homework and exercises - Astronomical Constant in Astronomical units?

I'm doing a computer simulation of the solar system and I'm having trouble working with big numbers (implementation specific problem). So what would be the Newtonian gravitational constant $G$ in relation with the Earth mass instead of kilograms and astronomical units instead of meters?

Answer

This is a typical "unit conversion" problem. Write $G$ in SI units:

$$G=6.6738\times10^{-11} \frac{\text{m}^3}{\text{kg}\cdot\text{s}^2}.$$

Now find out how many kilograms are in an Earth mass, and how many meters are in an astronomical unit. Also consider converting seconds to some other more convenient measure of time so that $G$ comes close to unity. (Thanks, Davidmh.)

All of this should help you convert units. See this page for further help.

quantum mechanics - Matter waves and de Broglie wave length

The wavelength of a particle of momentum p is calculated using De Broglie relation. The de Broglie relation was postulated for what is called a matter waves. Now according to the statistical interpretation of QM we know that there is no matter waves. It is an abstract wave called the wave function which describes the particle probabilistically.

1- Is de Broglie relation still valid although matter waves do not exist ? and why?

2- If the answer to 1 is affirmative then what is de Broglie wavelength of a particle that is localized in space? (because now the particle will not have sharp momentum, hence not a unique de Broglie wavelength.)

wordplay - longest sentence using only one word and variants

This is an open ended puzzle of wordplay. Here's an example of acceptable words: reed, read, read, red, etc. They are linked by either different spellings of the same pronunciation (reed and read), or different pronunciations of the same spelling (read, read). Only words in the OED are acceptable.

The puzzle is to create a long sentence using only words from such a pool. Not all words in the pool need to be used, and adjacent words do not need to be linked. Which sentence is the longest?

Answers must start with the proposed sentence in bold, followed by explanations or commentary as desired.

Degenerate approaches are not acceptable. For example, suppose some buffalo are named Buffalo, after the spicy chicken wings. Both of these words are in the OED, including the capitalization of the later, however the city name of Buffalo is not. Now suppose some of their offspring are named Buffalo Buffalo. And suppose some of their offspring are named Buffalo Buffalo Buffalo. This leads to English sentences such as "Buffalo buffalo buffalo.", where the first lowercase word is the verb, to quote the OED, "To overpower, overawe, or constrain by superior force or influence; to outwit, perplex.", and the second lowercase word is the common name of a species of quadrupeds. Similarly, another sentence is: "Buffalo Buffalo buffalo buffalo.", as is "Buffalo Buffalo Buffalo buffalo buffalo." And so on. Grammatically simple sentences of any arbitrary length can be formed. Without this exclusion, the puzzle certainly has no ultimate answer.

I'm including the tag 'open-ended' because I suspect the ultimate winning sentence is unknown, though potentially computable someday given an appropriate database to form the pool of words and NLP.

enigmatic puzzle - A princess fell in love

Once upon a time there was a princess.

She fell in love with a prince, wrote him a letter and sent it via Celeste, who was always willing to help. The prince was Laniff III and was in love with the princess, too.

However, there were a lot of political issues between the two kingdoms, so they should have kept it covert. Unfortunately, Celeste was caught and they hanged her for treason.

The princess was devastated and cried her eyes dry. She was ready to go to the prince and give up her crown. So she hopped on a horse and started her journey.

What was the message in the letter?

Answer

I am sure it is:

Select the third letter in the last word of each sentence.

Forming,

I love you

Kirex and TwoBitOperation (and OP)'s constant hints which made it possible to solve this:

In the story appear two names: Celeste and Laniff III, which anagrammed can be read as Select E and Final F and the III as third. If we get rid of the spare E and the spare F we obtain Select Final Third. Therefore we can reach the conclusion commented on the first spoiler: Select the third letter in the last word of each sentence.

In factit made it ridiculously easy.

thermodynamics - What happens as you approach/cross the Planck temperature?

According to IFLScience, above the Planck Temperature (absolute hot) conventional physics break down.

My question is what happens as you approach this temperature, and, if it is possible, what happens when you cross it?

Answer

I expect it's impossible to cross the Planck temperature, just like it's impossible to cross absolute zero or the speed of light.

At the Planck temperature, you start producing miniature Planck-mass black holes, which are the hottest black holes that can exist. If you try to put more energy in the system, you would get larger black holes, which are cooler, and they would start absorbing stuff and cooling things down.

dark matter - What is a flat rotation curve?

Was reading about dark matter and the distribution of it throughout the galaxy. it said "For example, if rotation curves are flat this means-" what exactly does this mean?

electromagnetic radiation - How does the energy transfer in the near field of an antenna work?

Answering the question What is the relation between electromagnetic wave and photon? I wrote

The EM radiation of an antenna is measurable and it was found out that the nearfield of an antenna has two components, an electric field component and a magnetic field component. This two components get converted in each other, the induce each other.

Rob commented

@HolgerFiedler If the fields are a quarter-turn out of phase, the average value for the Poynting vector is zero and the wave is not transmitting any energy.

How does the energy transfer in the near field of an antenna work? And how does a standing EM wave inside a box work?