The day is a unit of time and is an SI-derived unit with the symbol d.
On Earth, it is defined as 86,400 seconds and is approximately the time it takes for the earth to complete a full rotation around its axis. In the earlier days, this was measured by waiting for a cast shadow to match a template drawn from the previous day's shadow.
There are 365 days in a year and, on average, 30.42 days in a month.
The unit day has many different variants; depending on what is used to measure the Earth's rotation. In a sidereal day (a rotation with respect to a distant star or constellation, not the sun), there is actually 4 minutes less than 24 hours in a cycle.
The tropical year is a unit of time that is a multiple of an SI unit. We have used the symbol at.
The average tropical year up to the year 2000 was 365.2422 days of 86400 seconds.
The phrase “tropical” comes from the Greek for “turn”; tropikos. Following this, and where the “turn” referred to is the same as that defining the tropics of Capricorn and Cancer (the extreme latitudes North and South where the sun can still appear directly overhead or perpendicular to the Earth’s surface); a tropical year is known as the time it takes the sun to complete a full cycle of seasons and return to the same relative position to the observer on Earth.
In 1627, Johannes Kepler used the findings of Tycho Brahe and Waltherus (the Rudolphine Tables) to establish the mean tropical year as 365 solar days, 5 hours, 48 minutes and 45 seconds.