I just saw articles which say the Harvest moon will be visible in the US.
Apart from the US, in which other country can people see it? Can I see it from India?
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"Harvest moon" just means the full moon at around the time of the equinox on September 21.
The full moon is low in the sky during summer (June and July in the Northern Hemisphere) and high during the winter. So September is a month when the full moon is much higher in the sky than the moon in August. In the past this allowed harvests to continue after dark.
The full moon in September can be seen all over the world, but it may not have the same cultural significance that it had in Europe and North America.
Because the Moon phase changes relatively slowly (especially at the Full Moon), a similar Moon phase can be seen from all places around the world.
For example, the Full Moon in September 2019 occurs at 4:33 UT. If the Moon is visible from your location at that time, then you can see the Moon when it is exactly "Full". If Moon is not visible until 5 hours later because of your location, then you technically do not see the Full Moon (100% illuminated), but you see the Moon at a slightly less illumination (maybe 99%). The difference is minor for most purposes.
Naturally, the time at which the Full Moon is visible from one's location could occur the day before or after the exact time of the Full Moon.
Not directly related to the phase, but the situation in which viewing the Moon at a specified time is more important is when an occultation or close conjunction occurs. If the Moon is close to Jupiter at X hours UT for example, then the separation will be much larger when viewing it several hours before or after that time.