# Infer diameter of Pluto from orbiting Charon

• frozenguy
In summary, based on observations of a satellite orbiting a planet, it can be inferred that Pluto's diameter is about 3 times that of 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

## 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!

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?

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.

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?).

frozenguy said:
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!)

Delphi51 said:
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.
tiny-tim said:
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

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?

## 1. How can the diameter of Pluto be determined from orbiting Charon?

The diameter of Pluto can be determined from orbiting Charon by using a technique called mutual event occultation. This involves observing when Charon passes in front of or behind Pluto, causing a dip in the brightness of Pluto's surface. By measuring the duration of the dip and using the known orbital period and distance of Charon, scientists can calculate the diameter of Pluto.

## 2. What is the estimated diameter of Pluto based on observations from orbiting Charon?

The estimated diameter of Pluto based on observations from orbiting Charon is around 2,377 kilometers, which is slightly larger than previous estimates based on other methods. This is due to the precise measurements made possible by the mutual event occultation technique.

## 3. How does the diameter of Pluto compare to other planets in our solar system?

The diameter of Pluto is much smaller than the other planets in our solar system. It is only about 2,377 kilometers, while the diameter of Earth, the largest planet, is over 12,000 kilometers. This is why Pluto is often referred to as a dwarf planet.

## 4. What impact does Charon's orbit have on determining the diameter of Pluto?

Charon's close orbit around Pluto is what makes it possible to determine the diameter of Pluto using mutual event occultation. Without this close orbit, the dips in brightness caused by Charon passing in front of or behind Pluto would not be as precise, making it more difficult to accurately measure Pluto's diameter.

## 5. How has our understanding of Pluto's diameter changed with the use of mutual event occultation?

Our understanding of Pluto's diameter has significantly improved with the use of mutual event occultation. This technique has allowed for more precise measurements and has increased our estimated diameter of Pluto by over 100 kilometers. It has also provided a better understanding of the size and composition of Pluto's surface.

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