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#### 48.867Astronomer Dr. Elena Vega uses a telescope to observe a distant exoplanet that orbits its star every 240 Earth days. If she begins monitoring the system on day 0 and takes a detailed spectral analysis every 15 days starting from day 0, how many analyses will she perform by the end of the planets first full orbit, including day 240?
Dr. Vega performs an analysis every 15 days starting on day 0, so the days of analysis are 0, 15, 30, ..., up to and including 240.
This is an arithmetic sequence with first term 0, common difference 15, and last term 240.
Thus, she performs 17 spectral analyses over the 240-day period.
Dr. Vega observes that a newly discovered exoplanet emits thermal radiation proportional to the fourth power of its absolute temperature (Stefan-Boltzmann law). If its temperature rises from 300 K to 360 K, by what factor does the emitted radiation increase?
So, radiation increases by a factor of 2.0736.
So, the absorbed energy totals 31,824 kJ over 10 hours.
An exoplanets atmospheric pressure at sea level is measured at 98.7 kPa, which is 1.087 times Earths sea level pressure (101.325 kPa is Earths). If a probe designed for Earths 101.325 kPa must withstand a pressure margin equal to 15% above the exoplanets pressure, what minimum pressure must it be built to resist?
Thus, the probe must be built to resist at least 113.445 kPa.
The spectrograph on Dr. Vegas telescope can detect wavelength shifts with a precision of 0.002 nm. If an exoplanets host star shows a spectral line at 500.000 nm and a Doppler shift of 0.004 nm due to planetary motion, how many times the telescopes precision is the observed shift?