Gravity Question (1 Viewer)

[cutemouse]

Hi,

I have another question with Space, hopefull its my last one, but yeah thanks for answering my other one.

"Calculate how far an astronaut would need to be away above the Earth in order for his weight to be 0.01 of his weight on the Earth's surface"

I tried it but failed miserably (according to answer in back).

Thanks,

Jason

 

[ratcher0071]

Are you given the mass of the astronaut?

 

[cutemouse]

No I am not.

Thanks,

Jason

 

[crestor]

whats the answer? I got one but it looks horribly wrong :|

 

[lionking1191]

wouldnt it be 100x earth‘s radius？

 

[wogblogger]

Ok,
Since his mass isn’t going to change (unless he takes a shit on the way)
Then for his weight to be 0.01 of that on earth it means find the distance to the point where g (gravity) is o.01 of that on earth’s surface

So F*weight*=F*force between two masses*
i.e. m1g=(Gm1m2)/r^2
So g=(Gm2)/r^2

So therefore g is proportional to 1/r^2
Therefore g will be 0.01 of that on earth’s surface at a distance of 10times the earth’s radius

 

[cutemouse]

Answer is 1.93 * 10⁵ km

whats the answer? I got one but it looks horribly wrong :|

 

[Aerath]

I keep getting 5.75 x 10⁷m away from the earth. =\

I assumed the mass to be 100kg, it really doesn't matter, because either way you get the same gravity. Therefore, on earth:
W = 100 x 9.8 = 980
Since you're looking for when it's 0.01 of this, therefore W in space = 980/100 = 9.8
Therefore since W = 9.8, but m is constant at 100:
9.8 = 100g
g in space = 0.098

We also know that g = GM/R².
So g = 0.098, G = 6.67 x 10^-11, M = 6x10²⁴ (Mass of the Earth)

Therefore 0.098 = 6.67 x 10^-11 x 6x10²⁴ / R²
R² = 6.67 x 10^-11 x 6x10²⁴ / 0.098 = 4.08x10¹⁵
R = 6.39x10⁷

But that R is the length from the centre of the earth to the astronaut. We wanna find the altitude.
Altitude = 6.39x10⁷ - 6380000m = 5.75x10⁷.

If I did something wrong, could someone please show me how to do this question? Thanks.

 

[ubermale]

I keep getting 5.75 x 10⁷m away from the earth. =\

I assumed the mass to be 100kg, it really doesn't matter, because either way you get the same gravity. Therefore, on earth:
W = 100 x 9.8 = 980
Since you're looking for when it's 0.01 of this, therefore W in space = 980/100 = 9.8
Therefore since W = 9.8, but m is constant at 100:
9.8 = 100g
g in space = 0.098

We also know that g = GM/R².
So g = 0.098, G = 6.67 x 10^-11, M = 6x10²⁴ (Mass of the Earth)

Therefore 0.098 = 6.67 x 10^-11 x 6x10²⁴ / R²
R² = 6.67 x 10^-11 x 6x10²⁴ / 0.098 = 4.08x10¹⁵
R = 6.39x10⁷

But that R is the length from the centre of the earth to the astronaut. We wanna find the altitude.
Altitude = 6.39x10⁷ - 6380000m = 5.75x10⁷.

If I did something wrong, could someone please show me how to do this question? Thanks.

That's right, but the Earth's radius isn't given on the Physics data sheet so you would have to also work that out:

9.8 = (6.67x10^-11)(6.0x10^24)/r^2
r = sqrt((6.67x10^-11)(6.0x10^24)/9.8)
= 6 390 362. 642 m
= approx. 6.39 x 10^6 m

 

[crestor]

the answer in the back of your book is wrong.

The kid above me has the right answer, I got 57,382km

 

[Epistemophobia]

The answer is definately.. 5

 

[tacogym27101990]

The answer is definately.. 5

haha good input

 

[Epistemophobia]

thanks

 

[ratcher0071]

Could somebody tell me IF this is wrong:

