That depends how big an "object" you want to accept. Lots of micrometeorites - pieces of dust, basically - fall on Earth each day. The Wikipedia article on micrometeorites estimates about 1017 particles larger than 10 µm a year. That's many millions every second.
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There are two objects in the solar system which currently support life, those being the planet Earth and the international space station.
Many celestial objects, like planets, moons, stars, and galaxies, rotate on their axes. This rotation causes phenomena like day and night on Earth, and changes in visibility of certain parts of celestial bodies.
There are four seasons on planet Earth: spring, summer, fall (autumn), and winter. These seasons occur due to the tilt of the Earth's axis as it orbits the sun.
The sun does not orbit the earth. Instead, the earth orbits the sun, completing its orbit once a year. This movement is what creates the changing seasons on our planet.
The International Space Station orbits the Earth about 16 times a day, with each orbit taking approximately 90 minutes to complete.