Brightness of Mars as observed from earth.

[teh_game]

Hey, I've got a question which I hope you guys can help me with.

It is observed that Mars is somewhat brighter when in opposition (ie. sun- Earth - Mars in that order) that at other times. How can this be explained using
a) The Ptolemaic model and
b) The Copernican model of the solar system.
(Assume that Ptolomy's construction describes the actual motion of the planet)


I know that at diffrent times of the year, Mars appears brighter. I think it was a 2 yr cylce. It's 'cause Mars gets closer to Earth at that time.

"Opposition for Mars occurs about every two years, when Mars appears opposite the sun as seen from Earth. Now the planet rises in the east when the sun sets in the west and arcs across the sky -- a brilliant reddish light -- all night long. This happens, of course, around the time we on Earth are flying between Mars and the sun."

But does anyone have any good explanations?

I don't really understand this question either, if anyone can clarify it, it'd be great !

Thanks a lot !

 

[jim mcnamara]

Think about:

Does the intensity of light decrease with distance? yes.

Would a half moon or a full moon provide more moonlight? full moon.
When does a full moon occur? Following that, is there ever a "full Mars"?

 

[russ_watters]

Google for the radius of Earth's orbit and the radius of Mars's orbit. Calculate the distance between the two planets at conjunction and opposition for each model (iirc, in the Ptolmey's model, Mars was in orbit around the earth, but I'm not sure about the distance...). Now, do you know the relationship between distance and brightness? Ie, take the ratio of the distances at conjunction and opposition, apply the relationship and you'll get the brightness ratio.

 

[BobG]

You're trying to compare the heliocentric model of the solar system to the geocentric?

First, we'll virtually see the 'full' Mars all the time, since Mars is further from the Sun than the Earth is. There's a slight difference in the fullness of Mars because of the geometry, but not enough to make a difference in brightness to the naked eye.

There's a drastic difference in brightness due to the difference in distance bewteen when Mars is on the opposite side of the Sun and when Mars is on the same side of the Sun. Keep in mind, though, that when Mars is on the opposite side of the Sun, it would only be visible right before sunrise and sunset.

The Ptolemaic model used epicycles and deferrents to model the motion of the planets. This would change the distance between Earth and Mars and explain the retrograde motion. I don't know the details of the Ptolemaic model, but I would imagine it came fairly close to modeling real world observations. Everytime the model came up short, a new modification (putting the planet into an epicycle that followed its own epicycle, etc) was added. Unfortunately, the model had to keep getting more and more complex to fix the discrepancies in real world observations, to the point that a few astronomers (like Copernicus) began to think the model had to be more a creation of their own minds than a reflection of reality.

Galileo's telescope really threw a wrench into the model. The phases of Venus and Jupiter's moons were pretty hard to explain in a Ptolemaic model.

 

[NateTG]

It is observed that Mars is somewhat brighter when in opposition (ie. sun- Earth - Mars in that order) that at other times. How can this be explained using
a) The Ptolemaic model and
b) The Copernican model of the solar system.
(Assume that Ptolomy's construction describes the actual motion of the planet)

It's completely unimportant whether you're using a helio or geo-centric model of the solar system - rather, it's three spheres that are arranged in one of two geometries in space.

Assuming a constant albedo and constant level of sunlight, the amount of light that comes from Mars is going to be proporitonal to:
$$\frac{\cos{\theta_{\rm{sun \rightarrow Mars \rightarrow earth}}}}{D_{\rm{sun \rightarrow mars}}^2\times D_{\rm{mars \rightarrow earth}}}$$

It doesn't take a whole lot to figure out that this is mars, earth, and the sun are in line with the Earth in the middle.

 

[teh_game]

Oh, great!

Thanks!

 

[teh_game]

So, whenever the Earth is in the middle, Mars is brighter, regardless of the model.

Is that correct?

*need some reassurance* :)

thanks a lot !

Edit: wait, the question already tells us that

I know that for the copernican model, it's because the distance between Mars and Earth is the closest.

But am still unsure about the other model; is it because the sun will be in the way if they are in the set-up earth-sun-mars ?

 

[patcho]

I think the question is just wanting you to say that the ptolemaic model used epicycles/deferrents as BobG said to explain that Mars is sometimes brighter when in opposition than other times and that in the Copernican model, the fact that the Mars orbit is an ellipse means it is closer to Earth sometimes while in opposition as it moves in its orbit from perihelion to aphelion around the Sun.

On a side note, I don't think the copernican model used elliptical orbits so you couldn't answer that part of the question but I assume they mean heliocentric model as that makes more sense to me as it encompasses further advances in astronomy esp. Kepler's laws.