Height for 1/100 normal weight above Earth's surface

[Stratosphere]

How high above the surface of the Earth should a rocket be
in order to have 1/100 of its normal weight? Express your answer
in units of Earth radii.

Im not sure were to start with this one. I know that the moon is 60 times as far away as the core of Earth to the surface.

 

[chrisk]

Use the gravitational force equation

$$F = G\frac{Mm}{r^2}$$

and

F = mg

Setting the two equations equal to each other provides the acceleration due to gravity as a function of the distance, r, from the center of the earth.

 

[rock.freak667]

You'll need this formula

$$F=\frac{GMm}{r^2}$$


Where M is the mass of the Earth and m is the mass of the object.

 

[Stratosphere]

how do you get G or calculate the mass of the earth?And which one of you is right? Yor saying two diffrent things.

 

[chrisk]

Mass of the Earth and G are found in any physics book; usually in an appendix.

 

[Stratosphere]

i found the mass of Earth 5.9742*10to the 24 power and the radius but how do i know the mass of the rocket? Or G?

 

[Stratosphere]

Anyone?

 

[chrisk]

The mass of the rocket, m, is not required. When setting F = mg equal to the gravitational force equation the m on each side cancels.

G is the universal gravitational constant. You should be able to find the value in the physics book or on line easily.

 

[Prosthetic Head]

You already have the answers you need, G is a well known physical constant, get it from a textbook or find it online. And as for the mass of the rocket, equate the equations given by chrisk and you will discover why it is irrelevent.

 

[Stratosphere]

1 6.67300 × 10^-11 m³ kg^-1 s^-2 i hope i made it look right. So what do i put in for Kg and s and m?

 

[chrisk]

The appropiate units will cancel. Make sure the units for the Earth radius is in meters.

 

[Stratosphere]

i got 24485606.14 that's not right is it?

 

[chrisk]

I have not done the calculation but express the value in Earth radii then subtract one Earth radius from this value to give the height above the Earth surface.

 

[Stratosphere]

What i did to get G is 6.67300 × 10^-11

 

[Stratosphere]

i got 383.9 kilometers above earth.

 

[Prosthetic Head]

Thats not right, and you still haven't expressed it in units of Earth radii.

 

[Stratosphere]

im confused

 

[Stratosphere]

i looked up the real answer from a website and it said the answer is 57,402 and 9 Earth unit radii.

 

[Prosthetic Head]

That is the correct answer, if you still don't understand try posting your workings and I'll show you where you have gone wrong.

 

[Stratosphere]

first i did F= G*M/r²
M=5.9742*10²⁴
R=6378.1
G=6.67300 × 10^-11

 

[Stratosphere]

What did i mess up?

 

[Prosthetic Head]

after equating the two force equations you should have been left with:

g=G*M/r^2

you need to rearrange this for r and solve it

 

[Stratosphere]

What do you mean equating the two force equations?

 

[Prosthetic Head]

Use the gravitational force equation

$$F = G\frac{Mm}{r^2}$$

and

F = mg

Setting the two equations equal to each other provides the acceleration due to gravity as a function of the distance, r, from the center of the earth.

those are the force equations!

 

[Prosthetic Head]

equating:

F = F

LaTeX Code: mg = G\\frac{Mm}{r^2}

 

[Prosthetic Head]

oops that didnt work, I mean:

F = F
mg = GMm/[r][/2]

 

[Prosthetic Head]

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