Borzol said:
Hello,
I would like to know if it is possible to measure the current speed of the Earth relative to the point of big bang?
Phinds and Chronos gave you good answers already. I'll repeat with more detail in case you want a longer answer.
Expansion is a uniform pattern of increasing distances. It is not "away from" any point in space that we can point to and it has no unique direction. So it is not like ordinary motion which has some direction and where you are going somewhere.
So your question is not about expansion. It is about our small random motion relative to the absolute reference defined by the CMB.
Things have small random motions relative to the universal rest.
In the case of the solar system we are traveling roughly 370 km/s in the direction that is marked in the sky by the constellation Leo.
What is the CMB? It's a soup of ancient light that dates from around 380,000 years after start of expansion. That's when the cloud of hot gas cooled enough to allow light to run free and the glow of that gas was released to travel essentially forever. The ancient light comes equally from all directions (or very nearly, within 1/1000 of one percent). And it is the same thermal mix of wavelengths in all directions. It's uniformity reflects the uniformity of the original cloud of hot gas which is it the glow from.
That hot gas which was uniformly everywhere is our stationary reference for what we mean by being "at rest". So being at rest means being at rest with respect to the soup of ancient light.
In the case of the solar system we know we are moving in the direction of Leo because there is a Doppler hotspot in the ancient light in that direction. the frequency of the light is about 1/10 of one percent higher in that direction. Slightly more, but roughly that much higher. The light is said to be that much "hotter" in the direction ahead of us, and that much colder at the point directly behind us. A Doppler effect. The light itself is uniform and evenly distributed thru space, as far as we can tell, only our own motion thru the soup of light shortens the wavelengths coming from directly ahead and lengthens the wavelengths coming from directly behind.Things have these small random motions relative to universe-rest because after the cloud cooled enough it began to condense into lumps, by its own gravity. And as the lumps formed randomly they began to FALL TOWARDS each other, and sail past, and adopt orbits around each other, and so on. A lumpy wispy structure developed.
So pretty much all the objects we see have some random individual motion, typically a few hundred km/second. In no particular preferred direction overall. Only what is locally dictated by local gravity, orbits etc.