Orbital Radius, Area, Mass, Stars, Orbits

[jerm0225]

The distant star, ∆A_6325, is traveling at 70 km/sec away from us and has a peak observed brightness at 400 nm. An exoplanet orbits ∆A_6325 in a transit orbit, causing a 1.4% brightness drop as the planet crosses the star. The ratio of the star’s radius and the planet’s radius is 145:1. The planet was determined to have a density of 2.36 g/cm3. The orbital radius of the planet is 3.14 AU and has an orbital period of 6.32 years.

a) Find the mass of ∆A_6325.

b) Determine the distance of the star/system, using the most inaccurate method on the intergalactic distance ladder.

c) Determine the power of the star.

d) Determine the intensity of the star on the exoplanet.

 

so i dont need answers for all of these but it would be great if I knew how to get area for a orbital radius, or how to determine powers of stars or intensity, or what the inaccurate method is. I dont know what the intergalactic distance ladder is.

 

I'm 13 years old and this is for a science olympiad application and they expect all of us to get a lot of help from online since these questions are really difficult.

[Endy0816]

I'm guessing they are referring to the Cosmic Distance Ladder in the last bit:

 

https://en.wikipedia.org/wiki/Cosmic_distance_ladder

 

an easier to digest article on it:

 

http://www.farnham-as.co.uk/2010/07/measuring-distances-%E2%80%93-the-%E2%80%9Cdistance-ladder%E2%80%9D-by-peter-campbell-burns/

[Mordred]

there is also the mass to luminosity formula

 

https://en.m.wikipedia.org/wiki/Mass%E2%80%93luminosity_relation

 

Intensity is the amount of radiation per unit volume as a function of radius to the observer

 

[latex]I=\frac{L}{4\pi r^2}[/latex]

 

Not positive which distance ladder rung they consider the most inaccurate but judging from the questions I would surmise the inverse square law of luminosity. Reason being is that is only locally accurate where expansion has little influence.

Edited September 6, 2016 by Mordred