Satellite Orbit Problem what am I doing wrong?

[heyitslars]

I have a satellite orbit problem I'm not quite understanding...any help would be appreciated.

Homework Statement

Suppose a spacecraft orbits the moon in a very low, circular orbit, just a few hundred meters above the lunar surface. The moon has a diameter of 3500 km, and the free-fall acceleration at the surface is 1.60 m/s^2.

Homework Equations

1. How fast is this spacecraft moving?

The Attempt at a Solution

To find the speed, I used the equation v= square root of (G X M/R), with M being the mass of the moon (I had to look that up) and G being the gravitational constant.

v= square root of (6.674E-11)(7.36E22/1750)=52980.125=>52.9 m/s

The answer I got was an available option under the answer choices; however, I got it wrong. I can't figure out another way to come up with the velocity.

I also tried using the equation mg=mv^2/R; however, I got the same number as before.
m's cancel;
g=v^2/R
v= square root of g*R
Acceleration = g in freefall
V = square root of 1.60*1750km=>52.9 m/s

Both of these answers are incorrect. What am I doing wrong?

 

[D H]

Watch your units! Kilometers and meters are not the same.

 

[heyitslars]

Didn't I convert between them? For the first equation I used, 52980.125 is in kilometers, then I moved the decimals 3 places over to convert to meters.

 

[D H]

No, it is not. It is in goofy units. G is not just a number, and you used it is such. It has units. You used G=6.674E-11, more correctly, G=6.674×10^-11 m³ kg^-1 s^-2.