Why do we use gravitational force in earth by relating just the mass of an object with the acceleration produced by the gravitational field: F g = m ⋅ g → And when we're dealing with planets, we use a relation defined by the masses of two planets, distance squared and gravitational constant: F g = G ⋅ M 1 ⋅ M 2 d 2 I really don't get why we use just the first relation here on earth, because we're dealing with a interction between two objects... It's because our mass is irrelevant??

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Why do we use gravitational force in earth by relating just the mass of an object with the acceleration produced by the gravitational field:      F          g        =  m  ⋅            g      →      And when we&#039;re dealing with planets, we use a relation defined by the masses of two planets, distance squared and gravitational constant:      F          g        =  G  ⋅                    M                  1                    ⋅              M                  2                            d              2            I really don&#039;t get why we use just the first relation here on earth, because we&#039;re dealing with a interction between two objects... It&#039;s because our mass is irrelevant??

Corinne Choi · Accepted Answer

The second equation is always correct, and you can derive the first equation from it.Here on the surface of the Earth, d is the radius of the Earth       r    e   plus our height h.  F  =  G                    M        e                    M        2                    (              r        e            +      h              )        2            The radius of the Earth (6,371 km) is huge compared to our height above the surface (at least, when we&#039;re near the surface), so we can simplify the equation by assuming       r    e    ≫  h and therefore       r    e    ≈      r    e    +  h  F  =  G                    M        e                    M        2                    r      e      2      G,       M    e   and       r    e   are all constant, so we bundle them all into another constant   g  =            G              M        e                    r      e      2       and voila  F  =  g      M    2  It&#039;s because our mass is irrelevant?No, it&#039;s because the equation assumes that our height above Earth&#039;s surface is negligible compared to the radius of the Earth (which most of the time, for me at-least, it is).Example: Suppose I&#039;m a 70 kg man whose just spent the last week hiking up Mount Everest, which is 9 km above sea level. Using the correct equation we get  F  =  G            70              M        e                    (      6      ,      371      ,      000      +      9      ,      000              )        2              =  685  NUsing the approximate equation we get  F  =  70  g  =  687  Nwhich is about 0.3% different. Whether this is an acceptable error or not will depend on how precise you need your calculations to be, but for every-day purposes it&#039;s probably fine :)

Merati4tmjn · Accepted Answer

We use the first formula for earth based calulations because  G  ⋅            M              1                    d              2              =  gto a good approximation. We used the second formula for planets because we do not have an easy simplification. So to put simply, they are the same formula but one just has a nice simplification.

Why do we use gravitational force in earth by relating just the mass of an object with the accelerat

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