ROCKET SCIENCE 101

All spacecraft are limited by Tsiolkovsky’s rocket equation, named after Konstantin Tsiolkovsky, the 19th century Russian founding father of astronautics. Tsiolkovsky’s rocket equation determines the speed a rocket can attain, based on the rocket’s exhaust velocity, the “dry mass” of the rocket (without fuel), and the amount of fuel it carries. Here’s the essential take-away: for your rocket to go faster than the exhaust from its burning fuel, it needs to carry a lot more fuel. You need exponentially more fuel the faster you want it to go. And this is also true in reverse: if you are already going very fast, your rocket will need exponentially more fuel to slow down.

Here’s the math:

DV = Ve * ln ( (Md + Mp) / Md )

DV = Delta-V, total velocity change produced by rocket after all fuel is exhausted
Ve = Exhaust velocity
Md = Dry mass of rocket
Mp = Mass of propellant (fuel) carried by rocket

New Horizons has a dry mass of 400 kilograms, and carries about 78 kilograms of hydrazine fuel. That fuel has an exhaust velocity of about 2.2 km/sec. Plugging those numbers in, that means New Horizons’ rocket motors can change its speed by at most 390 meters per second. New Horizons is moving past Pluto at 14 kilometers per second. So this is not nearly enough to slow down and achieve orbit around Pluto. To shed 14 km/sec, New Horizons would need to burn 580 times its own weight - or 232 metric tons - of hydrazine fuel.

A more efficient fuel, like the liquid hydrogen and oxygen in the Centaur upper stage, has an exhaust velocity around 4.4 km/sec. That improves things quite a bit, but New Horizons would still have to carry 24 times its dry weight in fuel to slow down from 14 km/sec. For comparison, the Centaur upper stage which boosted New Horizons toward Pluto has a dry mass of 2.2 tons, and carried 20.8 tons of fuel. Its maximum theoretical delta-V is 10.2 km/sec. In other words, the fully fueled Centaur booster, carrying no space probe at all, could not slow itself down enough to enter Pluto orbit. Some even larger rocket would have to be built to slow the Pluto orbiter into orbit around Pluto.

And don’t forget - that Pluto orbiter and its 50+ tons of fuel would still have to be launched from Earth, on an escape trajectory toward Pluto, in the first place. The Atlas V that launched New Horizons couldn’t possibly do this. The largest rocket under construction - NASA’s Space Launch System - can deliver a maximum payload of 7 tons to Jupiter. That is hopelessly insufficient to deliver a Pluto probe with 50 tons of fuel to Pluto.

GOING SMALL

Instead of making a larger rocket, how about making a smaller payload? During the early 2000s, while New Horizon was in its early design phases, a (literally) small revolution was taking place in satellite design. The first CubeSats packed all the essential elements of an functioning satellite into a 10x10x10 cm cube weighing less than 1 kilogram, and were launched in 2003. To date, hundreds of CubeSats have been launched, and are becoming increasingly capable as technology advances. On the first SLS launch, scheduled for late 2018, NASA plans to deploy three CubeSats from the SLS upper stage as it passes the Moon, to see how well they’ll perform at interplanetary exploration tasks. (By the way: want to win $5 million? You can compete for the chance to launch your own lunar CubeSat on the maiden SLS launch. Here’s how: http://www.nasa.gov/cubequest/details

In 2014, a San Francisco startup called Planet Labs launched a constellation of several dozen CubeSats. These CubeSats are capable of imaging the entire Earth’s surface at a resolution of 5 meters, every day. Each of those “3U” CubeSats weighs about 4 kilograms. Suppose the next Pluto mission wasn’t a single orbiter, but rather 10 tiny 3U CubeSat Pluto orbiters. This whole fleet of Pluto orbiters would weigh 40 kilograms - about 1/10th the mass of New Horizons, and the same as a 6th grader. A single ton of liquid hydrogen/oxygen fuel could decelerate this tiny payload into Pluto orbit. Launch from Earth on an SLS, with Jupiter flyby and gravity assist, then direct orbit insertion around Pluto, becomes thinkable.

With this approach, there are a lot of benefits - you get ten Pluto orbiters instead of one - but there are a lot of challenges to overcome. Solar panels are useless at 40 times the Earth’s distance from the Sun. So our hypothetical Pluto CubeSat orbiters would need require tiny nuclear reactors for electricity. A large radio dish several meters across would be needed to beam any useful amount of data back home. Deploying such a dish from a spacecraft 10 centimeters across is not easy, although inflatables are currently in development. Interplanetary laser communication systems, as demonstrated in 2013 by NASA’s LADEE moon orbiter, may be the right answer. These are the cutting edges of today’s spacecraft technology, and you can see why NASA is funding competitions to spur their development.

A NEW DAWN

On September 28th, 2007, eighteen months after New Horizons launched, another NASA dwarf planet explorer lifted off. Less than four years later, in July 2011, the Dawn mission entered orbit around the asteroid Vesta. It departed Vesta in September 2012, and entered orbit around the dwarf planet Ceres just this past March.

Dawn is NASA’s first interplanetary mission to be propelled by electricity. Instead of a high-thrust rocket engine burning many tons of chemical fuel over the course of a few minutes, Dawn’s electric engines emit tiny amounts of electrically charged ions - at much higher velocities than chemical rocket exhaust. Dawn’s engines only consume three milligrams of fuel per second. But the ions emitted from Dawn’s engines have an exhaust velocity over 31 kilometers per second. That produces a thrust of 91 millinewtons, or about the force a piece of paper exerts on your hand when you pick it up. Still, the thrust is constant, adding 24 km/hour per day, day after day, to the spacecraft’s velocity. Over the course of 67 days, the accelerations adds up to a velocity of 1,000 mph. Dawn carried 425 kilograms of propellant (as opposed to the Centaur booster’s 20.8 tons), and yet Dawn can perform a velocity change of more than 10 km/sec over the course of its mission.

What if New Horizons were equipped with an ion engine, like Dawn’s? Some modifications would be needed. Again, solar panels are near-useless at Pluto’s distance from the Sun, so “New Dawn” would need a nuclear reactor quite a bit more powerful than New Horizon’s (whose nuclear reactor produces 250W of electrical power vs. Dawn’s 1400W solar panel array.) Dawn also weighs about twice as much as Hew Horizons (780 vs 400 kg dry.) It seems reasonable to guess that a nuclear-powered, ion-propelled Pluto orbiter with the same 30 km/sec exhaust velocity as Dawn could be built with a total spacecraft dry mass of one metric ton. Plugging those numbers into Tsiolkovsky’s rocket equation, our “New Dawn” Pluto orbiter would need 620 kilograms of Xenon fuel to decelerate from 14 km/sec cruise velocity into orbit around Pluto. Something like this could conceivably be launched from Earth by the same Atlas V 551 that actually launched New Horizons. It could certainly be launched by the Falcon Heavy or SLS.

How long might this spacecraft take to reach Pluto? Again, we’ll assume a gravity-assist slingshot by Jupiter, barreling toward Pluto at ~14 kilometers per second. “New Dawn”, firing its ion engine continuously, would need 1.7 years to shed this velocity as it approached Pluto. Given an 8-year cruise from Jupiter to Pluto, this seems amply doable.

Dawn was launched little more than a year after New Horizons. Its technological development schedule paralleled New Horizons’. The next time Jupiter and Pluto properly align for a gravitational slingshot maneuver will be in 2018-2019. Using today’s ion propulsion technology, NASA could conceivably mount a New Dawn-like Pluto orbiter mission in just a few years.

Continued in Part III...

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