Hello to all learned gentlemen,

My question is related to gravity. As all of us know that in our solar system, every planet is under gravitational pull of the Sun. So, why the spacecraft, spaceman etc. in zero-space (vacuum) do not fall towards the Sun?

The Earth orbits the Sun at 66,000 mph so centrifugal force which effectively wants to move it away from the Sun is balanced by the Sun's pull on the Earth so it stays about the same distance away. A spaceship has the same speed as the Earth (if it didn't, it would see the Earth fly away at 66,000 mph), so is not pulled towards the Sun either. If however a spacecraft lost it's velocity, it would then start to be pulled into the Sun.

There is no "balancing" of centripetal and centrifugal accelerations -- they are the same accelerations in difference reference frameworks. In Newtonian physics particles always move in straight lines at constant velocity unless they are subjected to a force. And the force that accelerates all these bodies away from straight-line motion at constant speed is gravitational acceleration.

They do fall toward the sun -- but they do not fall into the sun. If it were not for gravity all the planets and spacemen would move in straight lines with constant velocity.

Newton called his idea Universal Gravitation, because the same gravity that causes apples to fall to ground causes the moon to fall around the Earth. But the strength of acceleration is inversely proportional to the distance to the center of the Earth.

Apple: distance 6.4 million meters, acceleration 9.8 meters per second squared
Moon: distance 385 million meters, acceleration 0.0027 meters per second squared

So the constant of falling towards Earth is distance squared times acceleration:
≈ 4.0 × 10^14 m³/s² is the same for the Apple and the Moon and all the satellites.

(A reference book gives this same constant to higher precision: 3.98600433 × 10^14 m³/s² and for the sun, 1.3271244 × 10^20 m³/s² and in Newton's Universal gravitation this is the product of Newton's constant and the mass of the earth or sun. )

So do we fall towards the Earth or the Sun? We fall towards both at the same time -- but because everything on Earth is falling around the sun at roughly the same velocity and acceleration we rarely notice. But the tides of the ocean are related to both the Moon's and Sun's gravity on parts of the oceans being different due to slightly different distances.

CRC Handbook of Chemistry and Physics, 81st edition (2000)
The Astronomical Almanac for the year 2007, U.S. Government Printing Office, Washington, and The Stationery Office, London (2005).
http://pdg.lbl.gov/2008/reviews/rpp2008-re...l-constants.pdf