# Weight of a person a certain distance above the Earth

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1. Jul 31, 2017

### AfronPie

1. The problem statement, all variables and given/known data
The problem is stated in the picture.

2. Relevant equations
Fg=Gm.1m.2/r^2

3. The attempt at a solution
I found a similar question where someone wanted to find how high will the weight be half the weight on the surface. Here is one of the answers:
F =G.m1.m2/r^2
F´ =G.m1.m2/r´^2
so F/F´= r´^2/r^2 = (r´/r)^2.
So I tried applying it to my situation. I wrote 34/100=r'^2/(6.38*10^6)^2. Solving for r' I got an answer of x=3.72*10^6meters=3720km. The correct answer of 4600km is displayed in the screen shot attached. I really don't understand how to do these problems, though I do understand that Fg is inverse square proportional to r. Any help would be greatly appreciated. Thanks.

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• ###### Screen Shot 2017-07-31 at 9.28.25 PM.png
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2. Jul 31, 2017

### scottdave

Look again at your F and F'. You have them reversed. Then you will be solving for radius from center of Earth. You need to find height above the surface.

Last edited: Aug 1, 2017
3. Jul 31, 2017

### AfronPie

Can you please elaborate. How would I rewrite my original equation of 34/100=r'^2/(6.38*10^6)^2 .?

4. Jul 31, 2017

### ElectricRay

Am I mistaking something here? I thought we could write the equation as follows.

$$F = \frac {G*M1*M2} {r^2}$$

$$\frac F {F'} = \frac {G*M1*M2} {r^2} * \frac {r'^2} {G*M1*M2} = \frac {r'^2} {r^2}$$

Maybe I make a huge mistake so if I confuse the OP im sorry

5. Jul 31, 2017

### ElectricRay

Ahhh ok @scottdave ur right I see it my apologizes

F and F' are reversed in OP formula

6. Aug 1, 2017

### dean barry

is it not easier to disregard m2 ? (persons mass) the solution will be all but identical

7. Aug 1, 2017

### ElectricRay

Well in fact thats what's happening as far I understand. You disregard M1, M2 and G the only thing that matters here is the ratio of you weight with respect to when your on the surface of the earth and on a distance such that your weight is 34% less. For that you dont need M1, M2 and G because your weight is proportional to the inverse of r^2. I hope i'm using the right words here.

8. Aug 1, 2017

### AfronPie

Using your formula, I am still confused. I wrote the equation as F/F'=100/34=r'^2/(6.38*10^6)^2. Solving this for r' I get 10,940 km. I really don't get what I plugged in wrong. F/F' indicated that the original force is around three times greater then the ' force, and r is the radius of the earth.

9. Aug 1, 2017

### ElectricRay

Have you swopped F and F' ?

10. Aug 1, 2017

### ElectricRay

As far I understand it should be like this:

$$\frac {F'} F = \frac {G*M1*M2} {r'^2} * \frac {r^2} {G*M1*M2} = \frac {r^2} {r'^2}$$

Now it is important to think as that in the question is written that your weight reduces with 34%, so you can't plug in 34% you need to take care of that. If I do that I come on 4520 km. I think thats correct.

11. Aug 1, 2017

### AfronPie

How do you incorporate 34% into the equation without plugging in 34/100 or 100/34 to the equation????

12. Aug 1, 2017

### ElectricRay

The question states you weight is reduced with 34% so what percentage is left?

13. Aug 1, 2017

### AfronPie

You have 66 percent of your weight left. But even if I plug in 66 I get: 66/100=(6.38*10^6)^2/r'^2, getting an r' of 7853km?

14. Aug 1, 2017

### ElectricRay

$$0.34 = \frac {6380^2} {r'^2}$$

Then you get the distance from the centre of the earth, but they ask the distance form the surface of the earth. Im sorry if i dont explain myself good enough.

I come on 4561 km

15. Aug 1, 2017

### AfronPie

Thanks, I made 2 mistakes. I switched F and F', and also I didn't know that you had to subtract the distance 6371km but now I understand. Thanks for your help.

16. Aug 1, 2017

### ElectricRay

The key is in this problem is knowing that this formula applies from the centre of the mass and the question that was asked was from the surface of the mass.

Well if you swop everything you still come on the same answer:
$${r'}=\sqrt{ {6380^2} * \frac 1 {0.34}} = 10941.6$$
$$10941 - 6380 = 4561.6 km$$

I think it is a way of interpreting and applying the formulas I think. Thank you too because with trying to help you I learned something too ;)

17. Aug 1, 2017

### ElectricRay

Yes we got a small differnece I used your 6380 km but in fact according google it is indeed 6371 km

18. Aug 1, 2017

### epenguin

As you know of course if you weighed yourself up there using those Medic's balances where they load weights on some counterbalance you would measure yourself as the same weight as here. But if you weighed yourself with a spring balance that had been calibrated at the earth's surface you would get your result.

19. Aug 1, 2017

### scottdave

As a bonus, can you figure how the astronauts on the International Space Station (altitude approx 320 km) experience a weightless environment?

20. Aug 1, 2017

### ElectricRay

Yes because everything het 34% less right? Please dont tell me the calculation is still wrong ;)