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

### 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