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Suppose that the robot carrying the nuclear reactor has a mass of 40 tons. How big of a rocket do we have to use to send the robot to Mars?

Part 4: Mars Direct-style missions

One old proposal to send people to Mars, called “Mars Direct”, involves sending two missions to Mars:

  • The first rocket sent to Mars is a robot that will use materials on Mars, plus energy from a nuclear reactor, to produce propellant for a return trip to carry people back to Earth
  • Once the robot has produced enough fuel for a return trip, then and only then will we send the humans. They will go to Mars, do whatever they are doing there, and then return using the propellant produced by the first robot with its nuclear reactor.

Suppose that the robot carrying the nuclear reactor has a mass of 40 tons. How big of a rocket do we have to use to send the robot to Mars? (It does not need to carry fuel for the return trip, since it can produce its own once it gets to the Martian surface.)

Suppose that the rocket carrying the humans also needs to carry a payload of 40 tons (the crew plus the things needed to keep them alive). (It also is not coming home.)

How does the total mass of the two rockets in this mission compare to the one rocket in the “there-and-back” mission? Which sort of mission is more feasible?

Part 5: Exploring the Stars

Suppose that we wanted to send a robotic mission to Alpha Centauri, the nearest star system outside our Solar System. The issue with this is that it is so far away! The ΔV required to escape the Solar System isn’t that large — but, once the rocket escapes the Solar System, it needs to be traveling fast enough to get to Alpha Centauri within a reasonable amount of time.

The history of “human civilization” — roughly, from the development of agriculture to the present — spans about 10,000 years. Suppose that we want our robotic mission to get to Alpha Centauri around 10,000 years in the future. To do this, we would need a ΔV of 100,000 m/s — around ten times the ΔV required to escape Earth’s gravity.

The best chemical rockets, again, have an exhaust velocity of 4400 m/s. Using the rocket equation, calculate how many tons of rocket fuel we would need to send one ton to Alpha Centauri. (You should get a large number!) Is such a mission feasible?

There are a few technologies that can deliver higher exhaust velocities. One involves using a conventional nuclear reactor, of the type that we use on Earth to generate electricity, to heat propellant rather than chemical reactions. This sort of rocket would allow for an exhaust velocity around 10,000 m/s. 

With this sort of engine, what mass of rocket would be required to send one ton of payload to Alpha Centauri? Would this sort of mission be feasible?

A radical design for a rocket, but one that could be built with known technology, is nuclear pulse propulsion — essentially, building a spacecraft with a large steel plate behind it, then detonating nuclear explosives behind it. While this sounds dangerous and radical, remember that space is very big, and this would not be happening anywhere near Earth! The best-developed design for a rocket like this is “Project Orion” — see https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion) if you want to read details.

This sort of rocket might have an effective exhaust velocity of 60,000 m/s. Using this sort of design, what mass of rocket would be required per ton delivered to Alpha Centauri in 10,000 years? (The answer might surprise you!)

There are other technologies being developed to provide high exhaust velocities for rockets — things like ion engines, fission fragment engines, and many other exotic technologies. Based on your experience with this project, and with the exponential function that appears in the rocket equation, why are rocket scientists so focused on increasing the exhaust velocity of propellant, rather than just trying to make bigger rockets?

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