SPACE MATH @ NASA: Ice or Water

There are no known extremophiles that can exist at a temperature lower than the freezing temperature of water. It is believed that liquid water is a crucial ingredient to the chemistry that leads to the origin of life. To change water-ice to liquid water requires energy. 

First, you need energy to raise the ice from wherever temperature it is, to $0$ Celsius. This is called the Specific Heat and is $2.04$ kiloJoules/kilogram C Then you need enough energy added to the ice near 40$ C to actually melt the ice by increasing the kinetic energy of the water molecules so that their hydrogen bonds weaken, and the water stops acting like a solid.

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SPACE MATH @ NASA: The Ground Track of the International Space Station

As the ISS orbits Earth every $90$ minutes, Earth rotates ‘underneath’ the orbit of the ISS once every $24$ hours. This means that each ISS orbit advances in longitude by a fixed amount in longitude. The figure above shows the ground track of the ISS for two orbits. 

Each square is $10$ degrees on a side, with the Equator running horizontally across the middle of the diagram. The squares are shown at intervals of $5$ minutes.

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SPACE MATH @ NASA: NASA Satellite 'Sees' Carbon Dioxide

The Atmospheric Infrared Sounder (AIRS) instrument on NASA's Aqua spacecraft has been used by scientists to observe atmospheric carbon dioxide. The above map shows the concentrations of atmospheric carbon dioxide in units of 'parts per million', and range from $363$ ppm (dark blue) to $380$ ppm (red). 

The data was obtained in July $2003$, and the gas is at an altitude of $8$ kilometers. The map shows that carbon dioxide is not evenly mixed in the atmosphere, but there are regional differences that change in time. For example, the red 'clouds' move in time and change size and shape.

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SPACE MATH @ NASA: An Improved Model for Van Allen Belt Radiation Doses

Spacecraft engineers design spacecraft by considering the radiation environment, planned duration of the research program, and how much shielding is needed for the spacecraft to survive to the end of its mission. 

In this problem we will work with a more realistic model for the orbit path and radiation belt dose rates, and perform a simple graphical integration by estimating areas under curves.

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SPACE MATH @ NASA: Scientists Track the Rising Tide

The graph, produced by scientists at the University of Colorado and published in the IPCC Report-$2001$, shows the most recent global change in sea level since $1880$ based on a variety of tide records and satellite data. 

The many colored curves show the individual tide gauge trends. The black line represents an average of the data in each year.

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SPACE MATH @ NASA: Modeling the Radiation Dose of the Van Allen Probes

The Van Allen Probes orbit Earth within the Van Allen belts about once every $9$ hours. The radiation environment contains high energy electrons and protons that can damage satellite solar panels and delicate electronics without proper shielding. 

Typical spacecraft used for scientific research will become unreliable after they have accumulated $1000$ Grays of radiation, where $1$ Gray = $1$ joule of energy delivered to $1$ kilogram of material. Usually this energy is harmlessly deposited into the spacecraft shielding. Some of it can, however, damage electronic circuits.

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Katherine Johnson: Η Μαθηματικός που Άγγιξε τα Άστρα

Η Katherine Johnson, μια από τις πιο εμπνευσμένες προσωπικότητες της σύγχρονης επιστήμης, έφυγε από τη ζωή σε ηλικία 101 ετών. Παρότι για πολλά χρόνια τα επιτεύγματά της παρέμεναν άγνωστα, η ταινία Hidden Figures (2016) έφερε στο προσκήνιο τη ζωή και τη συνεισφορά της στη NASA.

Ας δούμε τη ζωή μιας γυναίκας που, παρά τις διακρίσεις και τα εμπόδια της εποχής της, έφτασε μέχρι τα αστέρια.

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Ποια ήταν η Katherine Johnson;

2024: Το Θερμότερο Έτος στην Ιστορία των Μετρήσεων

Το 2024 ήταν το θερμότερο έτος που έχει καταγραφεί ποτέ. Οι εμπειρογνώμονές μας συνεργάζονται με τους επιστήμονες της @NOAA για την παρακολούθηση της μέσης θερμοκρασίας της Γης, βασιζόμενοι σε εκατομμύρια μετρήσεις παγκοσμίως. 

Διαπίστωσαν ότι η φετινή χρονιά ήταν θερμότερη από κάθε άλλη τουλάχιστον από το 1880, αποτέλεσμα των ανθρώπινων δραστηριοτήτων: go.nasa.gov

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:  

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

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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