A community for students.
Here's the question you clicked on:
 0 viewing
PhoenixFire
 3 years 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
 3 years 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.

This Question is Closed

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you are using 'r' is kilometers ,that's it.

whpalmer4
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0Oh wow. That was amazingly smart of me. Thank you both!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.