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Geosciences LibreTexts

22: The Origin of Earth and the Solar System (Exercises)

  • Page ID
    2062
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    Q22.1 How do we know what other planets are like inside?

    Table 22.2 Find the fraction of volume that is core
      Earth Mars Venus Mercury
    Planet density (uncompressed) in g/cm3 4.05 3.74 4.00 5.30
    Percent core 16.8% 10.3% 15.8% 43.2%

     

    Table 22.3 Find the volume of the core for each planet
      Earth Mars Venus Mercury
    Unsqueezed planet volume – km3 1.47 x 1012 1.72 x 1011 1.22 x 1012 6.23 x 1010
    Core volume – km3 2.48 x 1011 1.77 x 1010 1.92 x 1011 2.69 x 1010

     

    Table 22.4 Find the percent of each planet’s radius that is core
      Earth Mars Venus Mercury
    Unsqueezed core radius in km 3900 1617 3581 1858
    Unsqueezed planet radius in km 7059 3447 6623 2458
    Percent of radius that is core (see diagram below) 55% 47% 54% 76%

    [KP]

    Q22.2 How do we know the sizes of exoplanets?

    Plot showing how the star Kepler-452 dims as the planet Kepler-452b moves in front of it.

    [KP, after Jenkins, J. et al, 2015, Discovery and validation of Kepler-452b: a 1.6REarth super Earth exoplanet in the habitable zone of a G2 star, Astronomical Journal, V 150, DOI 10.1088/0004-6256/150/2/56.]

     

    Table 22.5 Calculate the radius of star Kepler-452
      Sun Kepler-452 Ratio
    Temperature (degrees Kelvin) 5778 5757 1.0036
    Luminosity (x 1026 Watts) 3.846 4.615 1.20
    Radius (km) 696,300 768,317  

    * The temperatures of the sun and Kepler-452 are very similar, but the small difference is important. Keep 4 decimal places.

    Table 22.6 Calculate the radius of planet Kepler-452b
    Decrease in brightness* Earth radius (km) Kepler-452b radius rplanet (km) Kepler-452b radius/ Earth radius
    197x 10-6 6378 10,784 1.7

    * Because we know this is a decrease, you don’t need to keep the negative sign.

    **Answers provided by Karla Panchuk