Finding Altitude: Calculating Earth's Gravitational Field Strength

[slu1986]

1. (a) Find the altitude above the Earth's surface where Earth's gravitational field strength would be four-fifths of its value at the surface. Assume re = 6.371*10^3 km.

(b) Find the altitude above the Earth's surface where Earth's gravitational field strength would be one-fifth of its value at the surface.

Homework Equations

g= GMe/re^2
G= 6.67*10^-11 Nm^2/kg^2
Me= 5.98*10^24 kg



3. I am so lost when I try to solve this problem. Could someone please guide me in the right direction to solving this problem. I would greatly appreciate it.

 

[tiny-tim]

1. (a) Find the altitude above the Earth's surface where Earth's gravitational field strength would be four-fifths of its value at the surface. Assume re = 6.371*10^3 km.

Hi slu1986!

(try using the X² and X₂ tags just above the Reply box )

This is a dimensions question …

(like, if the radius is multiplied by three, how much is the surface area multiplied by?)

so ask yourself, on what power of r does the gravitational field strength depend?

 

[tomcue]

I would first like to commend you for attempting to solve this problem on your own and seeking guidance when you faced difficulties. This shows a strong determination to understand and learn, which are important qualities for a scientist.

Now, let's break down the problem into smaller parts. First, we need to understand the concept of gravitational field strength. Gravitational field strength is a measure of the force of gravity per unit mass at a given point in space. In simpler terms, it is the amount of gravitational pull experienced by an object at a specific location.

The equation provided in the question, g = GMe/re^2, is known as the gravitational field strength formula. In this formula, g represents the gravitational field strength, G is the gravitational constant, Me is the mass of the Earth, and re is the distance from the center of the Earth to the location where the gravitational field strength is being calculated.

Now, let's move on to part (a) of the question. We are asked to find the altitude above the Earth's surface where the gravitational field strength would be four-fifths of its value at the surface. This means we need to find the value of re when the gravitational field strength is four-fifths of its value at the surface (which we will denote as g0). So, we can rewrite the equation as:

g = GMe/re^2 = (4/5)g0

Next, we can rearrange the equation to solve for re:

re = √(GMe/(4/5)g0) = √(5GMe/4g0)

Now, we have all the values we need to solve for re. We know that G = 6.67*10^-11 Nm^2/kg^2, Me = 5.98*10^24 kg, and g0 is the gravitational field strength at the surface, which we can find by plugging in the values in the original formula:

g0 = GMe/re^2 = (6.67*10^-11 Nm^2/kg^2)(5.98*10^24 kg)/(6.371*10^3 km)^2 = 9.8 m/s^2

Substituting this value into the equation for re, we get:

re = √(5(6.67*10^-11 Nm^2/kg^2)(5.98*