How Mars's Gravity Affects you, and Spaghettification!? A Power BI Analysis.

October 24, 2018

 

There's a lot of talk around humans going to, and living on Mars recently. There are plenty of challenges that this brings - oxygen, temperature, fertile soil... But I think the biggest challenge would be overcoming the gravity differences. Humans just aren't accustomed to a low gravity environment. Let's use Power BI to see what the differences are. But why limit ourselves to Mars, let's check out other cosmic bodies as well!

 

 

Not only did I want to see the overall impact of gravity on us, but I also wanted to explore any tidal forces between our feet and head, i.e. spaghettification. Obviously there won't be a noticeable affect on us for smaller planetary bodies like Earth, but what about larger ones? What would tidal forces be like for us on Jupiter, or the Sun? What about larger stars? This is, of course, assuming we can somehow stand on the surface. So I'll be assuming that the visual surface is the surface for any non-rocky cosmic body. 

 

For comparison, I included the impact of tidal forces on the empire state building as well since the size is much taller than a human being. 

 

 

DISCLAIMER: I am not an astronomer or physicist of any kind - I'm just someone with an interest in the math. ;)

 

 

Spaghettification

The most interesting thing I found out through the visuals is that how different parts of a body and their unique weight significantly affect the force of gravity on that part. For example, the weight I assigned to the head portion of the visual is 6.27 kg and the feet portion was assigned 4.48 kg. Changing either the head or feet just a couple of kg's has a huge impact on the tidal force between the two.

 

I used 80.5 kg as the total mass of a human, and allocated the portion weights by using the number pixels in the image with Gimp (free software similar to Photoshop). I know this may not be an realistic way of doing it, but it provided some consistency.

 

 

Another interesting thing I noticed was that, according to the heat map, if you fell feet first into a black hole, you would "experience" the most amount of tidal force in your stomach first, as opposed to your feet. This is because the stomach area has more weight assigned to it, and therefore experiences a higher tidal force than the feet area. 

 

 

By the way, in the above picture, the distance is 250 AU (149,597,871 km) away from the M87 black hole. Are you safe? Heck no! Your stomach area is receiving 10,620 newtons of force more than your feet. That's 1083 kilograms! Ouch!

 

Planetary Gravity Comparison

For this page, I focused on two things: 1) How much would you weigh on the selected planetary (cosmic) body and 2) How much lighter you would weigh on that same planet at a height of the Empire State Building and Mt. Everest, respectively. 

 

Have you ever thought about how much lighter you would weigh at the top of those things? Well, on Earth, you would theoretically weigh 0.046% lighter at the top of the Empire State Building. That means if you weigh 170 lbs, you could easily shave off 0.08lbs just by riding up the elevator! On Mt. Everest you would weigh 0.278% less - possibly half a pound! (but lets be honest, you would definitely burn more weight in calories by hiking up all that way - your choice!)

 

What about Mars? The planet has a smaller radius and mass, so gravitational forces will be smaller - you therefore result in having a lighter weight (about a third). Let's transport the Empire State Building over to Mars and go to the top. How much less would we weigh? According to Mr. Newton, we would weigh 0.086% less. That's more of an increase than on Earth!

 

Okay, now what about Jupiter - the largest planet in our Solar System? If we remember that the force of gravity has an inverse relation to radius, we can predict that going up to the top of the Empire State Building on Jupiter will have less of an impact than on Earth. And as it turns out, it does at only a 0.004% weight difference.

 

 

If this is confusing... don't worry. It is. I like to think of it similar to the passage of time. At a young age (small radius), the passage of time seems really long (bigger affect). But as we get older (big radius), it seems to go by quicker (smaller affect). 

 

Power BI Techniques I used

Before I began, I had an idea of what to build, but it took me a while to plan it out and set it up. I ended up importing two table sets. One table was for the planets and cosmic bodies specifications like mass and diameter. The other was for the human body, Empire State, and Mt. Everest dimensions split out into the 7 levels you see above with assigned weights. 

 

 

I included a couple extra columns like Accumulated Weight, Weight Ratio and Unit Mass just in case I needed them. Mt. Everest's mass is either incalculable or unverifiable, so I did not include it.

 

I used the Height and Unit Weight columns to calculate the force of gravity with the following equation:

 

F = g*m1*m2 / r^2

 

Where g is the gravitational constant 6.674×10 N⋅m²/kg², m1 and m2 are the cosmic body's mass and unit weight mass respectively. Finally, r is the radius (or distance from black hole) of the cosmic body. 

 

 

DAX Calculations

Once imported, I got working on the measures. I took a fair bit of time doing this, but eventually worked it out. I began with the simpler calculations of just finding the total force on the entire body (human, empire state building) without considering the partitions.

Unit Gravitational Force =
var g = 6.67408 * 10^-11

 

// Getting Human Body, or Building specs.
var unitWeight = SUM(Specs[Unit Weight (kg)])
var rDiff = MAX(Specs[Height (m)])

 

// Getting the radius plus rdiff and mass of the planetary body
var r = LOOKUPVALUE(

      CosmicBodies[Diameter (km)],

      CosmicBodies[Cosmic Body],

      [Selected Cosmic Body]

      ) /2 * 1000 + rDiff


var bodyMass = LOOKUPVALUE(

      CosmicBodies[Mass (kg) Sci. N.],

      CosmicBodies[Cosmic Body],

      [Selected Cosmic Body]

      )

 

return
    g*unitWeight*bodyMass / r^2

That gives you force in newtons. I then converted it to kilograms with kg = n * 0.101971621

 

I could then use that DAX formula for other calculations and apply filters to it for re-use. For example, if I wanted the force only on Earth (for comparison) I used:

Force on Earth =

CALCULATE([Unit Gravitational Force],

      FILTER(All(CosmicBodies),

      CosmicBodies[Cosmic Body] = "Earth")

      )

By re-using the base DAX measure, I was able to come up with a number of comparisons and eventually get to the partitioned leveling for the spaghettification calculations.

 

Custom Visuals Used

For the first time I tried out the Synoptic Panel custom visual. You can upload any image you have and define regions as you like. You can then assign those regions to your data points. You can find more information on their website at Synoptic.Design.

 

I also used the Enrich Storytelling visual. You can feed in your data points and write complimentary phrases about them. It essentially concatenates words together but in a more engaging way. You can read more about it in my blog about Storytelling with Data.

 

I hope you enjoyed this article! Feel free to play around with the dashboard up at top. I enjoyed making it and discussing my thoughts. What did you think about it? Are you a professional astronomical physicist? Let me know how well I interpreted the results!

I really improved my DAX skills by reading Matt Allington's Supercharge Power BI. I would recommend it to anyone wanting to improve their skills as well.

 

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About the Author

Brent Jones loves spending time with his wife and trying out new activities together.  They traveled as digital nomads to many countries in South America, Europe and Asia. He can also speak Japanese!

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