The aliens have excess nuclear and chemical waste.
According to alien ethical codes, this can only be deposited on a planet with intelligent life. Fortunately, they have detected earth in range of their ships. About once every six hours, a ship will drop a million kilogram payload of highly radioactive waste on earth.
The more stringent aliens (around half of pilots) will responsibly insure their shipment lands on an area of high human inhabitant density. Morally lax aliens will dump at a random location on earth's surface. All aliens are required to approach close enough to earth for the shipment to free-fall, but it is too much effort to approach much closer than that. The only minor concern the alien CEO has is this might destroy human life on earth; if so he will be forced to spend all day locating a new planet with intelligent life.
Waste Quality Information:
Radioactivity levels similar to our own high level waste, may be arranged into chemicals not currently found on earth, may be toxic. It is a mixture of solid chunks, pastes, and liquids.
As long as one human is standing on earth, it is ethical to dump; however the aliens cannot be bothered to take special action to preserve human life.
Assume alien sensors can detect any humans present on the planet. On earth, humans are the only species counting as intelligent. The alien technology is sufficiently superior that humanity has no chance of winning a war against them. More aliens ships are continuously sent so a new vessel arrives at earth about once every six hours.
The aliens will dump on the largest population centers until no humans remain there, then switch to the next most populous place until no humans are left alive. While they aren't intending to kill of humanity, they will dump waste in this manner as long as any humans are alive. The only question is how long humans would survive, in our present condition if this kind of dumping happened.
How long can he expect to ethically dump before needing a new planet?