OK…While everyone else is worrying how to get to Mars, let’s take a really big step and figure out how to get to Pluto….in a month!
The biggest challenge for humans is surviving the long-term rigours of space hazards, but all that is nearly eliminated if we keep our travel times down to a few weeks.
Historically, NASA spacecraft such as the Pioneer, Voyager and New Horizons missions have taken many years to get as far away from Earth as Pluto. The New Horizons mission was the fastest and most direct of these. Its Atlas V launch vehicle gave it an initial speed of 58,000 km/hr. With a brief gravity assist by Jupiter, its speed was boosted to 72,000 km/hour, and the 1000-pound spacecraft made it to Pluto in 9.5 years. We will have to do a LOT better than that if we want to get there in 1 month!
The arithmetic of the journey is quite simple: Good old speed = distance / time. But if we gain a huge speed to make the trip, we have to lose this speed to arrive at Pluto and enter orbit. The best strategy is to accelerate for the first half, then turn the spacecraft around and decelerate for the second half of the trip. The closest distance of Pluto to Earth is about 4.2 billion kilometers (2.7 billion miles). That means that for 15 days and 2.1 billion kilometers, you are traveling at an average speed of 5.8 million kilometers per hour!
Astronomers like to use kilometers/second as a speed unit, so this becomes about 1,600 km/sec. By comparison, the New Horizons speed was 20 km/sec. Other fast things in our solar system include the orbit speed of Mercury around the sun (57 km/s), the average solar wind speed (400 km/s) and a solar coronal mass ejection event (3,000 km/s).
If our spacecraft was generating a constant thrust by running its engines all the time, it would be creating a uniform acceleration from minute to minute. We can calculate how much this is using the simple formula distance = ½ acceleration x Time-squared. With distance as 2.1 billion km and time as 15 days we get 0.00062 km/sec/sec or 0.62 meters/sec/sec. Earth’s gravity is 9.8 meters/sec/sec so we will be feeling an ‘artificial gravity’ of about 0.06 Gs….hardly enough to feel, so you will still be essentially weightless the whole journey!
If the rocket is squirting fuel (reaction mass) out its engines to produce the thrust, we can estimate that this speed has to be about 1,600 km/sec. Rocket engines are compared in terms of their Specific Impulse (SI), which is the exhaust speed divided by the acceleration of gravity on Earth’s surface, so if the exhaust speed is 1,600 km/sec, then the SI = 160,000 seconds. For chemical rockets like the Saturn V, SI=250 seconds!
What technology do we need to get to these speeds and specific impulses?
The most promising technology we have today is the ion rocket engine, which has SIs in the range of 2,000 to 30,000 seconds .The largest ion engine designs include the VASIMR engine; a proposed 200 megawatt, nuclear-electric ion engine design that could conceivably get us to Mars in 39 days. Ion engines are limited by the electrical power used to accelerate the ions (currently in the kilowatt-range but gigawatts are possible if you use nuclear power plants), and the mass of the ions themselves (currently xenon atoms).
Other designs propose riding the solar wind using solar sails, however although this works on the outward-bound leg of the trip, it is very difficult to return to the inner solar system! The familiar technique of ‘tacking into the wind’ will not work because for sailboats it relies on movement through manipulating pressure changes behind the sail, while solar wind pressure changes are nearly zero. Laser propulsion systems have also been considered, but the power requirements often compete with the total electrical power generated by a large faction of the world for payloads with appreciable mass.
So, some version of ion propulsion with gigawatt power plants (fission or fusion) may do the trick. Because the SIs are so very large, the amount of fuel will be a small fraction of the payload mass, and these ships may look very much like those fantastic ships we often see in science fiction after-all!
Oh…by the way, the same technology that would get you to Pluto in 30 days would get you to Mars in 9 days and the Moon in 5 minutes.
Now, wouldn’t THAT be cool?
If you want to see some more ideas about interplanetary travel, have a look at my book ‘Interplanetary Travel:An astronomer’s guide’ available at amazon.com.
Check back here on Monday, January 2 for the next installment!
Could an em propulsion system be deployed for use to travel to the Moon? I thought it needed to have more build up room and seems like stopping would be a problem also. We might need huge materials improvements and an inertial dampener to allow the ship and beings inside to survive that kind of acceleration and deceleration. Love the idea but may not be practical for such short hops.
Hi Gloria…I know that the ‘EM Drive’ is all the rage these days, but the physics have not been proven and it looks like there is quite a bit going on in the current testing that adds biases to the outcomes. I will settle for ion propulsion, which are hugely more certified in terms of physics and scalability.
Sten: I agree ion engines make the most sense for missions of this type but I do have a question about the 30 day flight time. Using “d = 0.5at²” works if there are no other accelerations involved. However, your Pluto probe would have to climb out of the Sun’s gravity well on its way out to Pluto and the Sun’s gravitational attraction would be slowing the probe down during its entire outbound trip. This is evident looking at New Horizon’s mission profile. It left Earth with a velocity of about 16 km/s. (However, its Heliocentric velocity at the start of the mission was actually much higher (about 45 km/s) due to the contribution from Earth’s own orbital velocity around the Sun.) By the time New Horizon reached Jupiter its velocity had decreased to about 19 km/s. The slingshot maneuver at Jupiter boosted its velocity up to 23 km/s, but it began slowing again as soon as it departed Jupiter. When New Horizon finally reached Pluto it was traveling at only about 14 km/s.
Based on the discussion above I offer the following points for consideration:
• The Pluto probe will need some kind of conventional rocket propulsion to give it a high initial velocity; one sufficient for it to climb out of the Sun’s gravity well. An ion engine by itself won’t provide enough thrust to do this.
• The Pluto probe won’t travel in a straight line from Earth to Pluto. It will follow some form of elliptical path, a Hohmann transfer orbit, between the two bodies making the actual distance traveled somewhat more than the 4.2 billion km minimum separation distance between the two bodies.
• Because of the Sun’s gravitational influence on the Pluto probe, the simple kinematic equation “d = 0.5at²” won’t yield the actual acceleration required to reach Pluto in 30 days.
Your thoughts would be appreciated.
Hi Mark! You make an excellent point, but because my rough estimate of the average speed of the trip was 1,600 km/s, any delta-Vs due to climbing out of the sun’s gravity well are only of order 10 km/s so they are negligible for this back-of-the-envelope exercise. I am not talking about New Horizons ion engine technology, which only provides about 3,000 seconds of SI, but a far more substantial system still based on ion propulsion but with much higher thrusts than a fraction of an ounce (90 milliNewtons). These systems are doable by scaling up current ion engine designs into the gigawatt-range, and using a heavier fuel that xenon. I leave the technical details to engine designers, as astronomers always do ;> Also, at these speeds, you do not do conventional Hohmann Transfer trajectories that are minimum-energy paths, but you get to use higher-energy ‘point and shoot’ trajectories, just like Star Trek!
Sten, the Moon in five minutes would not be cool; it would be squashing. The g forces would be horrible.
I agree that accelerating ions is the most promising form of motor that we can think of today. The interesting question is how much acceleration can we give them over how much time (i.e. the length of the motor) to get the maximum ejection velocity, and thus the maximum momentum?
Hi Ian. You are right, of course, but it was an eye-catching comment in the blog nonetheless! A bit of math shows that if we maintained a 2-G acceleration and deceleration profile, the fastest possible one-way time would be about 2.4 hours. Just enough time to watch 2001:A Space Odyssey!