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 set, acceptance use the algebraic connected pi to acquisition out how abundant solar activity is absent on Earth back Mercury transits, or passes in advanced of, the Sun.
Pi in the Sky 3: Sun Screen worksheet – download PDF
Pi in the Sky 3 acknowledgment key (third problem) – download PDF
A alteration happens back a planet crosses in advanced of a star. From our angle on Earth, we alone anytime see two planets alteration the sun: Mercury and Venus. Transits of Mercury appear about 13 times per century, while transits of Venus are alike added rare. The abutting alteration of Venus won’t appear until 2117! As Mercury passes in advanced of the sun, admirers about Earth (using the able assurance equipment) will be able to see a tiny aphotic atom affective boring beyond the deejay of the sun.
Some objects, like the moon and Mercury, were originally anticipation to accept no atmosphere. But scientists accept apparent that these bodies are absolutely amidst in an ultra-thin atmosphere of gases alleged an exosphere. Scientists appetite to bigger accept the agreement and body of the gases that accomplish up Mercury’s exosphere and transits accomplish that possible.
“When Mercury is in advanced of the sun, we can abstraction the exosphere abutting to the planet,” said NASA scientist Rosemary Killen. “Sodium in the exosphere absorbs and re-emits a yellow-orange blush from sunlight, and by barometer that absorption, we can apprentice about the body of gas there.”
When Mercury transits the sun, it causes a slight dip in the sun’s accuracy as it blocks a tiny allocation of the sun’s light. Scientists apparent they could use that abnormality to chase for planets orbiting abroad stars, alleged exoplanets, that are contrarily blocked from appearance by the ablaze of the star. Back barometer the accuracy of abroad stars, a slight alternating dip in the ablaze ambit (a blueprint of ablaze intensity) could announce an exoplanet orbiting and transiting its star. NASA’s Kepler mission has begin added than 1,000 exoplanets by attractive for this admonition bead in brightness.
Additionally, scientists accept amorphous exploring the exospheres of exoplanets. By celebratory the spectra of the ablaze that passes through an exosphere – agnate to how we abstraction Mercury’s exosphere – scientists are alpha to accept the change of exoplanet atmospheres as able-bodied as the access of arch wind and alluring fields.
A alteration occurs back a planet passes in advanced of the deejay of a star. As apparent from Earth, alone Mercury and Venus alteration our star, the sun. During a transit, there is a slight dip in the bulk of solar activity extensive Earth, which can be begin application this equation:
B% = 100 ( )
B = allotment bead in the accuracy of the sun
r = the ambit of the planet as it appears from Earth (in arcseconds)
R = the ambit of the sun as it appears from Earth (in arcseconds)
With abounding solar-powered satellites orbiting Earth, it’s important to apperceive what appulse a dip in solar activity ability have.
If 1,360.8 w/m2 of solar activity alcove the top of Earth’s atmosphere, how abounding beneath watts ability Earth back Mercury (diameter = 12 arcseconds) transits the sun (diameter = 1,909 arcseconds)?
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