Estimate the acceleration due to gravity at the surface of Europa(one of the moons of Jupiter)given that its mass is 4.9 * 10^22kg and making the assumption that its density is the same as Earth's.

Question

anonymous · Answer

I know I have to use this equation: $$g=Gm _{E}/r^2 where m _{E} is Europa$$

anonymous · Answer

So I get this:

$$(6.67*10^-11kg)(4.9*10^22)/(6.389*10^6m)^2=.08m/s^2 $$ is this right?

anonymous · Answer

yes that is correct :) glad u got it

anonymous · Answer

If thats the case then when I try plugging this into my computer its saying the answer is wrong. The exact answer on my calculator reads: .0800674759. It says use 2 sig figures in my answer so would it be 8.0*10^-2?

mos1635 · Answer

the radius you are using is wrong.
6,389*10^6 is the radius of earth
note your text, it says densidy og earth!!!!
use
m=d*V
m=d* 4/3*π*r^3 once for moon, once for earth to find radius of moon...

anonymous · Answer

okay i'll use that and see what I get. Thanks.

anonymous · Answer

The density for the earth is:
$$V_{e}=4/3\pi(6.389*10^6m)^3=1.09*10^{21}$$
$$D_{e}=5.98*10^24kg/1.09*10^{21}=5.48*10^{45}$$

mos1635 · Answer

10^24/10^21=10^3 !!!!!

mos1635 · Answer

but there is no need to calculate the De
1 for earth
2 for moon
M1=d*4/3*pi*R1^3
M2=d*4/3*pi*R2^3
thas
M1/M2=(R1/R2)^3
.......R2=

mos1635 · Answer

need to go hope you got it

anonymous · Answer

ok i'll try that then.

anonymous · Answer

Now I get .75m/s^2 but it says its wrong.

mos1635 · Answer

let me do the calculations and i will get back to you....

mos1635 · Answer

no time for accuracy
my value is 1.9699696....

mos1635 · Answer

i will do it again when i have more time

anonymous · Answer

alright. Maybe my radius was off, I got 2.773*10^6(I redid the problem and ended up getting this for a radius) My answer now is 1.178615...m/s^2 but i'll wait until you get back to me before submitting this answer.

mos1635 · Answer

i did again same resalt 1.969969......
according to my calculations radius of europa=1,288,045.447 m
i am  ......pretty sure tham i am right

anonymous · Answer

oh okay, so you were right then, I must of made a mistake somewhere. I'll retry this later and see if I can come up with the answer you got. Thank you.