I was watching the Mars Science Laboratory Lander (@MarsCuriosity) land and I thought about some of the discussions that had occurred during the NASA Social meeting to celebrate the 50th Anniversary of Cape Canaveral. We had people from the launch teams join us for some discussions. One of the comments that @NASA_Caley made resonated with me, “There are 7 minutes of terror for landing. For launch, we had 44 minutes of terror.” She then went on to explain all the things that were thought of in the process of planning the route for Curiosity.

I am sure that my post will gloss over some things, but I am still reeling at how many things had to be accounted for.

Let’s say you want to send a projectile (Curiosity) from a source object (Earth) to a destination object (Mars), what do you need to consider. Well first you need to think about the location of the objects relative to each other so that you can point the projectile in the proper direction. But what is the right direction?

If the two objects are stationary it is pretty easy, just aim from one toward the other. If the objects are rotating at different speeds, it gets more challenging. The Earth revolves around the Sun in basically 365.25 days, Mars since it is farther away makes the same revolution in approximately 688 days. As a result the relative position of the two objects changes constantly. The knee-jerk reaction is to say to send the projectile when the two objects are closest to each other. So let’s declare two basic variables, location of source, location of destination.

Oh wait, that is really a more complex variable than those simple statements of source location and destination location would indicate. These objects are not just spinning around the star at the center of our solar system, they are also spinning around their own axis. Their axis and orbital paths are also not perpendicular or parallel to each other. So these locations are not in one plane with just X & Y coordinates but actually in three axises.

Seems to make sense, the locations relative to each other will be the shortest distance and the shortest travel time. Yes, travel time, a new variable. The travel time has to be accounted for as the objects will move relative to each other as the projectile travels from the source to the destination. The easiest way to think about it, is leading a target, many of us do it while playing video games, or shooting rubber bands at people. So you have to account for the amount of time to get from Point A to Point B while both points are moving. You definitely need to know the speed of the projectile to know the travel time.

The speed of the projectile is not a simple value, it is also another variable of the equation that needs to be considered. The obvious answer is to make things travel as fast as possible. However there is always a trade off. To make things move quickly requires lots of thrust. So you need to have more fuel to allow for more thrust. Fuel has mass which means that you need more fuel to get that mass in motion. The designers need to determine the proper balance between speed, launch weight, and time to travel to destination. Don’t forget to include the mass of the projectile in there. Hopefully the mass has been determined but it might still be in flux. Is that one variable or four variables? I would say it is three interrelated variables, as the designers will work within a mass budget. What about the time it takes to get up to speed? I guess we can just use average speed… that 44 minutes of launch is not that significant compared to the approximately 253 days and 14 hours of cruise. It is just 0.012002182215% of the total time. That is tongue in check.

While leaving Earth there are some other things to consider. Such as not hitting the International Space Station or other satellites. Plus one also has to consider the biggest satellite out there along the way, the Moon. We have to steer clear of that, and its gradational pull. Wait we can use its gravitational pull to speed us up some more or to adjust the course.

So as you can see just a little math.

This math was done and allowed for landing within 1.5 miles of the desired landing site after a journey of approximately 350,000,000 miles. Yes, they can do some adjustments in flight, but those have to be calculated as well. To put this in perspective  to get the same resolution you would need to land on a single human hair (0.04mm) from 14km (8.7 miles) and not hit anything, seen or unseen, during the flight.

Did you remember to compensate for the satellites going around Mars?

Pretty impressive. It isn’t rocket science, it is math and physics.

So I use SmugMug to host my photos as they have some really cool features and people there. I also started following a few of them on Twitter, and there was a tweet that just made my head hurt, so I sat down to do the math on it. Okay, I also used Wolfram Alpha to help with it.

The Tweet from Baldy stated:

Whoa! Vincent LaForet‘s new Canon Mark IV vid on SmugMug used over 20 terabytes of bandwidth in 300,000 views in 14 hours.”

So I started to try and figure out how many megabits/second that was so I could compare it to typical network connectivity that I am more familiar with, 100BaseT or Fast Ethernet, and Gigabit Ethernet. Well it just became amazing.

  • First I converted 20TB to megabits
    • 20TB= 20,000,000,000,000 bytes = 160,000,000,000,000 bits =  160,000,000 megabits.
      Yes, that is 160 Billion megabits
  • The next thing was to convert hours to seconds
    • 14 hours = 840 minutes = 50,400 seconds
  • Now to convert to megabits/second
    • 160,000,000 megabits/50,400 seconds = 3,174 megabits/second = 3.2 gigabits/second.

So that is pretty freaking fast at to how quickly the data is coming out.

Wolfram Alpha had cool comparisons to put it in context. It is approximately equal to the text content of the Library of Congress. It is approximately equal to 1/8th of the  estimated data content of the surface web (~~ 170 TB ).

Dang no wonder they are in need of 2 TB  of flash memory for a server. You can see the picture and Don MacAskill CEO of SmugMug here http://bit.ly/3HlXzH