22: The Origin of Earth and the Solar System (Exercises)
- Page ID
- 2062
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Q22.1 How do we know what other planets are like inside?
| 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% |
| 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 |
| 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.]
| 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.
| 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