# Space Problems: A Science of the Story Extra

Space is ridiculously big. If you make a scale model of the solar system the outer planets will be miles away.

Now here's what will really bake your noodle: the Earth and Moon are so far apart that you can fit every planet in our solar system between them. If that's a bit hard to imagine, just line up Earths end-to-end. You can fit thirty Earths between the Earth and the Moon. Don't believe me? Here's the math:

• Diameter of the Earth: 7917.5 miles
• Distance from the Earth to the Moon: 238,900 miles
• 238,900 / 7917.5 = 30.17 Earths

It's really far.

If you fly at half-a-million miles per hour, it'll still take you half-an-hour to get there.

So, this is the problem I keep running into when I write science-fiction. Even with super-speedy reactionless RF drives, it still takes a while to get from point A to point B.

With current technology the maximum attainable speed is determined by the rocket equation. Put simply, if you throw mass out the back of your ship to accelerate, sooner or later you're going to run out of mass. Given the starting mass of the ship and fuel you can do the math and figure out what the final velocity will be when you use your last drop of fuel. The kicker is that increasing the fuel tank doesn't help because that additional mass offsets itself by decreasing the velocity change each bit of ejected mass imparts. Ultimately the only variable you can really change is the speed you eject the mass, and this is usually determined by the reaction properties.

There are some clever within-current-technology work-arounds for this. Stephen Hawking has proposed laser sails and postage-stamp sized probes. Because the probes don't carry their own propellant, they are not limited by the rocket equation and can potentially hit twenty percent light speed. There's quite a few barriers to Project Starshot, including not vaporizing the postage stamps with the lasers or shredding them with the 51,000 g acceleration.

With the Hayden's World stories RF drives exist and generate acceleration without ejecting mass. This sets the new speed limit at light speed. Great! But, humans can only tolerate high gee for so long (unless someone invents Star Trek's inertial dampeners). If people want a comfortable one gee acceleration it's going to take a year to accelerate near light speed.

James Hayden's ship sidesteps this by not moving his ship at all. Instead, space expands and contracts around the ship. He's able to go from zero to ninety-seven percent light speed in eight seconds because, from his reference frame, he's stationary.

For everyone else the quickest way to get anyplace is to accelerate halfway and decelerate the remainder. Relatively short distances can be problematic.

Consider the scene in Aero One where the Prosperity is in a lower orbit than Ward's ship. Let's say this is Earth and I put Ward's ship in geostationary orbit (35,786 km above Earth) with the Prosperity in low Earth orbit (200 km):

Problem A: Ward's orbital period is 24 hours and Jia's is 90 minutes, so Prosperity will slip over the horizon fairly quickly. If Ward steps on the gas pedal he'll increase his tangental speed relative to Earth and move into an even higher orbit. If Ward wants to catch her he has to decelerate, causing him to fall towards Earth into a lower orbit. While he's doing that she's still going to get away, at least until she orbits around again.

Problem B: Even if I completely ignore the orbital mechanics and have Ward accelerate at 1 g straight towards Jia (followed by deceleration to match position), it will still take him an hour to travel 36,568 km.

Problem C: Ward thinks this is taking too long and fires off his railgun-accelerated seeker slugs. Let's say the railgun accelerates the slugs to 100 kps (223,694 mph!). It still takes them six minutes to get there. They're guided, so they can still hit the Prosperity, but it's a long time (at least from a narrative standpoint).

So, these are the space problems I need to work out for each story. I decided to put Ward and the Prosperity fairly close to each other so the slugs can reach her in thirty seconds.

Fortunately as you travel greater distances the cumulative effect of the acceleration begins to greatly decrease the transit times.  Here's a few 1 g travel times (at half accel/half decel):

• Earth to Moon: 3.5 hours
• Earth to Lagrange Two: 7 hours
• Earth to Mars: 1.8 days
• Earth to Sun: 2.9 days
• Earth to Saturn: 8.3 days
• Earth to Pluto: 20.2 days
• Earth to heliopause: 1 month
• Earth to beginning of Oort Cloud: half a year

These are with 1 g continuous accelerations, which is something we can't currently do. For reference, the real-life Pluto New Horizons probe took 9 years to travel from Earth to Pluto.

Well, hope you enjoyed a little bit of space-geekery. Back to writing!