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Gravity is relate to distance in inverse square manner. It is a weak force yet had the highest reach of all 4 types (Electromagnetic, Gravitation, Strong Nuclear, Weak Nuclear). In modern physics, the gravity is explained in the manner of space-time curvature and gravity is like a dent from mass seated on the space-time field and the curvature would reduce at distance but never becoming zero.

Some fun fact to know, at ISS station the gravity is at 8.67 m/s2. Yes, there is gravity but the reason that they are in micro-gravity at only 400 km height is because the ISS station orbiting the earth at almost escape velocity of 10.8 km/s. If the ISS doesn't travel at such speed, the gravity would bring it down to earth within 5 - 10 minute.

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Q: Why value of g not become zero on any height?
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