SPACE MATH @ NASA | Rotation Velocity of a Galaxy

Stars orbit the center of a galaxy with speeds that decrease as their orbital distances increase. 

A simple function, $V(x)$ can model the orbital speeds of stars as a function of their distance, $x$, from the nucleus of the galaxy:  

$V(x)= \dfrac{350x}{(1+x^2)^{ \frac{3}{4}}}$.

For example: 

At a distance of $10,000$ light years from the center, $x = 1.0$ and the rotation speed is $V(1.0) = 208$ kilometers/sec.

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Journey Through Stars with NASA in New Minecraft Game

NASA invites gamers, educators, and students to grab their pickaxe and check out its latest collaboration with Minecraft exploring a new world inspired by the agency’s James Webb Space Telescope. 

The partnership allows creators to experience NASA’s discoveries with interactive modules on star formation, planets, and galaxy types, modeled using real Webb images.

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SPACE MATH @ NASA | Investigating Juno’s Elliptical Transfer Orbit

The Juno spacecraft was initially placed in an elliptical orbit near Earth soon after its launch on August 5, 2011. The orbit was elliptical and designed so that a Deep Space Maneuver in August 2012 would send the spacecraft into a flyby of Earth in 2013. 

This encounter with Earth would boost the spacecraft’s speed and place it into an elliptical transfer orbit that would intersect Jupiter’s orbit in 2016.

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SPACE MATH @ NASA | Investigating the Launch of the Juno Spacecraft

This sequence of images was taken of the launch of the Juno spacecraft on August $5$, $2011$ from Cape Canaveral. The images were taken, from left to right, at $T+21, T+23$ and $T+25$ seconds after launch, which occurred at $12:25:00$ pm EDT. 

The original video can be found on YouTube. The distance from the base of the Atlas-Centaur rocket to its top is $45$ meters ($148$ feet). As the video was produced, the camera zoomed-out between the $T+21$ image and the $T+23$ image. Both the $T+23$ and $T+25$ images were taken at exactly the same zoom scale

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SPACE MATH @ NASA | The Launch of the Juno Spacecraft - Ascent to orbit

The Juno spacecraft was launched on August 5, 2011 on a 5 year journey to Jupiter. This image was taken 120 seconds after launch and shows one of the solid rocket boosters being jettisoned. 

The camera is on the Atlas booster and looks down on the engines and the distant arc of a cloudy Earth. Scenes from the launch can be found on YouTube, and show a dazzling launch from multiple viewing locations on Earth and in space.

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SPACE MATH @ NASA: Mars Rover Landing Site

This NASA, Mars Orbiter image of the Mars Rover, Spirit, landing area near Bonneville Crater. The width of the image is exactly 895 meters. (Credit: NASA/JPL/MSSS). 

It shows the various debris left over from the landing, and the track of the Rover leaving the landing site.

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Space Math @ NASA | Exploring Two Nearby Stars to the Sun

The Hubble Space Telescope recently took a picture of the currently nearest star to our sun, Proxima Centauri, which is at a distance of $4.243$ light years ($1$ light year = $9.5$ trillion km). 

The orbits of several other stars near the sun are also known, and during the next 80,000 they will replace Proxima Centauri as the nearest star to our sun. For this problem we will study the two stars Ross $128$ and Gliese $445$.

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Space Math @ NASA | Exploring the Donut-shaped Van Allen Belts

The Van Allen belts were discovered in the late-$1950$s and resemble two donut-shaped clouds of protons (inner belt) and electrons (outer belt) with Earth at its center. 

A donut is an example of a simple mathematical shape called a torus that is created by rotating a circle with a radius of $r$, through a circular path with a radius of $R$.

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SPACE MATH @ NASA | Visiting the Planets at the Speed of Light!

The fastest way to get from place to place in our solar system is to travel at the speed of light, which is $300,000$ km/sec ($670$ million miles per hour!). Unfortunately, only radio waves and other forms of electromagnetic radiation can travel exactly this fast.

