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!

 

[asteriatic]

First of all, don't be too hard on yourself. It's common for mistakes to happen in scientific calculations, and it's important to troubleshoot and identify the source of the discrepancy.

One potential source of error could be the units used in your calculation. Make sure that all units are consistent and converted properly. For example, the value of G you used is in N m^2 kg^-2, while the value of M is in kg. This could result in an incorrect unit for μ.

Another possibility could be a transcription error. Double check all the numbers and make sure they are entered correctly into your calculator or equation.

Finally, it's always a good idea to compare your result with the accepted value and see if they are within a reasonable range. In this case, your result is significantly higher than the accepted value, so it's important to check for any mistakes in your calculations.

I hope this helps and good luck with your calculations!