Weird question I thought of about space trajectories

I wondered if space trajectories are straight. At first blush it would seem to be the most economical fuel-wise.

But then I remembered that most deep flights slingshot around other planets. So I googled it only to find NASA apparently thinks the most economical (and quickest) way to get to Mars is piggy-backing…

…Venus. WTF!?

I’m not arguing with NASA scientists but that seems like a long way out of the way. Looking at the diagrams it seems like the quickest way would just be to aim at where Mars will be, and aim for that.

In layman’s terms, why not? Also do we ever go anywhere in space by calculating future trajectories and aiming for that spot ( kind of like a quarterback’s Hail Mary [without the gravity of course])?

I would think this is the biggest thing; you can save a lot of fuel using those “piggy-backing” maneuvers.

At least, that’s how I roll in KSP (Kerbal Space Program)…

There’s quick, and there’s fuel efficient.

If you don’t have to worry about your Delta V budget, like if you have drives from The Expanse, then pointing a bit ahead of Mars and thrusting away is the fastest way to go. (Turnover about half-way.)

If you are limited to using chemical fuel rockets, as we are, then often a gravity assist or two can make it far more economical to send a probe or other object that doesn’t mind sitting in the cold of space for a while.

And it’s not just economics, there is a limit to the size of rockets that are available at any cost. If you have a large payload to get to Mars, it may not be possible with current rockets to send it on a direct trajectory.

Depends what you call a straight line as well. There are more possibilities than just Euclidean space.

A spacecraft is negotiating the gravitational field as it travels, and what is the best answer is more like a tricky shot on the St Andrews putting green.

Worse of course, the lay of the land is changing under your feet as the planets move.

As far as a planet is concerned, a circular orbit is really a straight line, a slight eccentricity is the planet being just off centre, wobbling either side. Imagine throwing a marble into a funnel so it perfects circles around. Depending upon your viewpoint, that is the straight line. It gets the planets to where they are going with no energy input needed.

(I did a round of the St Andrews putting green many years ago. It was frustrating beyond enjoyment.)

It depends where they are in their orbits round the sun.

Here’s the current position of the inner planets as at July 21, 2021:

From 3D Solar System Orbits Viewer

Wow, thanks. Good point. Venus is now BETWEEN Earth and Mars. I keep forgetting that that’s possible! So obvious when you see that diagram…and as soon as I look away and try to think about it, it’s not obvious anymore.

That’s actually irrelevant, though. All the planets are traveling counter-clockwise in this picture. A space vehicle would never be sent clockwise (i.e. directly toward Mars in this diagram)–there is far, far too much velocity to burn off from Earth’s motion. Instead, the vehicle would be sent inward slightly, but still counter-clockwise. It would meet Venus at the appropriate time, then use its gravity to change direction (often called a slingshot). Do it right, and you get boosted all the way out to Mars (or somewhere else).

Even getting to Mercury is a challenge, despite it seeming like you can just aim at the Sun and go. Reducing your forward motion from Earth is just too hard. Instead you make multiple flybys of both Earth and Venus to get there, and some extra flybys of Mercury to slow down (used by the MESSENGER probe).

Whether minimising mission duration or \Delta V, can you give some examples where you gain anything much from a planetary flyby (of Venus, or an extra Earth encounter, or whatever) compared to heading directly from Earth to Mars? Also, a burn manoeuvre in space at an intermediate point between Earth and Mars may sometimes be useful, but that does not imply it is a good idea to get near Venus.

There’s a fairly straightforward whitepaper here.

There are two basic classes of Mars missions, opposition-class and conjunction-class. You can see the trajectories on page 2. Opposition class is a short stay, while conjunction is longer. Total mission duration is roughly 1.7 years vs. 2.5 years respectively.

Opposition however requires more delta-V. That can be reduced via Venus flyby, though not down to conjunction class levels. In addition, Venus allows aborting back to Earth if a problem is found before the flyby.

Conjunction, on the other hand, spends less time in space and much more time on the Mars surface. That has upsides and downsides, but it doesn’t seem worth going to Mars if the explorers are only there for a month.

Another, slightly more detailed document from NASA.

Don’t think of space travel as just a matter of getting from this location to that location, like it is on Earth. Where you are is important, but how fast you’re going, and in what direction, is at least as important, if not more so. Right before a flyby of a planet, and right after, your position will be only a little different, but your velocity can be radically different, and big changes in velocity are very valuable in space travel, so valuable that it can be worth it to take the time to get to a distant location to get some of that free delta-V.

One catch to this is that the planets are always in motion with respect to each other, and so as they move, the best path is going to be different every time, and it can be quite difficult to find that best path for any given mission.

For instance, we got pretty lucky with the Voyagers. We happened to be ready to send a probe to the outer planets right when they lined up for the “grand tour”. We won’t get that favorable an alignment again for a couple hundred years.

