Wednesday, August 15, 2018

Numbers in the News: How Big is that Lake on Mars?

In case you missed it, last month NASA announced the discovery of what looks like liquid water on Mars: a 20-kilometer (12.4-mile) wide lake hiding under 1.5 km (~1 mile) of ice. A lake 20 kilometers across sounds like a lot of water, even if it is deep under the ice. Why did it take so long to find if it is such a large feature? Let’s put this into perspective and compare the size of the lake on Mars to the size of a dot on a basketball. The comparison might surprise you.

First, let’s shrink Mars to the size of a standard NBA basketball, by crunching some numbers. We can set up a proportion of the surface areas to figure out how big of a dot on a basketball is equivalent to the lake on Mars.

First, we calculate the surface area of Mars and the lake.
Then we calculate the surface area of the basketball.
Use a proportion to calculate the surface area of the dot.
Calculate the radius of the dot.
An equivalent “lake” on our Martian basketball has a radius of 358 micrometers. So our dot needs to be about 700 microns across. This is roughly twice the size of a period.

For the sake of contrast with the basketball, let's use whiteout to draw the dot on our Mars basketball.

Can you spot the lake?
Zooming in . . .
The lake on Mars.
That dot is pretty small when compared with the basketball. While 20 km (12.4 miles) might sound like a lot, it’s certainly not enough to provide irrigation to crops or the like on Mars. The same lake scaled to Earth would only be about 11.1 million square meters (428.6 square miles). That’s about 1.5% the surface area of Lake Superior. 

Compared to all the water on Earth, it’s really just a drop in the bucket.

—Amanda Babcock

1 comment:

  1. You kinda did the math the hard way. You can stick with one dimensional calculations to do it much easier and quicker.

    Mars Circumference/Basketball Circumference = Mars Lake diameter/Basketball Lake Diameter

    so

    Basketball Lake Diameter= Mars Lake Diameter*(Basketball Circumference/ Mars Circumference)

    Basketball Lake Diameter = 20x10^3 meters*(.76 meters/ 21x10^6 meters) = .76x10^-3 meters = 760 microns

    QED (in 3 lines instead of 4 post-it notes, but at least we agree)

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