Exoplanet transit I

Classical Mechanics Level 3

This figure shows the light curve caused by the transit of the exoplanet HD189733b, which orbits an star with 0.8M☉(solar mass). The vertical axis shows the normalized flux of the host star and the horizontal axis shows the time.

What is the ratio r R \frac{r}{R} between the radius of the exoplanet( r ) and the radius of the star( R ) ? Assumptions and details

  • M☉ = 2 × 1 0 30 2\times 10^{ 30 } kg

  • The orbital period of the planet is 2.218573 days.

Hint - You will have to use the graph

0.987 1.58E-2 0.158 9.87E-2

Fabrizio Melges Ferro by Fabrizio Melges Ferro , 17, Brazil

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1 solution

The amount of light that is blocked [ B ] (which can be determined by the graph) is about 1 - 0.975 = 0.025 ;This amount equals the area of the disk of the exoplanet divided by the area of the disk of the star

B= π r 2 π R 2 \frac{\pi { r }^{ 2 }}{\pi { R }^{ 2 }}

0.025= r 2 R 2 \frac { { r }^{ 2 } }{ { R }^{ 2 } }

0.025 = r R \sqrt { 0.025\quad } =\quad \frac { r }{ R }

0.158 = r R 0.158\quad =\quad \frac { r }{ R }

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