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SPACE MATH @ NASA | How Big is Our Solar System?

Our solar system is so big it is almost impossible to imagine its size if you use ordinary units like feet or miles. The distance from Earth to the Sun is $93$ million miles ($149$ million kilometers), but the distance to the farthest planet Neptune is nearly $3$ billion miles ($4.5$ billion kilometers). 

Compare this to the farthest distance you can walk in one full day ($70$ miles) or that the International Space Station travels in $24$ hours ($400,000$ miles).

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SPACE MATH @ NASA | Nuclear Arithmetic

Over $100$ elements have been discovered over the last century. The nucleus of each atom contains two kinds of particles: protons and neutrons. 

Scientists classify each element by the number of protons ($Z$) and the mass of the element ($A$). 

• $Z$ is called the Atomic Number 
• $A$ is called the Atomic Mass 

The number of neutrons ($N$) in the nucleus is given by the formula: 

$N = A - Z$

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SPACE MATH @ NASA: Space Math - III

These activities comprise a series of 36 practical mathematics applications in space science. This collection of activities is based on a weekly series of space science problems distributed to teachers during the 2006-2007 school year. 

The problems in this booklet investigate science and mathematics concepts such as radiation effects on humans and technology, solar science, algebra, trigonometry, and calculus.

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SPACE MATH @ NASA: Earth Math

This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2009-2010 school year. 

They were intended for students looking for additional challenges in the math and physical science curriculum in grades 9 through 12. The problems were created to be authentic glimpses of modern science and engineering issues, often involving actual research data.

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SPACE MATH @ NASA: Lunar Math

This collection of activities is based on a weekly series of space science problems distributed to thousands of teachers during the 2005- 2012 school years. 

They were intended for students looking for additional challenges in the math and physical science curriculum in grades 5 through 12. The problems were created to be authentic glimpses of modern science and engineering issues, often involving actual research data.

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SPACE MATH @ NASA | ISS - Orbit Altitude Changes

The International Space Station is a 400-ton, $160 billion platform that supports an international team of 3-5 astronauts for tours of duty lasting up to 6 months at a time. 

Like all satellites that orbit close to Earth, the atmosphere causes the ISS orbit to decay steadily every day, so the ISS has to be 're-boosted' every few months to prevent it from burning up in the atmosphere.

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SPACE MATH @ NASA | Changing Perspectives on the Sun's Diameter

Earth's orbit is not a perfect circle centered on the sun, but an ellipse! Because of this, in January, Earth is slightly closer to the sun than in July. This means that the sun will actually appear to have a bigger disk in the sky in January than in July…but the difference is impossible to see with the eye, even if you could do so safely!

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SPACE MATH @ NASA | Angular Size and Velocity

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SPACE MATH @ NASA: Fun With Gears and Fractions

Problem 1 

When Gear A completes one revolution, how many revolutions does Gear B make?

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SPACE MATH @ NASA | Black Holes - Hot Stuff!

When gas flows into a black hole, it gets very hot and emits light. The gas is heated because the atoms collide with each other as they fall into the black hole. 

Far away from the black hole, the atoms do not travel very fast so the gas is cool. But close to the black hole, the atoms can be moving at millions of kilometers/hour and the gas can be thousands of degrees hot!

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SPACE MATH @ NASA | Exploring Tidal Forces: Black Holes and Saturn’s Rings

The gravitational force between two objects varies as the inverse-square of the distance between them. On the surface of Earth, we do not notice that the gravitational force of Earth pulling on our feet is slightly larger than the force pulling on our head. 

For astronomical bodies, however, the difference in gravity can be so great that it pulls the body apart! This is called the tidal gravitational force. Around every body, there is a distance called the tidal radius within which an object will be gravitationally torn apart if the body is being held together by its own gravitational forces. 

This distance can be calculated using the formulae to the left. Let’s explore what this distance is for some common astronomical bodies.

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