What would it cost to send a cell phone to the moon? Wait – let’s back up a few steps.
There’s this thing called the Google Lunar X PRIZE, which hopes to award $20 million to the first privately-funded team to put a robotic rover on the moon, send back HD video and travel 500 meters. Although people generally start with the idea of how to design a rover, the more pressing questions is what’s the most cost-effective way to get to the moon?
JPL has enjoyed good success sending rovers to Mars, so let’s consider copying their method. Basically a lunar transit vehicle is boosted into Earth orbit. There it burns fuel to get up to escape velocity and falls towards the moon. At the moon the descent vehicle separates, and burns fuel to decelerate to the lunar surface where the rover deploys. We can calculate the cost by working backwards.
Let’s assume we want a rover about the same size as Sojourner, the first and smallest of the current family of six-wheeled Mars rovers. It was approximately 10 Kg (about 25 lbs, but metric is the only way to go when you’re doing rocket science). Let’s assume the descent vehicle – rocket engines, airframe, navigation system, power supply, etc. – is about 5 times the mass of the rover. That makes the rover plus descent vehicle 60 Kg. This is the “dry mass” (vehicle without propellant) we have to land on the moon.
The change of speed required to soft-land on the moon – “delta-V” in rocket terms – is about lunar escape velocity: 2400 meters per second (m/s). If we use solid rocket boosters, which are the simplest to implement and control, we need about twice as much fuel as the mass we want to land. So for a 60 Kg descent vehicle we need 120 Kg of “reaction mass” to slow it down, so the total mass for lunar approach is 180 Kg.
We can already see the terrible multiplying effect of the rocket equation. The rover weighs about as much as a typical desktop computer, but landing it on the moon takes a machine that weighs as much as two grown men. And it will be put into its lunar approach orbit by an even-larger transit vehicle. The transit from low Earth orbit (LEO) to lunar approach requires enough delta-V to make up the difference between LEO and Earth’s escape velocity. This is about the same as before, 2400 m/s, so the mass ratio using solid rockets is the same. If we assume that the transit vehicle is twice the mass of the descent vehicle (longer trip so bigger power supply) that would make it 100 Kg. The transit vehicle dry mass is 280 Kg, and fully fueled it would be 840 Kg.
So we need to loft nearly a metric ton of spacecraft and fuel into Earth orbit. At around $20,000 per Kg, this will cost about $17 million. The X Prize is not nearly so sweet if 85% of it is used just getting the raw mass into orbit. Anything beyond $3 million to build the vehicle we have to eat.
Of course the Prize is intended to spur innovation. We could double the mass of the transit vehicle and use an ion engine instead. Since an ion engine needs only 40 Kg of reaction mass to make the lunar transit, the whole thing would only weigh 420Kg and need $8 million to get into orbit, which gives us an extra $9 million. Of course we also have to develop an ion engine.
This is how all the traditional tradeoffs work. You can improve efficiency at any stage and get incremental reductions in booster costs, but the resulting technology is more complex, expensive to develop and prone to failure. It would be far better to use proven rocket technology and instead make the lunar payload smaller. Much smaller.
My cell phone weighs about 100 grams: 0.1 Kg. If you upgrade the camera to HD and replace the parts that aren’t needed on the moon – like display, keypad, and the motor that makes it vibrate – with a system for locomotion, it would make a serviceable moon rover. Using this same analysis the total mass of a vehicle to get a cell phone to the moon would be 8.4 Kg and cost about $170,000 to loft to LEO. Remarkably the dry descent vehicle weighs about the same as a can of beans, but this is a level of miniaturization that we take for granted on a daily basis and it totally changes the balance of the economics. The cost of the booster, which is normally the lion’s share of the total, becomes instead a background expense on a par with a single engineer’s salary. All the investment can be sunk into the technology to make it light, durable and reliable.
But we could go even beyond that. Imagine a rover massing only 10 grams – a little lighter than an iPod shuffle. Why couldn’t such a device carry a tiny camera, battery and transmitter? Setting it down softly on the moon could be done with a cell-phone scale descent vehicle burning less than a pop-can worth of propellant, and is made easier by the fact that smaller devices tend to be much more rugged than large ones. A 10 gram rover could hit the moon with considerable residual velocity and survive, reducing the required complexity of the descent vehicle. The complete transit vehicle, including its kilogram of solid fuel, would tip the scales at 1.6 Kg, less than the weight of a two-liter soda bottle. Cost to LEO: $32,000.
There are a couple problems to solve. A tiny transmitter is unlikely to be readable from Earth, so it needs a relay. This can be done by using the same transit vehicle but instead of the 0.3 Kg descent vehicle payload it could carry a simple radio relay. This would be launched after the descent vehicle and would act as repeater for the rover until it crashed on the moon, hopefully after mission objectives were complete. A relay with the power of three cell phones could certainly reach receivers on Earth.
Another problem is that wheels on such a small rover would be useless. Going the 500 meters required by the prize would take hours or days and could be thwarted by even small rocks or gravel. Fortunately the moon’s low gravity gives us another option: jumping. A tiny motor would tension a spring, and releasing the spring would kick off against the ground. The rover weighs almost nothing on the moon and could easily travel 100m in a single hop. Even taking more modest jumps the rover could cover 500m without taxing its battery. As long as the jumps could be properly stabilized, taking video from the apogee of a jump would be much more interesting than what you’d get just a few centimeters off the surface. Naturally there are many engineering problems doing this kind of miniaturization with respect to radiation and dust, but I think the reduction in launch costs are well worth the research.
Project Lunar Flea is not just my proposal for winning this X prize; it’s a vision for robotic space exploration in general. Why not have masses of tiny robots swarming over other planets rather than a few large rovers? Not only is it cost-effective but it also has benefits here on Earth in terms of learning how to make smaller, more rugged, more long-lived consumer devices. The main drawback may be the relative lack of “light-lift” rockets since most commercial systems are built to carry large payloads. Maybe it’s time to reconsider that approach.
- jack*
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