Trouble working out the GM product of Earth: u = GM.

[namtip]

Homework Statement

Don't laugh! I am scratching my head. Somewhere I am doing something very stupid, but I just don't know where. My problem is that my result of G*M of Earth is different than the accepted result of G*M.

Accepted value of G*M: μ = 398600 km^3 s^-2

Homework Equations

μ = GM

G = 6.673*10^-11 N m^2 kg^-2

M (Earth) = 5.977*10^24 kg

The Attempt at a Solution

μ = GM = 6.673*10^-11 * 5.977*10^24 = 3.9884521*10^14

So my results show μ = 3.9884521*10^14, while the accepted results give 3.986*10^8 (after allowing for the km to m conversion)

Where have all my extra zeros come from??! I am sure this is something really stupid.

 

[Fewmet]

It looks like a conversion error. Wikipedia gives 398,600.44 km³s⁻². To get the value in m³s⁻² you need to multiply by (1000 m/km)³. I suspect you forgot the cube.

 

[D H]

There are 1000 meters in a kilometer, so 1000²=10⁶ square meters in a square kilometer, 1000³=10⁹ cubic meters in a cubic kilometer.

You are dividing by 10⁶ when you should be dividing by 10⁹.

 

[namtip]

Ah, ok, so my problem here appears to lie with my grappling with the units. My answer comes out as 3.9884521*10^14 m^3 s^-2 (metres!) so, if I converted that into km^3 s^-2 I would have to divide that by 1000^3, thereby ending up with the accepted value! This would explain my confusion... schoolboy error...

Thanks a lot guys!