Does russia have the military strength to accomplish that?
Speaking purely in theory here.
Russia has the strength to take what you asked, yes, assuming no outside intervention. To be honest, unless foreign troops were in place ahead of time, they could do so even with foreign intervention unless there was a massive and prolonged war. That's not in the cards, so, yes, Russia can take up to the Dniepr.
If Russia is going to do an invasion and annexation, then I don't think they would stop at the Dniepr. I think they will take the southwest as well (Odesa), cut any rump Ukraine off from the Black Sea and possibly link up with Transdnistra.
That said, I could see Russia creating a client state (Malorus?) instead of outright annexation. It would be a puppet, of course, but it would be a russophonic buffer between the west and Russia proper. It would also allow them to claim to be liberators rather than conquerors. If the Donbas is anything to go by, it would be a sh*tshow though.
I could also see the Russians taking all of Ukraine and installing a Lukashenko-like puppet.
What will happen? I don't know.
Rant time. About the situation and the thread here.
The whole thing is wildly sad. None of it needed to happen. Yanukovich really screwed up the response to the Maidan protests. They were in the process of dying out when he turned the water cannons on in winter in below freezing weather. Ukrainians did not like him, but the Left Bank despised Timoshenko et al for their rhetoric and stupid infighting. However, when you turn the water cannons on at that time, well, people who live in very cold places can understand.
Russia screwed up their response. Ukraine was not going to let into NATO any time soon, probably not in my life time and even if they had become full members of the European Union. Had Ukraine started the process to join the European Union, it is highly probable Ukraine might get stuck like Turkey has: there are far, far too many fundamental problems to let Ukraine in. Even so, had Ukraine passed the sniff test, then it
still would have been beneficial for Russia. The borders of Ukraine are porous and corrupt: trade would have continued even if sanctions were ever levied on Russia. Money from the EU would have poured into Russia. Russia could have fully rebuilt its military without the economics hits Russia has taken. It could have also intervened even more so beyond Syria and Libya.
The post-Yanukovich government screwed up, but that had a lot to do with the fact they were as coherent as a scurry of methamphetamine addicted squirrels. They were worse than the Orange Revolution team.
Finally, America screwed up. Many, many times. There is a fundamental lack of understanding of the Russians and Russian culture. This has been wildly problematic since Clinton[1]. The dismissal of Russian needs and goals since the 1990s made this inevitable. The incident at the Pristina airport and the problems of Transdnistra should have been the writing on the wall Russia was going to respond badly at some point. The lack of US help when the banking crisis took place in the late 90s made average Russians turn against the US, too. Even Putin's attempted reset after 9/11 fell on deaf ears in Washington, DC, producing another screw-up. In addition, when Putin put the "Little Green Men" in Crimea, the US could have moved the 173rd into Crimea as well. No fighting would have happened if the Americas moved fast enough. The LGM may have melted away, the 173rd might have become peace keepers or Russia may have still received Crimea; however, the Donbas War would not have started. The reason the LGM were not wearing patches or insignia was to test how the West, especially, America would respond. Obama just talked. Russians - in my experience, from the poorest to the crazy richest - despise 'just talking' because, as the saying goes 'talk is cheap' and, in this case, it shows weakness in their mind. It made Russians believe the Budapest Memorandum was just more cheap talk - empty promises - by the Americans (and British).
In the end, people suffer and continue to suffer. There is
still a war going on in the Donbas. OSCE negotiates a ceasefire every New Year's, but many, many people die every year from shelling and snipers. Thousands of mortar and larger shells are fired every year from the Ukrainian Army and the DNR, LNR, etc. militias.
People I know and love have been killed due to this stupidity. People have lost homes they have had for decades. People have died alone because their friends and family were forced from the places they grew up in. People I know and love have extreme PTSD from the horrible things they have seen. People became refugees on both Banks and on both sides be despised from coming from the other. I see people who used to be friends now spitting at each other over flags. People I knew and loved to have dinner with, verbally joist with, and ranged from members of the Party of Regions to die hard anti Russians who lost family to the Holodomor or even the NKVD (some were not young at all).
ALL parties are at fault. This is a massive tragedy. The incompetent Ukrainian governments. The uncaring, self absorbed and distracted Americans. The Russians. The Europeans. ALL of them. There are no heroes here. There is just incompetence, paranoia and stupidity. And vast oceans of propaganda.
Ok, enough. I had hoped this thread would be interesting and informative. It is always good to hear other points of view and have people evaluate sources, scenarios and give information/perspective they may only have. Instead, I see only braggadocio and ignorance. Sift through data and tone down rhetoric. There are a number of well connected people here who can do interesting analysis. Do that.
Rant over.
MODs: if you think I am out of line, nuke the post and chastise as you see fit.
1. I heard it told once - as a snarky commentary, not meant to be taken literally - after the fall of the Soviet Union, Russia said to America, "Oh, good! We don't have to be enemies anymore! We can run the world together!" America is said to have replied, "Oh, good! We don't have to be enemies anymore! Now, I can ignore you!"