Show that the radius of the exoplanet is about 1/2 of Earth’s radius

[hraghav]

TL;DR Summary: For a transiting exoplanet, we find it takes 4.3 days from the start of the transit for the host star to reach a minimum brightness, which lasts for 10 days. Show that the radius of the exoplanet is about 1/2 of Earth’s radius if its orbital radial velocity is 17 m/s.

I am trying to use the equation 2Rexo = Vexo(t1 -t2) where Vexo = 17 m/s and I need to find the Radius of the exoplanet and then convert it to Earth radii where I should get my final answer as 0.5R⊕. But I am confused with the values of t1 and t2? What should they be? Could I simply just use T= 4.3 days instead of t1 and t2 ie 2Rexo = Vexo*T? I am really confused with this and it would be great if someone could please help me out with this. Thank you!

 

[haruspex]

TL;DR Summary: For a transiting exoplanet, we find it takes 4.3 days from the start of the transit for the host star to reach a minimum brightness, which lasts for 10 days. Show that the radius of the exoplanet is about 1/2 of Earth’s radius if its orbital radial velocity is 17 m/s.

I am trying to use the equation 2Rexo = Vexo(t1 -t2) where Vexo = 17 m/s and I need to find the Radius of the exoplanet and then convert it to Earth radii where I should get my final answer as 0.5R⊕. But I am confused with the values of t1 and t2? What should they be? Could I simply just use T= 4.3 days instead of t1 and t2 ie 2Rexo = Vexo*T? I am really confused with this and it would be great if someone could please help me out with this. Thank you!

It is not much use having a formula if you do not know what the symbols mean.
In the present case, it would appear that $t_1$ is the time at which the brightness becomes minimised and $t_2$ is the time at which it was last maximised. I.e., $t_1-t_2$ is the time to go from maximum brightness to minimum, 4.3 days.

 

[Orodruin]

It is not much use having a formula if you do not know what the symbols mean.

… and arguably also why the formula has the structure it has. Much more than memorizing formulas, a deeper understanding of physics requires not only knowing lots of formulas, but understanding how they arise and being able to derive them.