Many of us have an overly simplistic view of orbital mechanics that fall well short of how it works in the real world. Take the example of India's failed Vikram lander [1]:
> The official said that predicting orbits below 50 km is very tricky and usually they are estimated with an accuracy of plus/minus 1 km. If the lander`s predicted height was at 30 km, the actual orbit height may remain anywhere between 29 to 31 km.
> Similar will be the error in horizontal direction. Such errors occur as local gravity varies widely due to large variation of density of mountains and plains.
Newton's gravity equations deal with bodies like the Moon as having uniform mass. That's not he case and it matters.
Fun fact: China's Three Gorges Dam slowed down the Earth's rotation by 0.06 microseconds per day [2]. That's actually not a big deal because the rotation has variance all of its own from tides, weather, etc.
So even if you had a density map of the Moon you'd still have to account for variance added by rotational variation.
> Newton's gravity equations deal with bodies like the Moon as having uniform mass.
Let’s not make a joke of ourselves. Newton’s gravity equations deal perfectly well with non uniform masses. You just need to integrate properly.
But all of this is beside the point. Obviously you are not going to land open loop. You need sensors which tell you where you are and how fast you are going.
> China's Three Gorges Dam slowed down the Earth's rotation by 0.06 microseconds per day [2]. That's actually not a big deal because the rotation has variance all of its own from tides, weather, etc
I'm confused, how is the mean changing less impactful due to relatively high variance? If the was no variance at all, would .06us be a disaster?
It may be a disaster, but if we manage to live with variance that are higher than 0.06 microseconds per day, we should manage this small change in an average.
> The official said that predicting orbits below 50 km is very tricky and usually they are estimated with an accuracy of plus/minus 1 km. If the lander`s predicted height was at 30 km, the actual orbit height may remain anywhere between 29 to 31 km.
> Similar will be the error in horizontal direction. Such errors occur as local gravity varies widely due to large variation of density of mountains and plains.
Newton's gravity equations deal with bodies like the Moon as having uniform mass. That's not he case and it matters.
Fun fact: China's Three Gorges Dam slowed down the Earth's rotation by 0.06 microseconds per day [2]. That's actually not a big deal because the rotation has variance all of its own from tides, weather, etc.
So even if you had a density map of the Moon you'd still have to account for variance added by rotational variation.
[1]: https://www.zeebiz.com/india/news-on-indias-vikram-lander-di...
[2]: https://www.kinetica.co.uk/2014/03/27/chinese-dam-slows-down...