Calculating Venus Fly-By - How to calculate a flight using Venus?

bolbuyk · 2004-04-07 05:27:16

Last time I'm calculating a mission trajectory using on route to Mars a Venus-fly-by, often called a mission of the opposition-category. This results in general in a total mission duration of less then 2 years. The possibility of such a mission comes every 3 Mars-launchwindows, ti every 6.4 years.

However, calculating this is a thorough job. Maybe sombody has some work done on it and has some tips. I use formulas of orbital mechanics, including Lamberts Theorem. I want to correct for deviations from circular-coplanar, because I think these can't be neglected to get a realistic result.

The way I do it yet:

I guess some scenario, ti a depart date from earth, a Venus-fly-by date and a Mars-arrival date. I calculate with a program written by myself from orbital elements the three position-vectors and also velocity-vectors of the planets.

Then putting to vectors (FROM and TO) in a second program and giving a desired travel time a calculate, using Lamberts tehorem, ao the velocity-vectors of to and from. New calculations have to be made using new guesses to get the situation that v-hyperbolic for Venus is the some, both for coming from earth and going to Mars. Then I calculate the delta-v-fly-by and caluclate the r-periathenum (?, is this right terminology). If this is lower than 6330 kilometers, the spacecraft will fall into the paralyzing warmth of Venus and I have to do the whole mess again. This doesn't really proceed.

To it, I have to optimalize for delta-v both for departure from Earth and arrival at Mars.

I think the result will be 20 to 30 march 2018 as arrival at Mars and departure beginning april 2017, total delta-v about 9 km/s (taken is here hyperbolic excess speed). But a slight delta-v at periathenum could alter the situation and then a more optimal trajectory is maybe possible.

Can anyone help?

BTW: Ever noticed that the synodic periods of Venus and Mars have a nearly perfect 3 to 4 resonance?

SBird · 2004-04-07 10:36:46

I was under the impression that an opposition class mission requires a much higher delta-V than a conjunction class mission, not to mention a much higher radiation dose from going closer to the sun. Is there any particular reason to want to do this?

bolbuyk · 2004-04-07 15:38:23

The reason to do this is the much shorter duration of staying in space, about 40% less then in a mission using to hohmann-trajectories. Not only does this mean a lower possibility of getting troubles, but also an expected shorter time to handle these troubles. Beside that, I think that it is rather easy to skip a Mars orbit insertion if necessery and alter the trajectory, by delta-v of about 4 km/s at most. This possibility is not available in the normal case.

Most of the older designs use this type of mission, but the newer, I don't see it.

Maybe I consider to redesign"'my' mission, because I see more disadvantages than I had imagined.

RobS · 2004-04-07 18:39:42

As I understand it, the Venus flyby (or "fryby" as some jokingly call it) shorten the total length of the mission, but it does so by drastically shortening the time spent on the Martian surface and LENGTHENING the time spent in space.

Hohmann Earth to Mars: 270 days
Hohmann Mars to Venus: 230 days
Hohmann Venus to Earth: 146 days

Note the last two add up to 376 days. One can use more energy and fly between Mars and Venus faster. I don't know how much faster one can make that flight. The Earth-Venus leg can be reduced to 110 days with very little extra delta-v; I read in a book that Mariner 2 left Earth with a velocity of 25,700 mph (500 mph more than escape velocity) and reached Venus in 110 days. The other factor to consider is that Venus has to be in exactly the right place in its orbit with respect to Mars AND with respect to Earth to make the Venus flyby useful. Sometimes that does not happen on either the outbound trip OR the inbound trip, though I think it is likely to happen on one or the other. Venus and Earth have a synodic period of 19 months, Mars and Earth 26 months, Mars and Venus 335 days.

