Dot Point Question? (1 Viewer)

[aero135]

This question is from Dot point by Shadwick. B

3.4.2 - Calculate how far an astronaut would need to be away above the Earth in order for his weight to be 0.01 his weight on the earths surface.

answer is1.93 X 10^5 km

CAN YOU PLEASE SHOW WORKING

cheers!

 

[shady145]

depends what the astronaughts mass is

 

[shady145]

then u go
f=ma
0.01=the mass x gravity
we are trying to find gravity here

so gravity at the point where this person weighs 0.01kg is given by
g=0.01/the mass

now find a formula that has gravity and radius in it and yea keep going

 

[Aerath]

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 = 5.75x10⁷m.

 

[Aerath]

I forgot to add, therefore the answer in Dotpoint is wrong.

 

[aero135]

cheers Aerath thats what i wanted to hear thanks alot mate=)