So, it seems to me that if we determine that the we’re headed to the Oort Cloud from Earth, the time involved to do that would be important to know. For those that don’t know, the Oort Cloud is incredibly far away, compared to planetary distances in the Sol system.
(Courtesy Bing.com)
As can be seen above, the intimidating size of our solar system as we normally consider it is dwarfed utterly by the extent of the Oort Cloud. It’s 9.3 Trillion (with a T) miles away, in fact. There is a simple equation that generally addresses a travel of constant acceleration to get somewhere you want to go.
This is a flight that assumes that you are accelerating half of the way to the destination, then turning around to accelerate heading into the destination to slow to zero final velocity when you get there. It’s important to note that the orbital mechanics aren’t arctually going to work out that way, since the Earth is moving, and to return back on a reasonable trajectory you’d need to plot an orbit instead of a straight line. We’ll talk about why that’s okay shortly.
If you solve the equation to give a time for the trip, with an acceleration of 1g, the time to the Oort Cloud is 1.75 years. See Acceleration Calculator | Definition | Formula (omnicalculator.com). That is quite a long time to get somewhere, that’s for sure. Really, it seems like a hard thing to imagine, right? I mean, heading to the Oort cloud, what would be that mission, anyway? Again, there’s a reason that’s okay.
Assuming that you want to return to Earth, that’s about 3.5 years per round trip. So, why would I calculate it this way? Well, the Oort cloud is such a far outlier for a round trip mission, the baseline distance envelopes distances to many other locations in the Sol system, and multiple trips, so it’s a decent way to get your hands around the idea of how far you could go, and how long the service life would be. Let’s think about that missing precision regarding the orbital mechanics. In this simple calculation, let’s say we account for that missing bit of detail from the calculation by extending the trip time from 3.5 years to 10 years, and let’s also double and round up the distance to 20 trillion miles. These are just approximations, and meant to be on the high side.
Here are some requirements then that we can glean from this exercise:
Minimum Mission Duration: 10 Years
Minimum Nominal Flight Acceleration: 1g
Minimum Mission Distance: 20 Trillion Miles
That’s not a bad basic starting point. It leads to considerations for power needs, propulsion capability, and other things. All of that will generate more questions to solve.