Transit duration of an exoplanet

In summary, the conversation is about a student asking for help with a problem involving exoplanets and their transit across a star. They are specifically looking for guidance on which units and equations to use. The student has attempted to solve the problem but has run into difficulties, possibly due to an error in the provided link. They are seeking help to identify any mistakes they may have made.
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Homework Statement


Hi, I'm a senior taking a course on exoplanets right now. I have a question regarding their transit across a star. I understand how it works in theory, but I had some questions regarding the equation to use. Here's the problem:

A 0.05 solar radius planet orbits a main-sequence K star of radius = 0.8 solar radii and mass = 0.8 solar masses at an orbital radius of a = 0.5 AU. If the inclination of the planet's orbit to the plane of the sky is i = 89.8o, calculate the duration and depth of the observed transit. What is the maximum orbital radius at which a transit would still be detected?

I'm checking into ask what units I'm supposed to use for this sort of problem, and to make sure that I'm using the correct equations.

Homework Equations



I'm using the equation found here: https://www.paulanthonywilson.com/e...tion-techniques/the-exoplanet-transit-method/

The page has helped me understand the transit method better, and I am using teh equations it lists for transit duration, impact parameter and flux ratio.

The Attempt at a Solution



The first thing I did was convert the solar radii values to AU. Solving the problem this way gives an impact parameter of .469, which is a fine number, but when I attempt to solve for transit duration I end up with an imaginary number in the term for transit length since the star plus planets' radii squared is so much smaller than 5 AU. This is the reason I've come to this forum for help. Was converting the units a mistake? Am I using the wrong formulas? Or does my error lie elsewhere? Finding the flux ratio and maximum orbital radius shouldn't be too hard, since the listed site gives a formula for flux ratio and for the maximum orbital radius I can set b to 1 and then solve for a. Thank you for you help, and please let me know if you're able to spot any errors I've committed.
 
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It appears that the link has an error in figure 1. The side of the triangle shown as ##b## in the figure should actually be ##bR_*## due to the way ##b## is defined. Thus, the figure should be as below.

In the formulas for ##2l## and the transit time, you will need to use ##bR_*## in place of ##b##.
 

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What is the transit duration of an exoplanet?

The transit duration of an exoplanet refers to the amount of time it takes for the planet to pass in front of its host star as viewed from Earth. This duration can range from a few hours to several days, depending on the orbital period and distance of the exoplanet from its star.

How is the transit duration of an exoplanet measured?

The transit duration of an exoplanet is measured by observing the changes in brightness of the host star as the planet passes in front of it. This change in brightness is known as the transit light curve and can provide valuable information about the exoplanet's size, orbital period, and distance from its star.

Why is the transit duration of an exoplanet important?

The transit duration of an exoplanet is important because it can help us determine the characteristics of the planet, such as its size, mass, and distance from its star. This information is crucial in understanding the potential habitability of the exoplanet and whether it may contain life.

Can the transit duration of an exoplanet change over time?

Yes, the transit duration of an exoplanet can change over time. This can be caused by a variety of factors, such as the planet's changing orbital distance or the influence of other planets in the system. However, these changes are generally small and can be accounted for in calculations.

How does the transit duration of an exoplanet differ from its orbital period?

The transit duration of an exoplanet is the amount of time it takes for the planet to pass in front of its host star as viewed from Earth. The orbital period, on the other hand, is the time it takes for the planet to complete one full orbit around its star. These two measurements are related, but the transit duration is typically shorter than the orbital period.

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