Weight Force =mass x acceleration due to gravity (W=mg) and
g=(GM)/r²

sub g=(GM)/r² into W=mg

W= (GmM)/r²
where;
G=6.67 x 10^-11
m=mass of astronaut
M=mass of Earth
r=radius of earth (+altitude, if needed)

let weight force on EARTH'S SURFACE be 1

1=((6.67 x 10^-11) x m x (5.98 x 10²⁴)) / (6.38 x 10⁶)²
4.07044 x 10¹³ = 3.98866 x 10¹⁴ m
m=0.102050312

let weight force at some distance away from Earth be 0.01
0.01 = =((6.67 x 10^-11) x 0.102050312 x (5.98 x 10²⁴)) / r²
0.01 r² = 4.07044 x 10¹³
r² = 4.07044 x 10¹⁵
r=6.38 x 10⁷

therefore astronaut would have to be:
r=6.38 x 10⁷ - 6.38 x 10⁶
r= 5.742 x 10⁷ metres away

 

[FakeOHNerdS]

yes it is wrong.
y did u do the mass of the earth - the previously calculated 'r'(6.something x 10^7).
u should have done the total distance - radius of earth.

 

[addikaye03]

I keep getting 5.75 x 10⁷m away from the earth. =\

I assumed the mass to be 100kg, it really doesn't matter, because either way you get the same gravity. Therefore, on earth:
W = 100 x 9.8 = 980
Since you're looking for when it's 0.01 of this, therefore W in space = 980/100 = 9.8
Therefore since W = 9.8, but m is constant at 100:
9.8 = 100g
g in space = 0.098

We also know that g = GM/R².
So g = 0.098, G = 6.67 x 10^-11, M = 6x10²⁴ (Mass of the Earth)

Therefore 0.098 = 6.67 x 10^-11 x 6x10²⁴ / R²
R² = 6.67 x 10^-11 x 6x10²⁴ / 0.098 = 4.08x10¹⁵
R = 6.39x10⁷

But that R is the length from the centre of the earth to the astronaut. We wanna find the altitude.
Altitude = 6.39x10⁷ - 6380000m = 5.75x10⁷.

If I did something wrong, could someone please show me how to do this question? Thanks.

i got same as this guy

 

[rips]

Ratcher
your maths is ok except the last formula of yours which sez r = 5.98 x 10^24 - 6.38 x 10^6. You put the wrong figures in, yu put the earth's mass rather than distance.

should have been r (from Earth's surface) = your figure of 6.38 x 10^7 - 6.38 x 10^6 = 5.74 x 10^7 m from the Earth's surface.

Incidentally if you simply divide one by the other (ratio) you get 10 x which is how far the Astronaut was from earth expressed as a ratio of Earth's radius.

 

[Continuum]

You guys got all the right answer but wouldn't it be better if you played with the ratios abit, rather than subbing in stuff first?

I did it like:

W_e=mg_e and W_s=mg_s
W_e=100W_s
mg_e=100mg_s
Therefore, g_e=100g_s

g_e=(Gm_e)/(r_e)² and g_s=(Gm_e)/(r_s)²
Remember that g_e=100g_s
Therefore, (Gm_e)/(r_e)²=(100Gm_e)/(r_s)²
Rearrange this to get (r_s)²/(r_e)²=(100Gm_e)/(Gm_e)
Square both sides and cancel out Gm_e to get r_s/r_e=10
Therefore, the distance you have to be in space is 10 times the radius of earth (r_s=10r_e)
Since you're finding the distance above earth's surface however, you need to take one earth radius away from r_s, giving you a total altitude of 9r_e - which should be around the same answer as all you guys

 

[Aerath]

You guys got all the right answer but wouldn't it be better if you played with the ratios abit, rather than subbing in stuff first?

I did it like:

W_e=mg_e and W_s=mg_s
W_e=100W_s
mg_e=100mg_s
Therefore, g_e=100g_s

g_e=(Gm_e)/(r_e)² and g_s=(Gm_e)/(r_s)²
Remember that g_e=100g_s
Therefore, (Gm_e)/(r_e)²=(100Gm_e)/(r_s)²
Rearrange this to get (r_s)²/(r_e)²=(100Gm_e)/(Gm_e)
Square both sides and cancel out Gm_e to get r_s/r_e=10
Therefore, the distance you have to be in space is 10 times the radius of earth (r_s=10r_e)
Since you're finding the distance above earth's surface however, you need to take one earth radius away from r_s, giving you a total altitude of 9r_e - which should be around the same answer as all you guys

You have no life if you spent the past half an hour doing subs and sups.

I don't have the same Mathematical talent as you, so I would probably just use direct substitution, however, towards the end of your explanation, I started to make some sense of it, and the answer is pretty much the same. Nice work Jonathan.

 

[henry08]

Meh, subbing in is easier than ratios.