Transiting the Sun

[Perfection]

Duh, you're smarter than I am and know way more about science and math than I do. But I am actually a pretty smart guy all around, and I try very hard to undo my own ignorance when I'm confronted with it. Tell me what I'm forgetting, or give me a hint, and I can probably figure things out for myself.

He's just being a dickbag. Posturing is the recourse of those without skillz.

[KrazyHorse]

Yes, I lack the skillz to do a 2d geometry problem...

[KrazyHorse]

I'm not sure if my favorite mistake is 1.3 = 1/0.7 or 2.8/0.4 ~ 3.8

[giblets]

Right. So, closer to 147 km/s across Earth's surface, meaning it will last 2 hours and 37 minutes. Which is Perfection's result (coincidentally?). Which KH says is crap.

So it travels a total of 1.4 million kilometers across the Earth's surface?

[Lorizael]

I'm not sure if my favorite mistake is 1.3 = 1/0.7 or 2.8/0.4 ~ 3.8

Exactly what am I supposed to learn from this?

[KrazyHorse]

Have you not realized I'm talking to perf, not you?

[giblets]

My calculations are showing that in terms of the percent of time the sun is completely obscured, the orbital period doesn't matter, it seems to depend completely on Earth's orbit and the solar radius. In any year, no matter what the period (so long as it's within the orbit of Earth ) of the body is, you will spend on average about 13 hours completely obscured. Since there are 5 transits a year under your scenario each one is about 2 hours 35 minutes.

The total transit time (that is the time the sun is partially obscured), does depend on the orbital radius (the closer the object is, the more time spent partially obscured). In this case the time is 11 Hours 10 minutes each transit.

Note that I've made some small angle approximations here, the results might be off by a small fraction.

Explain this to me:

diameter of the sun/(2pi*1 AU) * 1 year

Why are you dividing the diameter of the sun by the circumference of the Earth's orbit? I think the slice of the Earth's orbit that is blocked from sunlight by an object the size of the sun wouldn't be the diameter of the sun. If you hold up an object next to a light source its shadow will be larger than the object itself.

[Perfection]

I'm not sure if my favorite mistake is 1.3 = 1/0.7 or 2.8/0.4 ~ 3.8

I made no such mistake.

Explain this to me:

Why are you dividing the diameter of the sun by the circumference of the Earth's orbit? I think the slice of the Earth's orbit that is blocked from sunlight by an object the size of the sun wouldn't be the diameter of the sun. If you hold up an object next to a light source its shadow will be larger than the object itself.

The penumbra (where only part of the sun is obscured) of the shadow fans out but the umbra (where the sun is completely obscured) does not. If you look, you'll see I calculated both the umbra and penumbra (time completely obscured, vs. total transit time).

Here's a diagram with sight lines that should help illustrate. In the Umbra you cannot draw an unblocked line to the sun, in the penumbra you can draw an unblocked line to some parts of the sun, but not the whole sun.

[Perfection]

So it travels a total of 1.4 million kilometers across the Earth's surface?

The shadow itself is 1.4 million km wide (the width of the sun)

[giblets]

Thanks

[Egbert]

Have you not realized I'm talking to perf, not you?

Have you not realised that you are indeed, as Perfs pointed out, a posturing dickbag who has actually contributed nothing useful to the discussions in this thread?

[Perfection]

Have you not realised that you are indeed, as Perfs pointed out, a posturing dickbag who has actually contributed nothing useful to the discussions in this thread?

Sure he knows this, but of course, he won't admit it and will instead continue with the dickbaggery.

[Lorizael]

Have you not realized I'm talking to perf, not you?

I get that, but you could actually help me rather than just laugh at people who make mistakes. You're obviously under no obligation to do so, but it would be the less dickish thing to do as long as you're going to hang around the thread.

[KrazyHorse]

I get that, but you could actually help me rather than just laugh at people who make mistakes. You're obviously under no obligation to do so, but it would be the less dickish thing to do as long as you're going to hang around the thread.

I already helped you out twice: once by telling you not to use perfie's numbers and once by explaining that the structure you invented is ridiculous, because its components do not describe free orbits.

[KrazyHorse]

I made no such mistake.


The penumbra (where only part of the sun is obscured) of the shadow fans out but the umbra (where the sun is completely obscured) does not. If you look, you'll see I calculated both the umbra and penumbra (time completely obscured, vs. total transit time).

Here's a diagram with sight lines that should help illustrate. In the Umbra you cannot draw an unblocked line to the sun, in the penumbra you can draw an unblocked line to some parts of the sun, but not the whole sun.

This is the right picture. Now write down your expression for the ratio of the penumbra + umbra to the umbra...