## How long will it take to get to each of the planets by various means?

In my book 'Interplanetary Travel:An Astronomer's guide' I discuss current and planned technologies for interplanetary travel.

The bottom line is that it depends a lot on the particular trajectory that you take. Usually, the trajectories are in the form of a 'great arc' that gracefully connects a launch time at Earth with a destination point. These arcs are usually many times longer that the straight-line distance between the two planets at a particular moment in time. For reduced-cost travel, astrodynamicists often rely on gravity assists 'Slingshot Orbits' from the inner planets to reach Jupiter, and by Jupiter to reach more distant worlds. These loop-de-loops add years of extra travel time to a mission. Let's assume for our calculations that we just take the simplest direct approach and use the minimum 'opposition' distance between Earth and a planet.

The table below gives you some sense for how long it takes to get to each planet at different speeds.

The Space Shuttle, of course, can't leave Earth orbit but its speed is typical of manned spacecraft. The Galileo spacecraft which explored Jupiter traveled twice as fast. These travel times are based upon using a big chemical rocket on Earth to blast the spacecraft into the right trajectory. But there is another technology that has been used for several decades.

Ion rocket motors get their speed by being constantly accelerated 24-hours a day for many months, and two versions of this technology are given for a low-power and high-power ion engine. Ssatellites orbiting earth often use ion engine technology for station-keeping. NASA has also used ion engine technology on two interplanetary spacecraft: Deep Space 1 and Dawn. Both spacecraft used very low thrust engines operating for thousands of days to get the spacecraft to asteroids (Dawn visited Ceres and Vesta; DS1: 9969 Braille) and comets (Borrelly) for study.

Finally, and at least on paper, solar sails can reach speeds of nearly that of the solar wind (500 km/sec), and engineers are hopeful that this technology will be tested in space very soon.

As you can see, we are currently stuck in the mode of travel where it takes nearly 10 years to get to Pluto. Perhaps in another hundred years, this travel time will be reduced to a year or less...assuming Humanity feels a compelling economic need to continue this kind of exploration.
 Method= Shuttle Galileo Ion A Ion B Solar Sail Speed = 28,000mph 54,000mph 65,000mph 650,000mph 200,000mph Mercury 52d 27d 22d 2.2d 7.3d Venus 100d 52d 43d 4.3d 14d Mars 210d 109d 90d 9d 29d Jupiter 1.9yr 1yr 303d 31d 100d Saturn 3.6yr 1.8yr 1.5yr 55d 179d Uranus 7.3yr 3.8yr 3.1yr 113d 1yr Neptune 11.4yr 5.9yr 4.9yr 179d 1.6yr Pluto 15.1yr 7.8yr 6.5yr 238d 2.1yr

Assumptions: Ion Drive using a constant thrust of A) 0.1 pounds B) 1 pound with turnaround deceleration added. Two years acceleration to reach top speed. Solar Sail estimated speed 450 km/sec or one million mph)

Another way to gauge the maximum speed of a spacecraft is by the exhaust speed of its engines. Engine exhaust speed is related to an engineering parameter called the Specific Impulse. SI is the exhaust speed divided by the acceleration of gravity at Earth's surface. For example, chemical rockets have SI=250 seconds and so their maximum exhaust speeds are 250 x 9.8 m/sec2 = 2.4 km/sec. SInce no rocket payload can travel faster than its exhaust speed, we can compare planetary transit times in terms of the SI of the rocket technology.

In this table, I assume that the rocket continuously accelerates from Earth until it reaches half its destination distance, then turns around and decelerates for the second half of the trip. The relevant equations are

distance = 1/2 acceleration x Time ^2
speed = acceleration x time

With: distance in meters, time in seconds, speed in m/sec and acceleration in meters/sec^2

 Destination a=0.05 a=0.15 a=0.2 Planet Time-A Time-B Time-C Max-SI Days Days Days Seconds Mars 24 14 8 34000 Jupiter 80 46 25 110000 Saturn 113 66 36 160000 Uranus 166 96 53 230000 Neptune 214 124 68 300000 Pluto 214 124 68 300000

So if we could design a ship, call it System A, that produced a constant acceleration of a = 0.05 meters/sec^2, we could get to Mars in just 24 days. Similarly for System C with an acceleration of 0.2 meters/sec^2 the Mars trip takes only a week! For engineers,we can also estimate for System C that the Mars configuration would need SI=34,000 seconds to get us there in 8 days. If we wanted to get to Pluto with the same acceleration, it turns out that accelerating for half the 68-day trip would get you to a maximum speed of about 2900 km/sec which sets the limit to our exhaust speed and leads to a maximum SI of about 300,000 seconds! These SI estimates are far larger than the chemical rockets provide of 300 seconds, and so we have to look to entirely different technologies to make these travel times possible. Sadly, it doesn't matter if we drag along huge fuel tanks to run our chemical rockets. They will never provide the high exhaust speeds we need to carry both our fuel and payload to our destinations. We have to use technologies that enormously increase the exhaust speeds themselves.