TGEO 110 ‘Search for Life beyond the Earth’
Spring 2012 (TTh at 2:45-4:05 PM; HU 112)
Professor John W. Delano
**** NUMERICAL PROBLEM ****
Your results will be recorded using your iClicker in class on Thursday, March 22.
Kepler’s Third Law is
P2 = (4π2/GM)a3
T
G = gravitational constant = 6.67 x 10-11 m3 / kg sec2
Mass of Sun = 1.99 x 1030 kilograms
Radius of the Sun = 6.97 x 108 meters
24
Mass of Earth = 5.98 x 10 kilograms
1 Earth-year = 365.25 days = 8766 hours
Average distance from center of Sun to center of Earth = semi-major axis = 1.49 x 1011 meters = 1 AU
Radius of the Earth = 6.37 x 106 meters
Circumference of a circle = 2r where r = radius of circle
4
1 Earth-day = 24 hours = 8.64 x 10 seconds
1 light-year = 9.46 x 1012 km
Area of circle = r2
-12
2 4
 = Stefan-Boltzmann constant = 5.67 x 10 watt/cm K
L = luminosity (watts; W) of the star;
A = albedo of the planet; R = distance (cm) of the planet from the star;
NASA’s Kepler spacecraft has observed the systematic dimming of a star located about 265 light years from
Earth. The fraction of observed dimming as the planet transits the star is 0.000405. The period between each of
that planet’s transits of the star is 110.37 Earth-days. The star has a radius that is 0.79 of the Sun’s radius. The
star has a mass that is 0.746 of the Sun’s mass. Determine the semi-major axis of that planet’s orbit in (1)
meters, and (2) in astronomical units (AU). Determine the radius of the planet in (3) meters and (4) in Earth
radii.
Estimate the average temperature (in degrees Kelvin; K) of this exoplanet’s surface using values for its global
albedo, A, of (5) 0.30 and (6) 0.55. Based on your results, (7) which of those values for the albedo indicate(s)
that the average surface temperature of this exoplanet lies between the freezing and boiling points of pure water
(273 K and 373 K, respectively)? The star is known to have a surface temperature of 4808 K compared the
Sun’s surface temperature of 5778 K (i.e., the star is cooler than our Sun). The star is known to have a
luminosity, L, of 1.15 x 1026 watts compared to the Sun’s luminosity of 3.84 x 1026 watts (i.e., the star is
dimmer than our Sun). (8) Determine the duration of a full transit in hours of this exoplanet (i.e., exoplanet
traverses the full diameter of the star).