The Allies estimated that there would be a half million to a million casualties from a mainland invasion of Japan, just on the Allies side. And estimates of Japanese dead would be in the millions. These estimates have been debated and continue to be, but they played into the decision to drop the bombs.

In Japan, anyone over the age of 12 was conscripted into a homeland defense force and women/children were being trained to repel invaders with pikes. The Allies would be faced with fighting peasants clutching spears, slaughtering them with modern weapons. And as we saw in Vietnam and Iraq, guerrilla insurgencies can cause many casualties even against better armed occupiers.

Also, Japan was facing starvation already, and a drawn out invasion would only make this worse.

Can it ethically be justified? The common wisdom is that the ends don't justify the means. If you believe this, then the bombs weren't justified. If you believe that the bombings saved millions of lives, then you can justify the acts.

This topic is still debated today and strong arguments are made on both sides.

No; the strategic bombing of civilians is always indefensible from an ethical standpoint, the atomic bombs detonated over Hiroshima and Nagasaki simply being two of the more egregious examples of this given both their nuclear nature and timing after the effective defeat of Japan. In almost all systems of ethics, murder is one of the most severe wrongs possible. To engage in it on a mass scale, via any means, against defenseless non-combatants is as disgusting as it is wrong and is explicitly contrary to International Law.

The most common justification for the wholesale murder of civilians in the specific case of Hiroshima and Nagasaki is that the bombings were required to force the capitulation of Japan; that without them, the Japanese would have mounted a defense of the Home Islands to the last man, woman and child. That this surrender was needed to save the (frequently claimed) millions of Allied soldiers from death in the invasion.

Looking at the estimates of force depletion in Operation Downfall (the planned invasion of the Home Islands by the Allied Forces) by the commanders and staff actually involved in the theatre of operations in the time period immediately before the bombings, we see an estimated 45,000 causalities in the first 30 days (Nimitz) and 23,000 in the first 30 days, and 105,000 after 120 days (MacArthur). These estimates are actually significantly lower than the casualties sustained when compared to the iconic Operation Overlord aquatic invasion of Europe, in large part due to the advanced state of attrition which the Japanese military forces had already suffered. The bulk of its Army was abroad, confined to areas the Empire had conquered by the destruction of the Imperial Japanese Navy. The situation, from the perspective of the Japanese military, kept going from bad to worse. If you look at the numbers present in these two studies, the one by Nimitz's staff in May, and MacArthur's in June, you see this reflected in the reduction in estimated Allied losses; the Japanese have less and less capacity to inflict damage on the invaders, and the models used to determine the risks in an invasion reflect this evolving situation. Earlier reports and estimates are consistently higher than those which were made closer to the actual time frame of operational execution, accounting for their inaccuracy with regards to the situation on the ground at the time of the bombings.

Ultimately, the fact that Operation Downfall would have been less bloody than the already accomplished Operation Overlord and subsequent liberation of Europe is besides the point, as Japan was already effectively defeated. Resource-poor and it's pre-war stockpiles long since expended, it's Navy defeated and surrounded by hostile powers, Japan had no real capacity to project force by the time the bombs were dropped on Hiroshima and Nagasaki. That elements of the Imperial Government were already seeking a negotiated peace is a fact. One of the principle sticking points, the disposition of the Emperor following Japan's surrender, was left murky in the Potsdam Declaration on the Allied Powers' war goals with regards to Japan. This uncertainty was compounded by the demands of the Allies for an unconditional surrender. Clarity on behalf of the Allied Powers on this particular topic would have sped the eventual, conditional surrender which ultimately retained the Emperor in any event. Finally, the tipping point was not the destruction of Hiroshima and Nagasaki, but the declaration of war by the Soviet Union (long dreaded by the Japanese Empire); against the might of the Red Army, even the most optimistic of the Japanese High Command knew they had no hope.