# Orbital Period

1. Apr 29, 2009

### Immy2000

1. The problem statement, all variables and given/known data

On each of the apollo missions the command module was placed in a very low aprox circular orbit above the moon. Assum the avrg hieght was 60km above surface of moon and moons radius is 7738km. (Mass of moon=7.34x10^22kg)

What was the command modules orbital period?

M=7.34x10^22kg
r=7738+60
G=6.67x10^-11

2. Relevant equations

t^2=4pi^2r^3/GM(source)

3. The attempt at a solution

T^2=4pi^2(7738+60)^3 / (6.67x10^-11)(7.34x10^22)

T^2= (1.87...x10^13) / (4.89...x10^12)

T^2= 3.8237...

T=Square Root(ANS)

T= (1.9554.. Days x 24 Hours) = (46.93.. Hours)

But the back of my worksheet says the answer is 17.2 hours or 6.18x10^4 seconds

GAH I am so confused! >_< Your help is much appreciated!

2. Apr 29, 2009

### LowlyPion

Isn't the radius of the moon 1,738 km?

3. Apr 29, 2009

### Immy2000

Yeah it is but I am assuming I am supposed to use what the question gives me.. let me redo the calculation with 1738km's though...

Alright so I get to the part where you have to square root T^2 and I get 0.21649... days (I think) and if I multiply that by 24, I should get hours, but when I do so I get 5.19...which is off from 17.2 hours..

JEEZ I think I made a really silly mistake. Radius is in "m" right? I plugged in Km! Oh my!

Yeppers, it was the conversion. Wow. Please Lock or Delete this thread. :)

Last edited: Apr 29, 2009
4. Apr 29, 2009

### nasu

Why do you think the result of the calculation will be in days?
If you use the quantities in SI units, the period will be in seconds.
Then you can convert in hours, of course.
The answer is around 1.8 hours.

5. Apr 30, 2009

### Immy2000

Yeah I later realized it was in seconds but as far as the answer goes, its 17.2 hours. Thanks for the help guys! :)

6. Apr 30, 2009

### nasu

If you take the radius 7738 then you get something close to 17 hours. But I thought this value is just a typo. This will mean the Moon is bigger than Earth....

7. Apr 30, 2009

### Immy2000

I know its quite silly however the answer was calculated with that number. Therefore I assume that it was typoed and then answered, then printed and handed out to the students.