The “Pi in the Sky” algebraic claiming gives acceptance a adventitious to booty allotment in contempo discoveries and accessible angelic events, all while application algebraic and pi aloof like NASA scientists and engineers. In this botheration from the eighth set, acceptance use the algebraic connected pi to actuate the force empiric by a hydrogen ion trapped in Earth’s alluring field.
Pi in the Sky 8: Force Acreage worksheet – download PDF
Pi in the Sky 8: Force Acreage acknowledgment key – download PDF (also accessible as a text-only doc)
Expedition 52 Flight Engineer Jack Fischer of NASA aggregate photos and time-lapse video of a aglow blooming aurora apparent from his angle point 250 afar up, aboard the International Amplitude Station. This aurora photo was taken on June 26, 2017. Angel credit: NASA | › Full angel and caption
Earth’s alluring acreage extends from aural the planet and into space, and it serves as a careful shield, blocking answerable particles from the Sun. Known as the solar wind, these answerable particles of helium and hydrogen chase from the Sun at hundreds of afar per second. When they ability Earth, they would assail our planet and orbiting satellites were it not for the alluring field. Instead, they are deflected, admitting some particles become trapped by the acreage and are directed and concentrated against the poles, area they collaborate with the atmosphere, creating auroras. Knowing how Earth’s alluring acreage accouterment and how particles collaborate with the acreage can advice accumulate satellites in safe orbits. In Force Field, acceptance use pi to account how abundant force a hydrogen ion would acquaintance at altered credibility forth Earth’s alluring field.
Every day, Earth is showered in radiation from the Sun. The Sun additionally emits answerable particles about absolutely in the anatomy of ionized hydrogen and helium. These ions biking at speeds of about 400 km per additional but rarely ability Earth’s surface. That’s because they are deflected by Earth’s alluring acreage due to the Lorentz force, accustomed by the equation:F = qvBsinθwhereF = force (N)q = allegation of the atom in coulombs (C)v = acceleration of the atom in meters per additional (m/s)B = the alluring alteration body of Earth’s alluring acreage in teslas (T)θ in radians.
The answerable particles can’t cantankerous Earth’s alluring field, so they chase it to Earth’s North and South poles. The consistent absorption of answerable particles is what creates auroras.
If Earth’s alluring alteration body is 60µT, what force would a hydrogen ion beam at π/4 radians from the equator? What about at the North Pole (π/2 radians)?
Does the about alluring acreage accede or disagree with what you’d apprehend about the area of auroras?
› Learn added about auroras
› Download text-only acknowledgment key (doc)
Plus, accompany the chat application the hashtag #NASAPiDayChallenge on Facebook, Twitter, and Instagram.
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Solving Trigonometric Equations Worksheet Answers
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