Gravitational force near and away from earth's surface

[kindlin]

So, I asked myself the question, "why does the Earth's force of gravity effect us so dramatically on the surface of the earth, but seems nonexistent while just a couple hundred miles up?"

I answered that question myself, after thinking more about it, because the idea of an orbit is that you constantly fall towards the earth. So just like the simulated weightless environment a plane can create, so is a space station a simulated weightless environment.

However, in trying to answer this question I tried to calculate the Newtonian gravitational force one one would feel at the surface, and here's what I got: (m1=earth, m2=unity)

F = G * m1 * m2 / r^2 = 6.67e-11 * 5.97e24 * 1 / (6378.1 / 2)^2 = 39191036.5 N/kg

So if I weighed 80kg, I would experience 39191037*80 = 3135282921 N

So, what did I do wrong? My feet obviously aren't holding up 314e6 N.

Also, knowing that we feel 9.81*m Newtons sitting on the surface, it would follow that G*m1/r^2 = 9.8:
G = 9.8*r^2/m1 = 9.8* (6378.1 / 2)^2 / 5.97e24 = 1.6705e-17

Thoughts?

 

[Drakkith]

1. You're using Kilometers for R. Use meters instead.
2. Don't divide your value by 2. 6,378 is the radius of the Earth in Km, not the diameter.

 

[mpresic]

The radius of the Earth needs to be expressed in meters not kilometers also do not divide the radius by 2?

 

[kindlin]

Oh man, I'm bad. Thanks guys, lol...

 

[PJC01]

I can provide an explanation for why the gravitational force near and away from Earth's surface seems to differ. The concept of gravity is based on the mass of an object and the distance between two objects. The closer the objects are, the stronger the gravitational force between them.

On the surface of Earth, we are only a few hundred miles away from its center, which means we are very close to the mass of the Earth. This results in a strong gravitational force that we can feel and experience. However, as we move away from the surface, the distance between us and the Earth's center increases, resulting in a decrease in the gravitational force.

Moreover, as you correctly pointed out, objects in orbit are constantly falling towards the Earth, but their horizontal velocity keeps them from actually hitting the surface. This creates a feeling of weightlessness because the gravitational force is constantly changing as the object moves closer and farther away from the Earth's center.

In terms of the calculations you provided, it is important to note that the formula you used (F = G * m1 * m2 / r^2) is for the gravitational force between two objects. In this case, you are calculating the force between yourself and the Earth's center, which is not the same as the force between yourself and the surface of the Earth. The force between yourself and the surface of the Earth would be much smaller, as the surface is not the center of the Earth.

I hope this explanation helps to clarify why the gravitational force near and away from Earth's surface differs. It is a complex concept, but understanding the relationship between mass and distance can help to make sense of it.