How to check a statement about orbital angles of exoplanets?

In summary, the conversation discusses the use of the Radial Velocity technique for detecting planets and how the unknown inclination angle affects the measurement of the true mass of the companion. The authors explain that although this limitation is important for individual systems, it does not greatly impact statistical studies of exoplanet populations. This is because inclination angles are randomly distributed in space, with angles close to 90° being more frequent than pole-on configurations. The authors use the distribution function for inclination angles to show that the average value of sin(i) is equal to π/4 (0.79) and that there is an 87% chance that sin(i) is larger than 0.5. The conversation ends with the speaker asking for further clarification on how
  • #1
Fabioonier
12
0
Hi, everybody. Mi name is Fabio Onier Osorio Pelaez and I'm from Colombia.

I hope to be finishing my Bachelor´s degree in Physics at University of Antioquia by next August. I'm doing my final project on the detection of planets by the Radial Velocity technique and I have a question about an statement of Christophe Lovis and Debra Fischer in a paragraph in the third page or their article (page 29 in the book Exoplanets). I quote the complete paragraph emphasizing the statement in which I am interested:

"The unknown inclination angle ##i## prevents us from measuring the true mass of the companion ##m_2##. While this is an important limitation of the RV technique for individual systems, this fact does not have a large impact on statistical studies of exoplanet populations. Because inclination angles are randomly distributed in space, angles close to 90° (edge-on system) are much more frequent than pole-on configurations. Indeed, the distribution function for ## i ## is given by ## f(i)di=\sin(i)di ##. As a consequence, the average value of ##\sin(i)## is equal to ##\pi/4## (0.79). Moreover, the a priori probability that ##\sin(i)## is larger than 0.5 is 87%."

I wondered if you may tell me how did they conclude that. I'll be thankful if you can help me with that information. It will be very useful for my work.
 
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  • #2
Welcome to PF;
The authors tell you: "Because the inclination angles are randomly distributed..."
 
  • #3
To give you another hint, imagine a six-sided die (i.e. a cube) being thrown. Pick anyone pair of opposite sides - these represent the poles of the orbital arrangement. The remaining four sides represent the edges. As you can already see, there's more possibilities of an edge-on result (4 of 6) than of a pole-on result (2 of 6).
Generalise the cube to a sphere and see if you can get the same result the authors got.
 

1. What are orbital angles and why are they important in studying exoplanets?

Orbital angles refer to the orientation of an exoplanet's orbit around its host star. These angles play a crucial role in understanding the exoplanet's climate, potential habitability, and interactions with other objects in its system.

2. How do scientists measure orbital angles of exoplanets?

Scientists use a technique called radial velocity or Doppler spectroscopy to measure the changes in a star's light caused by the gravitational pull of an orbiting exoplanet. This can provide information about the exoplanet's mass, distance from its star, and orbital angles.

3. Are orbital angles constant or do they change over time?

Orbital angles can change over time due to various factors such as the gravitational pull of other objects in the system, tidal forces, and interactions with the host star. However, these changes are typically small and can be accurately calculated and predicted by scientists.

4. Can orbital angles affect the habitability of an exoplanet?

Yes, the orbital angles of an exoplanet can have a significant impact on its habitability. If the angles are too steep, the planet may experience extreme temperature fluctuations, making it difficult for life to exist. Additionally, certain angles may also lead to tidal locking, where one side of the planet always faces the star, making it inhospitable for life.

5. How does knowing the orbital angles of exoplanets help in the search for extraterrestrial life?

Studying the orbital angles of exoplanets can provide valuable information about their potential habitability and the likelihood of liquid water, a key component for life, on their surface. It can also help scientists narrow down the search for potentially habitable exoplanets and prioritize future study and exploration missions.

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