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PhoenixFire
Group Title
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.
 one year ago
 one year ago
PhoenixFire Group Title
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.
 one year ago
 one year ago

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

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

whpalmer4 Group TitleBest ResponseYou've already chosen the best response.1
If 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\[9.81953 \text{ N}\text {/kg}*(1 \text{ kg m s}^{2}/1 \text{ N}) = 9.81953 \text { m}/\text{s}^{2}\]
 one year ago

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