# Scatch space mod prob. is need a formula and answer check

1. Dec 13, 2003

### cowgiljl

i think i got it right it wants to know the speed of the command module and the time it takes to do 1 revolution
mass moon = 7.35E22 kg
altitude 60 mi

fromula used was Vcm^2 = GMm/Ro

the speed of the module was 1634 m/s

The time formula thans to enigma was

P = 2\pi \sqrt{\frac{a^3}{\mu}}}
T = 6511 seconds/60
T = 108 min

is this right?

2. Dec 13, 2003

### gnome

Your speed looks correct, using your value for mass of the moon.

But I don't follow what you're doing to get the period.

I'm using Kepler's 3rd law:
$$T^2 = (\frac{4\pi^2}{GM_m})r^3$$
and here r = (1.74 x 106 + 1609 x 60) so using G=6.67x10-11 and Mm=7.35x1022 I'm getting
T = 7063 s or 118 min.

(Incidentally, my book lists the mass of the moon as 7.36x1022 kg, but what's a mere 100,000,000,000,000,000,000 kg among friends?)

3. Dec 13, 2003

### cowgiljl

you re right gnome

I wrote down and typed the wrong answer but my calculations were correct. the mind was quicker than the pen

thanks again

4. Dec 13, 2003

### gnome

Sometimes its good to step back & think about what we're doing.

While I was walking my dog, I was wondering why we're using that crazy formula to get the time of 1 revolution. (Heresy -- calling Kepler's 3rd law a crazy formula!!! )

We already know the speed. Just divide the circumference of the orbit by the speed & get the same answer.]