Universal law of gravitation

[ryryguy]

Homework Statement

At what height above the Earth's surface is the acceleration due to gravity 10% of that at sea level?

Homework Equations

F= Gm1m2/r(squared)

The Attempt at a Solution

I think some how one of the masses is moved over so that F/m=a and I think .10 is multiplied times something like (r squared) or (r + x)squared.

 

[G01]

As you said, F/m=a. When at the surface of the Earth at sea level:

$$\frac{F}{m}=\frac{GMm}{m(r+x)^2}=\frac{GM}{x^2}$$

where x= radius of Earth, and since at the sea level r would be zero.

Now what is 10% of this? After you find this, can you set up an equation and solve for the distance from Earth? If you need more help feel free to ask. Good Luck!

 

[m2003]

I can provide a response to this question by using the Universal Law of Gravitation, which states that the force of gravity between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. Mathematically, this can be represented by the equation F = Gm1m2/r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

To determine the height above the Earth's surface where the acceleration due to gravity is 10% of that at sea level, we can set up the following equation:

F/m = a = Gm1m2/r^2

Where F/m represents the gravitational acceleration at a given height above the Earth's surface. We can then solve for r by rearranging the equation to:

r = √(Gm1m2/(a*m))

Where m represents the mass of the Earth. Plugging in the values for G, m1, m2, and a (which is equal to 10% of the acceleration due to gravity at sea level), we can find the value for r. This will give us the height above the Earth's surface where the acceleration due to gravity is 10% of that at sea level.

It is important to note that this calculation assumes a point mass for the Earth and does not take into account the Earth's rotation or its varying density. Therefore, the actual value may differ slightly from the calculated one. Overall, the Universal Law of Gravitation allows us to understand and predict the gravitational forces between objects at different distances and can be applied to a variety of scientific problems.