1. The variation in gravity due to height is given by g'=g(1-2h/R). Here, if the value of height is kept just equal to the radius value, then the result is -ve. This implies that when a body is projected from the earth, after it crosses the boundary of gravitational pull of the earth, then there must be another heavenly body just after that boundary to pull the object towards it since only the direction is changed not the magnitude, isn't it?

2.

3. I am no Physicist - BUT.

There is no such thing as "crosses the boundary" - EVERY single Object in the Solar System exerts SOME Gravity - no matter how far away you get from it.
There is still a Gravitational Component from the Sun - right out at the edge of the Solar System, the edge of the Oort Cloud - which is believed to possibly extend for nearly 1 Light Year into Space.
Hell - the Sun attracts Proxima Centauri and vice versa.

There is no place where there is not Some attraction from the Earth - as the Gravitational Force g = G x Mass / radius^2.
Where G is the Gravitational Constant - something just over 6.0 x 1^-11 m/sec^2.
You can see that there is No Place in the Universe where the Result will be ZERO - so there is no "boundary of gravitational pull".

Sorry - but I have been looking at Gravitational forces at VERY BIG distances - and this is true.

Regrettably - I do not remember the Exact Value for G the Gravitational Constant ( off hand ) - but it is something like 6.3 something x 10^-11.

4. The formula you posted is only an approximation valid for heights much less than the earth's radius.
Variation of Gravity

5. Originally Posted by prafulla
The variation in gravity due to height is given by g'=g(1-2h/R). Here, if the value of height is kept just equal to the radius value, then the result is -ve. This implies that when a body is projected from the earth, after it crosses the boundary of gravitational pull of the earth, then there must be another heavenly body just after that boundary to pull the object towards it since only the direction is changed not the magnitude, isn't it?
You seem to be mixing (at least) two different issues:

1. The variation of gravitational acceleration with height above the Earth (Harold already commented on that)
2. The "two-body problem". See here.

6. it's 6.67*10^-11

7. That's Gravitational constant!

8. Btw, are we slightly lighter at noon when the sun is above you (pulling us a bit up?) than at midnight when the sun is on the other side of the planet?

9. Yes, the Suns gravitational influence is on you but so is the Moons and a big building you might be in at that moment. The building shows more gravitational attraction to you than the Sun.

10. Everything attracts everything else. Your laptop or desk top is attracting you and you are attracting it also. The greatest pull you experience is that of the earth due to the fact that r^2 is So small. And the distance between you αη∂ sun or moon is far too much Ƒor the gravitational attraction to have any major influence in our day to day life(but it those) and plus your mass is too small.

11. Originally Posted by icewendigo
Btw, are we slightly lighter at noon when the sun is above you (pulling us a bit up?) than at midnight when the sun is on the other side of the planet?
Not quite. you are lighter at noon and midnight than you are at sunrise and sunset. This is the result of tidal forces (the differential in the Sun's gravity over the diameter of the Earth).

12. Originally Posted by Neverfly
Yes, the Suns gravitational influence is on you but so is the Moons and a big building you might be in at that moment. The building shows more gravitational attraction to you than the Sun.
Well, maybe not. Consider something like the QE2. In order for its gravitational attraction to be equal to the Sun's, you would have to be 1.8 m from its center of gravity. But that puts you inside the ship and this means you don't feel the full pull all all of its mass.

13. I don't know how much mass the QE2 has.

The pull of the Sun on a person is approximately 6 mm per second per second, given a distance of 149,000,000 km. That's still very slight.

14. Originally Posted by Neverfly
I don't know how much mass the QE2 has.

The pull of the Sun on a person is approximately 6 mm per second per second, given a distance of 149,000,000 km. That's still very slight.
QE2 has a displacement of ~ 70,000 tonnes gross.

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