Wikipedia:Reference desk/Archives/Science/2024 March 29

= March 29 =

Looking for Map with Eclipse Path and Actual Weather Conditions
I'm looking for an interactive map showing the path of totality of the Solar eclipse of April 8, 2024 and current weather conditions. I live near Chicago so I'm primarily interested in the weather for Illinois, Indiana and Ohio. I've found plenty of maps showing the path of totality and plenty of maps showing the probability of clouds based on historic data, but I have not yet found a map showing the path of totality and current weather conditions. To put it another way, if today was the eclipse, where can I find a map showing the path of totality and today's weather forecast? A Quest For Knowledge (talk) 14:04, 29 March 2024 (UTC)

How much carbon could there be in a planetary system?
I see that in our solar system (according to this article, about 0.4% of mass is in carbon. What would be the upper bound for that percentage in a hypothetical planetary system?  Perhaps one derived from the death of a carbon star? -- Avocado (talk) 16:59, 29 March 2024 (UTC)


 * The materials used to form a planetary system aren't generally from the death of a single star. Rather, the planetary systems form from the collapse of part or all of a molecular cloud whose composition is determined by both big bang nucleosynthesis and whatever supernovae and other events in the area have deposited.
 * The younger the star forming region, the more time the universe has had to form heavy elements and contribute them to that region.
 * Relatively speaking, the solar system is quite young, and so the abundances present are probably relatively close to the current theoretical maximum. PianoDan (talk) 18:17, 29 March 2024 (UTC)


 * There are carbon planets where the core is iron, the crust is carbon, the rivers are oil, the mantle is carbide, the water became oxides and hydrides of carbon instead cause there's too much carbon and if the star's far enough the air's mostly CO2 and/or monoxide with lots of carbon smog and if it's really far the surface is frozen and/or liquid carbon oxides and frozen and/or liquid hydrocarbons like tar and methane. Maybe the base of the carbon crust could be pressurized enough to be diamond though, with diamond-carbide volcanos. Sagittarian Milky Way (talk) 19:29, 29 March 2024 (UTC)
 * Ooooh, that might be exactly the information I was looking for. Thank you! -- Avocado (talk) 22:24, 29 March 2024 (UTC)

Lorentz transform question
The Lorentz transform is given as:

$$\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right)  \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end{align}$$

since y' and z' do not change, focusing on just the t' and x':

$$\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right)  \\ x' &= \gamma \left( x - v t \right) \end{align}$$

My question is, if we already know the time parameter t will transform as:

$$\begin{align} t' &= \gamma \left( t - \frac{vx}{c^2} \right) \end{align}$$

then why can we not utilize the already transformed t' parameter and take a shortcut directly in the target reference frame by simply multiplying the transformed time t' by -v (the velocity has a negative sign because, to the primed/target reference frame, the unprimed/original reference frame is moving in the opposite direction with same speed v, hence velocity is -v) to get the transformed x' in the target reference frame, as follows?:

$$\begin{align} x' &= -vt' \\ &= -v\gamma \left( t - \frac{vx}{c^2} \right) \\ &= \gamma \left( -vt + v \frac{vx}{c^2} \right) \\ &= \gamma \left( -vt + \frac{v^2}{c^2}x \right) \\ &= \gamma \left( \frac{v^2}{c^2}x - vt \right) \end{align}$$

However, doing so results in a wrong transformation for x'. But I am wondering what the reason for this is, is it because of a failure to take into consideration length contraction aspect in addition to the time dilation when dealing with the spatial parameter x'?

Many thanks for clarification. L33th4x0r (talk) 19:40, 29 March 2024 (UTC)
 * I do not understand why you think that multiplication of t' by v will give you the coordinate x'? Ruslik_ Zero 20:47, 29 March 2024 (UTC)
 * I thought x' is a sort of distance, calculated by multiplying the velocity by the (dilated) time. I am reading over this exposition on the Twin Paradox on Stack Exchange by John Rennie where in his follow-up post in the thread "Appendix - what did the twin observe?" he calculated through Lorentz Transform the stationary twin's coordinates in the frame of reference of the moving twin to be -γvt which I took to be (-v)(γt) which is the velocity multiplied by the dilated time in the moving twin's frame of reference, when the moving twin is trying to calculate how far the stationary twin has moved in the x-direction. L33th4x0r (talk) 00:04, 30 March 2024 (UTC)
 * But the twin's coordinate $$x$$ in their own coordinate system is zero by definition. So, Lorentz transform means that $$x'=-\gamma vt$$. Ruslik_ Zero 20:41, 30 March 2024 (UTC)
 * Many thanks Ruslik for fully clarifying this issue. Now I understand. L33th4x0r (talk) 14:36, 3 April 2024 (UTC)
 * Classically |v'| and |v| are invariant (|x|/t=|x'|/t') and independent of motion. However, |v'| is not equal to |v|, which you discovered, because the intervals of x and t are not invariant and classical and are incorporated into spacetime due to its invariant lightspeed that is independent of motion. Of course, there are plenty of derivations of the formula which you can consult for further details. Modocc (talk) 21:38, 29 March 2024 (UTC)
 * Many thanks for your detailed analysis Modocc. Really appreciate it. L33th4x0r (talk) 19:42, 30 March 2024 (UTC)

Mirror radiation pressure and energy conservation
Electromagnetic radiation reflected on a mirror communicates part of its energy to it in kinetic form. What is the difference between the original ray and the reflected ray? its frequency decreases? Malypaet (talk) 23:01, 29 March 2024 (UTC)


 * Yes. PianoDan (talk) 01:03, 30 March 2024 (UTC)