Database design for search of geocoordinates

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In a MySQL database I have tracking data of animals (elephants). Currently the design is a follows:

timestamp(INT) | individualID(INT) | longitude(DECIMAL) | latitude(DECIMAL)

Now I'd like to ask several questions to the database

  1. What is the closest individual at time t?
  2. Which individuals are around (perimeter 50km) at time t?
  3. Which individuals are present in the reservation at time t? (reservation is given by a polygon)

Is there some built-in functionality available for MySQL? Should I choose a different database?

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