target object to be right point of its circle when you get there?

 

[hhhmortal]

Just to clarify, the original question you asked was about the minimum wait time. Did you figure out what you needed to account for?


And for the

"V(excess velocity)² = v(initial velocity)² - v(escape velocity)²"


I'm assuming v(escapevelocity) is vfinal velocity, and V(excess velocity) is Vdelta. That's just the pythagorean theorem for the triangle formed with the three vectors...you still need to use the equations from the Hohmann transfer to calculate the actual values for the delta V required for each burn. So you need both, basically.

Oh right! So you use the equations for hohmann transfer to get the deltaV for the hyperbolic escape trajectory which takes it clear of the Earth's sphere of influence. And once you get deltaV1 for hohmann transfer and deltav1 for hyperbolic escape trajectory..you add both values to get the total deltaV for first stage?