I'm very sorry for being insistent, but how does that predicts expansion of the universe. In many articles I read this:
"From that portrait [CMB] we are able to accurately measure the ingredients in the universe. How much normal matter, how much dark matter, how much neutrinos, how much...
I've been searching for weeks and still with the doubt.
I just know scientist look the content of the CMB and with general relativity calculates the expansion rate today that is 73 km/s/Mpc, but nowhere does it say how exactly. What does the contents of the universe have to do with the...
In the IB diploma program, they ask for a "Mathematical Exploration", where I have to deal with a topic with mathematical tools.
For example:
How to get the perfect exit of Gymnastics Bars?
In "exploration" you have to see the measurements, the angles, velocity trajectories, mathematical tools...
<Moderator's note: Moved from another thread.>
The spacecraft is Orion, with a Speed of 10.000 km/s. The spacecraft will use the gravitational asisstance of the Sun in order to get to Alpha Centauri.
Which trayectory have to take? It's on January, feel free to mention angles or other math...
I want to know what mathematical tools I would use in the event that we have the right technology. So far I have only calculated the distance to Alpha Centauri using parallax.
I need any other tool: hypothetical speeds of ships, trigonometry, vectors, trajectories, any tool that is necessary...
I honestly don't know, that's why I'm asking. I just want to know if the mass of spacecraft affects the speed of this one after the gravitational assistance.
The spacecraft "Helios 2" (with 100 kg of mass) used the Sun to get a speed of 250.000 km/h using gravitational assistance, I want to know if the mass of the spacecraft influences the result of the speed. I mean, if the spacecraft mass 10.000 tons, the speed would be less of more?
https://en.wikipedia.org/wiki/Future_of_an_expanding_universe "Over an infinite time there could be a spontaneous entropy decrease, by a Poincaré recurrence or through thermal fluctuations (see also fluctuation theorem)"