Weight in Terms of Distance From Earth

In summary, the conversation discusses the calculation of an astronaut's weight at a certain height above Earth's surface. The formula for weight in terms of distance from Earth and the Earth's radius are mentioned, and the process of solving for the desired distance is explained. Ultimately, the solution is found to be 2651km above the Earth's surface.
  • #1
bfr
52
0
[SOLVED] Weight in Terms of Distance From Earth

Homework Statement



At what height above the Earth's surface will an astronaut have a true weight that is one half his weight on earth?

Homework Equations



F=G(m1*m2)/r^2
(GM)/(4*pi^2)=(R^3)/t^2

The Attempt at a Solution


I did:
F/2=(G*m1*m2)/r^2
r=sqrt((2*G*m1*m2)/F)

My teacher got sqrt(2) times the radius of the earth. Where do I go from there?
 
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  • #2
bfr said:
F=G(m1*m2)/r^2

I did:
F/2=(G*m1*m2)/r^2
r=sqrt((2*G*m1*m2)/F)

Hi bfr!

You're confusing yourself by using the letter r for two different distances.

Hint: call the Earth's radius r, and call the radius you're looking for s.

Then write two equations, one with r and one with s.

Then … does that help? :smile:
 
  • #3
g=GM/R^2

so g is directly proportional to 1/R^2
g'/g = R^2/R'^2
1/2=R^2/R'^2
let R = 6400*1000 m
R'^2 = 2R^2
R' = sqrt2 R = 9050km
atitude = 9050-6400 =2651km above the Earth's surface

of coz , u may realize that
GM =gRe^2 , where Re is the radius of the Earth
then
g'= gRe^2/R'^2
which is the same.
 
  • #4
Yes! :smile: But a bit long-winded.

You could just say:

F =G.m1.m2/r^2
F´ =G.m1.m2/r´^2
so F/F´= r´^2/r^2 = (r´/r)^2.

Do you see the advantage now of being careful to use different letters?! :smile:

[size=-2](if you're happy, don't forget to mark thread "solved"!)[/size]​
 

Related to Weight in Terms of Distance From Earth

Question 1: What is weight in terms of distance from Earth?

Weight in terms of distance from Earth is a measure of how much gravitational force an object experiences at a certain distance from Earth's surface. It is a combination of an object's mass and the strength of the gravitational pull from Earth.

Question 2: How does weight change as distance from Earth increases?

As distance from Earth increases, weight decreases. This is due to the inverse square law of gravity, which states that the force of gravity between two objects is inversely proportional to the square of the distance between them. Therefore, the further an object is from Earth's surface, the weaker the gravitational force it experiences, resulting in a decrease in weight.

Question 3: Does weight affect an object's mass?

No, weight and mass are two different measurements. Mass is a measure of the amount of matter in an object, while weight is a measure of the force of gravity on an object. An object's mass will remain constant regardless of its distance from Earth, but its weight will change.

Question 4: How is weight in terms of distance from Earth different from weight on Earth's surface?

Weight in terms of distance from Earth takes into account the object's distance from Earth's surface, while weight on Earth's surface only considers the object's mass and the strength of Earth's gravitational pull at its surface. Weight in terms of distance from Earth also changes as the distance from Earth changes, while weight on Earth's surface remains constant.

Question 5: How does weight in terms of distance from Earth affect objects in space?

Objects in space experience weight in terms of distance from Earth, which means that their weight will decrease as they move further away from Earth. This can have practical implications for spacecraft and other objects in orbit, as the decrease in weight can affect their trajectory and stability. It also means that objects can feel weightless when they are far enough from Earth's gravitational pull.

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