Final answer:
The temperature of a water droplet falling from a height of 5050 kilometers on a planet similar to Earth, but lacking an atmosphere, would experience negligible changes since atmospheric effects such as friction or air compression, which could affect temperature, are absent.
Step-by-step explanation:
When considering how the temperature of a water droplet would vary as it falls from a height of 5050 kilometers on a planet similar to Earth but without an atmosphere, we have to take into account that there are no atmospheric effects such as air friction or heat exchange with the surrounding air. Therefore, the temperature of the droplet would primarily be affected by adiabatic heating due to compression under the influence of the planet's gravity. However, since there is no atmosphere to compress the droplet, the change in temperature would be negligible.
In the absence of atmospheric friction, the droplet would accelerate due to gravity and reach its terminal velocity, converting potential energy into kinetic energy. On Earth, a water droplet's temperature can be affected by the adiabatic lapse rate, which describes how air temperature changes with altitude, but in a vacuum, this process does not apply.
It is important to note that if the planet had an atmosphere, things would be substantially different. As the droplet fell, it would pass through different temperature zones and could possibly evaporate into water vapor if the temperatures were high enough. Additionally, contact with the atmosphere could result in frictional heating, which would raise the temperature of the droplet. But in a vacuum, these effects are nonexistent.