Apparent Magnitude Question (Again)

[Via Lactea]

Me with my apparent magnitude obsession again!

I was wondering whether anyone could tell me whether a transit, or near-transit of Mars across Jupiter in our night sky would create a bigger star to our eyes, with a higher AM than those planets' respective brightnesses.

Simply put, say Mars and Jupiter "meet" in Gemini. If Mars is either skimming past or transiting Jupiter to our eyes on a given night or nights, would we see a "bigger star" from our vantage point? And main question: if Jupiter has an apparent magnitude of -2.21ish on that night(s), and Mars is either transiting or very near, with its own magnitude of, say, -1, does that mean the "JupiMars" would have a combined magnitude greater than -2.21?

Cheers guys, VL

[crashtestdummy]

i would have though that it wouldn't be brighter than the brightest of the two i.e. if mars went infront of Jupiter it would just dim Jupiter rather than make mars stand out more.there would obviously be a negligible size increase but I doubt you would be able to tell with the naked eye size wise but you would with the dimming.

[Via Lactea]

Good point re the brightness. And their apparent diameters are small too, so I guess it would just look like a normal star. Perhaps for noticeable brightness a Venus-Jupiter transit...

[Knight of Clear Skies]

It would be at it's brightest just before Mars began its transit of Jupiter. To the naked eye the conjunction would appear as a single point source so it would appear brighter than Jupiter by itself, until Mars started to obscure it.

[Via Lactea]

Thank you Sir Knight! And I'm guessing that if Mars didn't transit, but merely skirted over the "top" of Jupiter, then they would remain two separate points of light. Cheers!

[Lancashire Astroguy]

If the disk of Mars was completely inside the disk of Jupiter, then the combined object would be brighter (i.e. have a more negative apparent magnitude) than either planet individually. This is because the disk of Mars will be brighter than the portion of the disk of Jupiter it is replacing. Mars is (on average) 3.4 times closer to the Sun than Jupiter, and therefore receives much more illumination from the Sun. If its surface was as reflective as Jupiter's cloud, then its surface brightness would be 11.6 times that of Jupiter (3.4 squared - light intensity drops as an inverse-square law). In fact, Mars is less reflective than Jupiter (albedo of 0.15 rather than 0.52). This means the Martian disk has a surface brightness 3.3 times that of the Jovian disk (3.3 = 11.6 * 0.15 / 0.52)

In other words, the disk of Mars is 3.3 brighter than that part of Jupiter it would be blocking during a transit. This allows us to do a few simple calculations. Lets say the transit occurred near opposition of both planets when Jupiter had a app mag of -2.5 and Mars had an app mag of -2.1. The hidden part of Jupiter's disk would have a magnitude 1.3 fainter than Mar's disk, e.g. -0.8 (1.3 = 2.5 * log 3.3). This corresponds to 20.9% of Jupiter's total brightness (0.209 = 10^^(0.4 * -1.7)). Thus Jupiter's brightness has been reduced to 79.1% of its original value. However, if we multiply 20.9% by 3.3 we get 69% ... adding this onto 79.1% we calculate that the combined object will have a brightness 148% (or 1.48 times) that of Jupiter on its own before the transit. Converting this back into magnitudes we finally get our answer ... magnitude -2.9 for the combined object (2.5 * log 1.48 = 0.42, so approx 0.4 magnitudes brighter than -2.5).

[crashtestdummy]

So essentially undetectable to the Human eye?

[Lancashire Astroguy]

So essentially undetectable to the Human eye?

You would be hard pressed to casually notice a difference between magnitude -2.5 and -2.9. By comparison, the difference between Castor and Pollux (the two main stars of Gemini) is also 0.4 mag and they look pretty much the same brightness to me (albeit Pollux being slightly orange). I guess its down to the human eye being a logarithmic rather than a linear detector of light. Nonetheless, I understand seasoned observers of variable stars can sometimes estimate magnitudes to within +/-0.2 or even +/-0.1 if there is a suitable comparison star in the field of view.

Interestingly though, using the numbers above (mag -2.5 and -2.1 for the two planets), then just before and after the transit they would appear to be a single object that was even brighter (mag -3.1), given that none of Jupiter's disk would be hidden. A difference of 0.6 mag (0.57 mag to be precise) should be more noticeable. Much more than an arcminute apart, however, and your eye would start to seperate them.

[crashtestdummy]

I think the colour of stars does make a difference to apparent visual magnitude.thanks for explaining it fully,better to know why rather than just know

[Lancashire Astroguy]

I think the colour of stars does make a difference to apparent visual magnitude.thanks for explaining it fully,better to know why rather than just know

The apparent visual magnitude of an object is based on the radiant intensity of the object as viewed through a "V" band photometric filter. Given that the "V" band filter is a reasonably close (though not perfect) match to the spectral response of the human eye, comparing visual app mags of different objects should (in theory at least) give an indication of their relative brightness as viewed by the eye, regardless of their colour.

A good example of this is Betelgeuse and Rigel in Orion. Both stars have roughly the same intrinsic luminousity across all wavelengths (about 120,000 x Solar Luminosity). However, Betelgeuse is significantly closer than Rigel to us, so one might expect Betelgeuse to appear brighter than Rigel. In fact it clearly appears dimmer and this is reflected in its apparent visual magnitude (0.42 compared to 0.12 for Rigel). The reason of course is that Betelgeuse being a much cooler star emits more of its energy towards the red end of the visual spectrum, but this peak is heavily attenuated by a "V" band filter (and the human eye).