top of page
Writer's pictureJay Stevens

Are we there yet? Why is this taking so long?

My last few posts explored whether we are even capable of transporting people to Mars, and the answer is almost certainly yes. We can do it, and we can do it with today's technology, but it won't be fun. The trip will be cramped, boring, stressful, and dangerous, and it will take a long time. This post (and probably the following one or two, it is a big subject) will discuss whether we have realistic options to make the trip better.


But first, what would "better" look like?


It could mean faster. For example, shortening that six-month trip to three months would reduce Leonard's exposure to risks, such as Coronal Mass Ejections, reduce stress, and cut the mass of food, water, and air in half. In short, it would confer many tangible benefits. So why don't we do that? Sure, it will use more fuel but it can't be THAT much, can it? It should be pretty easy to figure out, so let's take a look.



How the Hohmann Orbit Works.


Our planet travels around the Sun in an ellipse, varying from a distance of 147M km to 152M km, and at a speed of approximately thirty kilometers per second. To get to Mars, we add speed in the direction that the Earth is traveling by 3.8 kilometers per second and our intrepid little spacecraft will alter the ellipse so that the aphelion (furthest point from the Sun) is in Mars orbit and the perihelion (closest point from the Sun) is in Earth orbit. Our spacecraft will climb away from the Sun (uphill) for (more or less) seven or eight months, and then drop back (downhill) to Earth orbit for the next seven or eight months, at which time the Earth will no longer be there, but there you go. (If you added a teensy more velocity and made the trip each way in six months, Earth would be there waiting for you when you returned!) That least-velocity ellipse is called the Hohmann Transfer Orbit from a guy named, you guessed it, Mister Hohmann. We can easily shorten the time down to six months by adding a modest amount of velocity. The ideal Hohmann Orbit requires approximately 3.8 kilometers per second, while you can purchase a six-month orbit at the ticket office for an additional 0.5 kilometers per second. But getting travel time much below that takes more fuel, less payload, or a new ship with a bigger fuel tank, and then at some point we can't do it at all. I've added a "porkchop plot" below depicting the 2026 launch window to give you a better idea of the relationship and the trade-offs between launch date, change in velocity (delta vee), and trip length. If you visit (http://sdg.aero.upm.es/index.php/online-apps/porkchop-plot) you can see how the delta-vee changes as you move your mouse around the plot. These numbers are based on several assumptions and are approximate. The "cheapest" window (center of the light blue) is 210-240 days, but for a modest increase in fuel, we can shorten the trip to 180 days.



Porkchop Plot for the 2026 Launch Window.


The trip to Mars in our previous post assumed a change in velocity of 4.35 kilometers per second, which in a good launch window (every window is different in this solar system as the orbits are not perfect circles) delivers a 180-day travel time. That assumed a total ship mass of 125 tons, of which 85.5 tons was fuel, and an exhaust velocity of 3.43 kilometers per second, which is the current output of the SpaceX Raptor Vacuum engine. If we wish to shorten that trip time from six months to three months, we would need to travel along the ellipse that crosses Mars orbit in three months rather than six months, and it looks like this.



The red line is a 90-day path from Earth to Mars.


Okay, how much of a change in velocity will we need to achieve that ninety-day ellipse? Well, that's the icky part. That ellipse requires an acceleration of thirty kilometers per second from LEO, and when you get to Mars, you will zip past at twenty-five kilometers per second if you don't slow your ship down. Our existing ablative materials can only withstand eight or nine kilometers per second of aerobraking, so we will need more fuel to slow down another seventeen kilometers per second and we will need extra fuel at the beginning of our trip to transport that extra fuel.


The Tsiolkovsky Rocket Equation (independently derived by at least four people over the years but attributed to Tsiolkovsky) helps us sort all of this out. It works with the exhaust velocity of the rocket, the initial "wet" mass, the final "dry" mass, and the total change in velocity (delta vee). If you have any three terms, you can derive the fourth.


There is a convenient online calculator (https://www.omnicalculator.com/physics/ideal-rocket-equation) which is an excellent tool to illustrate the implications of rocket efficiency on the payload. Plugging our numbers in, we find that to accelerate our thirty-five-ton ship by forty-seven kilometers per second, we will need- just a tad over thirty-one million tons of fuel. Well, that ain't gonna happen. Suppose we found some magical material that would allow us to aerobrake all of our excess speed in Mars's atmosphere. Then we would need to accelerate our ship by only thirty kilometers per second! Well, that would require just 220,000 tons of fuel. Keeping in mind that our pusher unit, the Falcon Heavy Second Stage, can hold a maximum of 107.5 tons, that is also obviously impossible. Well then, let's work with what we've got. If the maximum that our pusher unit can carry is 107.5 tons, how much can we accelerate our thirty-five-ton spacecraft? The Rocket Equation gives us 4.816 kilometers per second, and our Porkchop Plot indicates that 4.816 kilometers per second will buy us a trip time of- 160 days. So that's it. If we send up another Falcon 9 with 22 tons of fuel and figure out some way to refuel our pusher unit in space, we reduce the trip time from 180 to 160 days. If we want to shorten trip time beyond that, we need a fundamental change in technology like nuclear-thermal rockets. Increasing our exhaust velocity to 6,000 meters per second with nuclear-thermal would get us there in ninety days.


Sadly, we are bereft of nuclear-thermal pusher units, as we abandoned the highly successful and very promising experiments in nuclear-thermal rockets 50 years ago. This post is already getting long, but I need to vent a little about the missed opportunity of nuclear-thermal rockets and our need to develop them not now but right now, so I will dedicate the next (shorter, I promise!) post to nuclear.


Thanks for being here!


1 view0 comments

Comments


bottom of page