Homework Help: Mass of Io

1. Jan 30, 2010

BoldKnight399

Io, a satellite of Jupiter, has an orbital period of 1.43 days and an orbital radius of 4.35X10^5 km. From this data, determine the mass of Jupiter.

So step one: I cried.
then I tried to use the equation:
T^2=4(pi)^2/(GXMj) X R^3
thus
(123552)^2= (39.478)/(6.672X10^-11)(Mj) X (4.34X10^5)^3

35161.29=(39.478)/(6.672X10^-11)(Mj) X (8.17465X10^16)

Mj=1.3756X10^24

Apparently I was wrong...
Anyone have any ideas what I did to mess this up?

2. Jan 30, 2010

tiny-tim

Hi BoldKnight399!

(please don't use X for "times" … either use * or nothing … oh and have a pi: π and try using the X2 tag just above the Reply box )
I'm not sure what your fomula is , but anyway where did 35161.29 come from (did you take a square-root instead)?

3. Jan 30, 2010

BoldKnight399

I just used the formula:
T^2=(4(Pi)^2/G*M)*R^3

and i have no idea what I did to get 35161.29 in addition, what do you mean about having pi=n?

4. Jan 30, 2010

BoldKnight399

ok so I tried it then having the time correctly squared:
(1.526X10^10)=(39.478/(6.673*10^-11)(M)) * (8.321*10^16)
and i got that the Mass of Jupiter was 3.19*10^18

that was wrong. I don't understand what I am doing wrong

5. Jan 30, 2010

tiny-tim

Try using m instead of km !

(oh, and it wasn't n, it was π )

6. Jan 30, 2010

BoldKnight399

alright, so it became:
(1.526X10^10)=(39.478/(6.673*10^-11)(M)) * (8.321*10^19)
M=3.2259*10^21

still wrong. I thought I had everything right.

7. Jan 30, 2010

tiny-tim

erm

cubed?

8. Jan 30, 2010

BoldKnight399

wow...I am not having a good physics day I guess. Thank you so much. I got:
3.16*10^27 and that was right.