The droplets of water outside the glass likely came from condensation. When warm air comes into contact with a colder surface, such as the glass, the air cools down and can no longer hold as much moisture. This excess moisture then forms droplets on the cooler surface, which is the condensation you see on the outside of the glass.
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A rainbow forms when sunlight is refracted, reflected, and dispersed by water droplets in the air. The water droplets act like tiny prisms, separating the sunlight into its various colors, which we see as a rainbow.
The water in the outer cup likely came from condensation due to the temperature difference between the cold inner cup and the warmer room temperature. As the air inside the cup cools down, the moisture in the air is released and condenses on the outside of the cup.
Fog forms when the air near the ground is cooled to the point where it can no longer hold all of its moisture, causing the excess water vapor to condense into tiny water droplets suspended in the air. This condensed water droplets scatter and reflect light, making the fog visible to our eyes.
The gases in Earth's early atmosphere likely came from volcanic activity, outgassing from the Earth's interior, and impacts by comets and asteroids. These processes released gases such as water vapor, carbon dioxide, methane, and ammonia into the atmosphere.
Water on the planet is believed to have originated from comets, asteroids, and volcanic outgassing during the early formation of the Earth. These sources brought water to the planet, which then accumulated in oceans and other bodies of water over time.