If the sun pulls such a big mass like earth with its gravity, then won't the astronauts be pulled towards it a much nearer?

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Solution

Objects in orbit are attracted to each other, it's just their mass is small enough that the force of gravity between them is infinitesimal. Gravitational acceleration is dependent on mass and distance. In a scenario where a 150 kg astronaut is 10 m from a 80,000 kg Space Shuttle, the astronaut would be pulled toward the Shuttle at 5.336e-8 m/second squared. That's 0.00000005336 as opposed to the Earth's surface gravity of 9.8 m/second squared, and ~ 8.7 m/second squared at orbital altitude of 375 km. In other words, the Earth's force on the astronaut would be over 160 million times stronger, if it wasn't balanced by the exactly opposing centrifugal force due to their orbital speed of 7,682.5 m/s at that same orbital altitude.

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