Is it possible theoretically to know where and when the Long March 5B will be landed approximately?
Take it from Jonathan McDowell @planet4589's tweet:
The EU SST prediction is narrow enough that we can start to talk about location now!
In particular, none of the orbits within the predicted window cross the northwestern US or the mid Atlantic seaboard.
At the time of asking, No, but as we get closer the answer increasingly becomes Yes.
We can see from https://aerospace.org/reentries/cz-5b-rocket-body-id-48275 that the uncertainty in the time of reentry is currently1 +/- 8 hours. About 2.1 days ago it was +/- 21 hours.
1actually about 7 hours ago
07 May 2021 18:55:50.470 UTC the latest updated prediction posted on the site as of the time of writing.
Orbit Epoch 07 May 2021 18:55:50.470 UTC
Predicted Reentry Time 09 May 2021 04:19 UTC ± 8 hours
Contributors to uncertainty include variations in the density of the Earth's atmosphere primarily around 150 km and below (where the spacecraft does most of its velocity loss) and the aerodynamic drag of a rocket body of unknown orientation (probably tumbling).
Past performance is not indicative of future results
From CNN's Rocket debris expected to crash into Earth soon
CNN’s Kate Bolduan: It seems even the smartest people aren’t able to calculate where this is going to land, yet. Why can’t they?
Ret. US Astronaut2 Scott Kelley: Well it’s because the satellite is spinning, and when something is spinning like that it doesn’t have a stable trajectory; it’s hard… and so the drag is always changing.
2 cmdr STS-118, EXP-26, EXP-45, EXP-46
click for larger
left: "Doppler variations with a period of 4.5 seconds detected by radar MFDR-LR during the pass, which help infer the rotation of the object" right: "Signal-to-Noise Ratio (SNR): the ratio of the signal power to the noise power detected by radar BIRALES during one pass, with periodicity of the peaks visible about every 2.5 seconds"
The orbital period is about 88 minutes now, so an uncertainty of 8 hours means that currently one can only narrow down the location to a large swath of the Earth (roughly half of the Earth's surface) where it will happen.
As we get close, this will be come narrowed down first in terms of what part of the Earth the orbits cover (each orbit moves by about 22 degrees in longitude).
So when the uncertainty narrows to +/- 1.5 hours you'll know it will reenter +/- 22 degrees in longitude from the next-to-lat orbit and +/- 41.5 degrees in latitude, since that's the inclination of the orbit and it can't go (much) farther north or south than that.
Further: if you want to consider probabilities, those orbits spend most of their times far from the equator, so the most likely areas are concentrated between say 30 and 41.5 degrees both sides of the equator.
above: Source captured at
2021-05-08 02:00 UTC below: Source captured at
2021-05-08 04:00 UTC
We can talk latitude probabilities any time!
From this answer to the 2018 question Tiangong-1 reentry impact place probabilities:
From the pros, from the Spaceflight 101 article Tiangong-1 Re-Entry, click for full size:
Even more interesting is the time-binned histogram rescaled by $1/ \cos(\lambda)$ for surface area rather than latitude, as recommended by @Litho's comment. If you were looking for debris, or looking to avoid getting hit by debris personally, this would be the plot for you.