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PhoenixFire
 one year ago
Confused here...
\[F=mg=m \frac{GM}{r^2}\]
We know 'g' is an acceleration which is \(ms^{2}\)
Now to calculate 'g' we use \[g=\frac{GM}{r^2}\]
\(G=6.674 \times 10^{11}\)
\(M=5.972 \times 10^{24}\)
\(r=6371\)
putting all this into that equation I get \(9.81 \times 10^6\)
Acceleration due to gravity is definitely not 9 million.
Can anyone tell where I messed up? or what I'm not understanding.
PhoenixFire
 one year ago
Confused here... \[F=mg=m \frac{GM}{r^2}\] We know 'g' is an acceleration which is \(ms^{2}\) Now to calculate 'g' we use \[g=\frac{GM}{r^2}\] \(G=6.674 \times 10^{11}\) \(M=5.972 \times 10^{24}\) \(r=6371\) putting all this into that equation I get \(9.81 \times 10^6\) Acceleration due to gravity is definitely not 9 million. Can anyone tell where I messed up? or what I'm not understanding.

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whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1well, you don't have any units on any of this, which is problematic.

Diwakar
 one year ago
Best ResponseYou've already chosen the best response.1you are using 'r' is kilometers ,that's it.

whpalmer4
 one year ago
Best ResponseYou've already chosen the best response.1If you'd kept the units on the numbers while working the problem, you would have discovered the issue yourself. \[g = \frac{GM}{r^2} = \frac{(6.674*10^{11} \text{ N m}^2\text{/kg} ^2)(5.972*10^{24}\text { kg})}{(6371 \text{ km})^2 } \rightarrow [num] \frac{\text{N kg }\color{red}{\text {m}^2} }{\text{ kg}^2\color{red}{\text{ km}^2 }} \]and you see right away that a conversion hasn't been applied because the units don't cancel/combine properly. Include the missing conversion factor and it comes out properly, as we see below: \[g = \frac{GM}{r^2} = \frac{(6.674*10^{11} \text{ N m}^2\text{/kg} ^2)(5.972*10^{24}\text { kg})}{((6371 \text{ km})(1000\text{ m}/1 \text{ km}))^2 }\]\[ = 9.81953 \text{ N}\text {/kg}\]or if you prefer\[9.81953 \text{ N}\text {/kg}*(1 \text{ kg m s}^{2}/1 \text{ N}) = 9.81953 \text { m}/\text{s}^{2}\]

PhoenixFire
 one year ago
Best ResponseYou've already chosen the best response.0Oh wow. That was amazingly smart of me. Thank you both!
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