How long do you expect transit to last?

[duder1234]

I have a homework problem that I am having troubles with. There are 2 parts

A transiting exoplanet with a diameter twice that of the Earth orbits a sun-like star in a circular orbit of radius 1.5 AU

a) How much reduction in the flux of the star occurs during the transit?
Earth's diameter=Planet's radius (R_p) =8.5175×10^-5 AU
And because it says a "sun-like" star, I used the same values as the sun for radius
Star's radius (R_s) =4.649×10^-3 AU
And I can use the formula $\frac{ΔF}{F}$=$\frac{R^{2}_{p}}{R^{2}_{s}}$
By plugging in the values, i got 0.03% reduction in flux

b) How long do you expect the transit to last?
I am stuck on this one. I was not told the impact parameter b so do I assume that the transit happens through the centre?
or do I use the formula τ=$\frac{2(Rp+Rs)}{V}$
where τ= transit duration, Rp=diameter of planet, Rs=diameter of star, V=velocity

Any help is appreciated, thanks in advance!

 

[mfb]

b) How long do you expect the transit to last?
I am stuck on this one. I was not told the impact parameter b so do I assume that the transit happens through the centre?

I guess you have to assume this, yes. It is a bad problem statement, it should give this.

or do I use the formula τ=$\frac{2(Rp+Rs)}{V}$

Why "or"? That is the right formula for a central transit.

 

[duder1234]

Thanks for the reply!
I just want to check but I can get the velocity with the formula:$V_{s}$=$\frac{2πr_{s}}{P}$ where P=Period and $r_{s}$=radius of the star
and the period formula being $P^{2}$=$\frac{4π}{GM}a^{3}$
M=Mass of star, a=semi-major axis

 

[mfb]

If you add the radius of the planet to the stellar radius is a matter of taste, depending on the definition of "start" and "end" of transit. And this is an approximation that works if the orbital radius is much larger than the stellar radius only.

Apart from that, it looks fine.