The 2016 movie, Hidden Figures, has a strong emphasis on African-American women working for NASA, specifically in the mathematics section of flight. These women show the impact of mathematics in space exploration back in the 1960s, as well as today, with much-improved technology.

**Calculations**

Mathematics are used constantly for space exploration, even with the highly advanced technology and experts we have today. Even the most common and basic equations help NASA get the exact number they need for a successful mission. Some examples of mathematics used in space exploration are:

Optimal trajectories

Planet’s orbit’s shape and velocity

Coding of images

GPS

Exploitation of Lagrange points for strategic placement of satellites

With mathematicians using their skills to perfect the numbers for these movements and technology, we are able to use this technology for satellites and probes like the Hubble Space Telescope, the Genesis mission, and many others. The ideas and math calculated by Albert Einstien and Issac Newton have been modified and improved to still be used in the modern day in these specific technologies as well.

**Trajectory Motion**

Trajectory and orbital motion, as seen in the Hidden Figures movie as well, is crucial mathematics for space exploration, it is what get the equipment into space to study what is out there. This mathematics was first started by Issac Newton, with his law of motions, most important being his second law: The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. The equation of “Force = mass * acceleration” is derived from this specific law and has been a basic starting equation that has been developed for trajectory motion. This is how gravitational forces reacted with acceleration, velocity, parabolic trajectory, and other variables.

Some important equations for orbital dynamics -

Getting the maths exactly correct is crucial for a successful mission, one wrong calculation, and the program as to be completely restarted which takes a long time and a lot of money.

**Coding Images**

When rovers, probes, satellites, or astronauts go to explore a planet, moon, or celestial object, photos is what a space program needs and wants to be able to really explore and investigate this new environment. The most basic form is the coding in the photo’s pixels that go into creating the image. For example, the image shown below is a 7x7 grid that has been coded with binary to fir the different shades necessary to show the image using black as “111111”, white as “000000”, and gray as “000111”.

This process is used with NASA when they are transporting images back to Earth, they use binary and many pixels to give the viewers the colors and sections for the mathematicians to decode.

*Written by: Ellie Humphreys*

*Ellie Humphreys is the *__Board Member__* for Voyager Space Outreach for writing Blog posts on STEM/Space Topics.*