Infer diameter of Pluto from orbiting Charon

[frozenguy]

Homework Statement

Imagine viewing an eclipse of Charon by Pluto. Assume the satellite orbit is nearly circular, of known radius a, and is viewed edge-on. Explain how you could use the observations to infer a diameter for Pluto

Homework Equations

Orbital radius R=a

The Attempt at a Solution

Pluto is totally covering Charon right?

Does it sound like I should be able to look up the radius of Charon? Or just use a?

I'm really stuck with this one.

Thanks for your help!

 

[Delphi51]

Imagine you are looking out your window at a neighbour's light across the road. A little car goes by and blocks the light for a moment. Then a bus goes by and blocks it. How will these two events look different?

 

[frozenguy]

Hey Delphi51 thanks for your response.

So as I see the car drive by the light will be blocked for a time x.
When I see the bus drive by the light will be blocked for a time y.
And y>x

I'll say it takes Pluto a time t to cross Charon. But how do I know how far out 'a' extends. And don't I need to know the radius of Charon? Or am I just going to use relative sizes?

Thanks again.

 

[Delphi51]

As I read the question, you aren't asked to calculate anything - just explain how it could be done. If the orbital radius would be needed in a calculation, you just mention it (extra marks for describing how that radius could be found?).

 

[tiny-tim]

And don't I need to know the radius of Charon?

logically, if you can see Pluto eclipsing Charon, you must also be able to see Charon transiting Pluto …

so at least you'll know the ratio of their diameters!

(or be able to say that Charon's diameter is negligible!)

 

[frozenguy]

As I read the question, you aren't asked to calculate anything - just explain how it could be done. If the orbital radius would be needed in a calculation, you just mention it (extra marks for describing how that radius could be found?).

Sorry ya, that's what I mean. I guess I just got confused with what we can and can't use to infer the diameter.

logically, if you can see Pluto eclipsing Charon, you must also be able to see Charon transiting Pluto …

so at least you'll know the ratio of their diameters!

(or be able to say that Charon's diameter is negligible!)

Hey thanks for your response..

So I can see how many Charon equatorial diameters the orbital radius a equals and find out how many equatorial diameters Pluto is and relate plutos diameter to a?


I can say a is 5 Charon diameters and Pluto diameter is 3 Charon diameters. Therefore 5/3 Pluto diameters equals a. Or Pluto diameter equals 3a/5

 

[tiny-tim]

actually, now that I've checked it in wikipedia, charon is actually about half the radius of pluto (600 km and 1160 km), so visually timing when it goes behind pluto is going to be rather difficult …

(i'd assumed they were like phobos and Mars )

perhaps you'll need to measure how the brightness of the pair varies?