Exploring the Relationship Between Gravity and Mass: Why Does F=mg?

[stallion]

I am trying to figure out why F=mg corresponds to question number two below.

First let's assume a object with mass 70kg and then calcutate the force of gravity in two different scenarios:

Determine the force of gravitational attraction between the Earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.37 x 106 m from Earth's center.

Crunching the numbers yields 688.1 N

#2

Determine the force of gravitational attraction between the Earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above Earth's surface. This would place the student a distance of 6.38 x 106 m from Earth's center.

This yields: 686 Newtons at a distance of 40,000 feet.

Now use the 2nd law

F=mg (70kg)(9.8m/s^2) equals 686 N

Why is the 2nd Law calculation the same as the calculation at 40,000 feet?

I realize that this is a very small difference (less than 1%) between the two
numbers.

Thanks

 

[Yegor]

The 2nd law is the same in all inertial coordinate frames.
You can try using F=G*m*M/(r^2) (F=mg is approx. formula near the Earth's surface). Is there a noticable difference?

 

[yourdadonapogostick]

g changes with distance

 

[stallion]

g changes with distance

I know but what I am saying is that the force of gravity in #2 above (40,000) feet above the Earth is closer to f=mg than example one at sea level.

It would seem that the sea level calculation would be closer to f=mg.

 

[krab]

The acceleration of gravity is not an absolute constant. It would be constant if the Earth's density was spherically symmetric and if the Earth were accurately a sphere and if there was not centrifugal component (earth not spinning). None of these 3 are true. In fact the variation in g is 1/2% from pole to equator at sea level. So though your 1/3% discrepancy can be accounted for by an elevation change, it can also be accounted for by a latitude change.

 

[peterbone]

g is the acceleration experienced at the surface of the earth. That's how it's defined.