This conversation is a good explanation of why experts in rocket science are held in such high esteem. Charting an efficient course is damn complicated.

Well, yes and no. We won’t get the alignment for that particular course again for a couple hundred years. But if the alignment were different, we’d have found a completely different course, that might have been almost as good, or might have been slightly better. And precisely what criterion are we using for “better”, anyway?

Because there’s no way to get the accelerations you need to do that.

Sure, it’s complicated but it’s not ro…oh.

We can only get to other planets and objects in space by “calculating future trajectories and aiming for that spot”; however, it is important to understand that everything in the Solar System is moving at a speed that makes high velocity bullets look slothful. It isn’t enough for the spacecraft to just get to the position of a destination like a planet or asteroid but it also to closely match the speed and direction of it, lest your spacecraft just flies past it or smashes into it with enormous kinetic energy. When Keanu Reeves has to get onto the bus that can’t slow down lest it explodes, it isn’t enough to just catch up to where the bus is going to be; he has to commandeer a car and drive along side at the same speed lest he end up a grease spot on the highway.

Everything in orbit is moving in ‘straight lines’ or what mathematicians refer to as geodesics; it is just that spacetime is warped due to the presence of masses, and so those ‘straight lines’ mapped onto that warped plenum are actually conic sections (ellipses, parabolas, or hyperbolas). It literally is not possible for an object in space to move in what you would perceive as a ‘straight line’ in the projection down on the ecliptic plane without constantly thrusting because it is continually falling around the Sun (or for things in Earth orbit, around the Earth). The same is true on the Earth, as well; whenever you fly in a straight line, you are actually flying about the curvature of the Earth which is why navigators talk about “great circle” routes, although for most terrestrial or short duration applications you can essentially treat it as a straight line compared to the curvature of the Earth.

The reason it is (slightly) easier to go from Earth to Mars via Venus rather than directly is also because of their relative velocities. The average orbital speed of Earth is 29.78 km/s; Venus is 35.02 km/s, and Mars is 24.01 km/s. Comparing of |VEarth - VVenus| and |VEarth - VMars| shows a difference of over 500 m/s, and while that may not sound like much it is a lot when you consider the difference in the amount of propellants required, all of which have to be lifted into orbit at enormous expense per unit mass. The difference is made up by the spacecraft sapping away a small amount of momentum from Venus to change its trajectory. It also allows for a different set of possible trajectories that may be more favorable for certain missions, albeit at the expense of spending more overall time in space (and closer to the Sun, which is unfavorable for a crewed mission due to the solar particle radiation).

The alignment is at approximately 175 year intervals, and yes, we happened to be at the point in development of interplanetary probes to take advantage of that alignment, although it took a lot of subterfuge to get the Voyager program funded and then expand the Voyager 2 mission to visit Uranus and Neptune. This was discovered due to analysis by Gary Flandro, who I actually first encountered because of his work on combustion instability in solid rocket motors and only later learned of this mission analysis work. You’ve probably never heard of him if you are outside the rather narrow circle of propulsion science but he should be much more widely celebrated has having contributed as much to space exploration as anyone in living memory.

‘Better’ is a trajectory closely passing all four planets that could be met just by planetary swing-by maneuvers and no other propulsion beyond the initial transplanetary injection maneuver. Because of the required sequence to hit all four planets (Jupiter, Saturn, Uranus, and Neptune) and in particular the long orbital periods of the last two (84 and 165 years, respectively) there is no other planetary configuration that would permit visiting all four planets, and indeed, it would only be possible to visit both Uranus and Neptune on a single trajectory nearly once a century.

Although the Apollo program is the mostly highly celebrated space effort in the public consciousness and the Mars rovers have more recent attention, the Voyager program is arguably the most audacious and technically ambitious space exploration program to date, done at a tiny fraction of the cost of Apollo or Shuttle, and with an unprecedented yield of scientific information. Only Cassini-Huygens has even approached the complexity and scientific wealth of the Voyager program. A Uranus or Neptune exploration mission would be fantastic and has been recommended in the last couple of Decadal Surveys but both technical and budgetary limitations render such missions unlikely in the foreseeable future.

Stranger

Being able to visit all 4 of the outer planets with one probe.

However, “calculating future trajectories and aiming for that spot” is the idea of a basic porkchop analysis: given your origin, destination, and travel time, you can solve the Gauss–Lambert problem for a ballistic transfer and plot the resulting energy requirements. This will give you an initial idea of feasible launch opportunities. Certainly you can porkchop-plot more complicated trajectories as well, especially if you already have an idea of whether the mission will involve planetary flybys and/or deep-space manoeuvres.

Obligatory comedy sketch: https://www.youtube.com/watch?v=THNPmhBl-8I

If you can come up with the right slingshot maneuver under impossible time pressures you will be forever known as a steely-eyed missile man.