Oh, another interesting fact: A spacecraft takes about the same length of time to travel from Venus to Mars by Hohmann trajectory (230 days) as it takes Venus to orbit the sun (225 days). This means a Venus Hohmann to Mars Hohmann straight back to Venus is possible; Venus will have made exactly two revolutions around the sun. Then the spacecraft has to wait almost exactly a Venus year and the two planets line up for another Venus to Mars to Venus. As noted, Mars and Venus are in alignment for flight every 1 1/2 Venus years (=335 days) and every half Martian year (=335 days). So some day Mars may be a major supplier to a Venus orbit station. A cycler would be very easy to set up.

-- RobS

bolbuyk · 2004-04-08 05:40:21

The position of Venus in relation to Mars and Earth for this mission is easily determined, because of the resonance of the synodic periods of Mars and Venus. So, taking going to via Venus, this will be possible 1 in 3 launch-windows. Every next opportunity to take this scenario is roughly the same, but turned about 140° in prograde direction. This can easily be calculated.

The situation is then:
The Earth-Venus trajectory is a lengthened Hohmann-trajectory with perihelion about 0,65 AU, which has to be passed. With big amounts of fuel, shielding for the sun is rather easy, so this is not a topic. Solar cells are very efficient. The Aerth-Venus will take about 5 months. Then the Venus-Mars trajectory will last about 7 months, a shorteened Hohmann-trajectory. Further shorteningg of this trajectory is possible, paying it by dramatically increase of delta-v for deceleration at Mars. But when aerobraaking is used, this doesn´t need to be a point.

Then follows the journey back, taking a shorthened or lenthened Hohmanntrajectory, because the pure Hohmann-launch-window has passed when the mission arrives at Mars. By adding a little delta-v this is rather easy to obtain.

In all, this mission is much moree complex to calculate, but I think still for the crew-considerations (total length and abort-possibilities) preferable.

SBird · 2004-04-08 11:05:21

The problem is that you're cutting Earth->Mars trip time from 9 months to 7 in exchange for higher radiation doses, greater solar flare risk and a much higher delta V. The elder Bush's Mars plan used this trajectory and it's the primary reason the projected cost ballooned to $600 billion and got canned. Zubrin makes very persuasive argumetns as for why the conjunction class approach is much sperior with current technology. With future, high Isp drives, a Venus assist trajectory might work but you're probably just as well of with non-Hohmann direct trajectories that can cut travel time down to a few months.

John Creighton · 2004-04-08 21:47:30

Still, all said I'd like to see the callculations.

bolbuyk · 2004-04-09 03:56:34

Of course, that is my question: How to calculate, not why. I can even display what I have calculated on this forum, but that will be quite much information. Beside that, the overall result will more go in the direction of 10 km/s.

Easy to show is the resonance of the synodic periods of Venus and Mars, and thereby (as a consequence) the relative motion of Mars with Venus as reference.

Earth-Mars:779.9 days x 3 = 2339.8 days
Earth-Venus:583.9 days x 4 = 2335.7 days
Venus-Mars:333.9 days x 7 = 2337.4 days

Largest difference: 4.1 day ~.2%

This means that the relative position of these planets is after ~2337 days neraly the same, only moved as a whole to the east by 143 degrees.

Remarkable.

RobS · 2004-04-09 12:44:41

That really is amazing. Put another way:

2337 = 10.4 Venus years
2337 = 6.4 Earth years
2337 = 3.4 Mars years

The 0.4 equals 144 degrees.

-- RobS

Bill White · 2004-04-09 12:52:12

That really is amazing. Put another way:
2337 = 10.4 Venus years
2337 = 6.4 Earth years
2337 = 3.4 Mars years
The 0.4 equals 144 degrees.
-- RobS

A cosmological constant?

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#1 2004-04-07 05:27:16

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#2 2004-04-07 10:36:46

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#3 2004-04-07 15:38:23

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#4 2004-04-07 18:39:42

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#5 2004-04-08 05:40:21

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#6 2004-04-08 11:05:21

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#7 2004-04-08 21:47:30

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#8 2004-04-09 03:56:34

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#9 2004-04-09 12:44:41

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

#10 2004-04-09 12:52:12

Re: Calculating Venus Fly-By - How to calculate a flight using Venus?

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