Universal Gravitation problem - Satellite Orbit

[Thewindyfan]

Homework Statement

http://prntscr.com/9huihp
Given,
Mass of the Earth = 6*10²⁴
Mass of Satellite = 45 kg
Radius of Satellite's orbit = 4.2*10⁷
G = 6.67*10^-11
Find the velocity of the satellite.

Homework Equations

Gravitational Force F_g = (G*M_e*M_s)/(R_s²)
Newton's second law:
F_g = M_s*a where a = v²/R_s due to uniform circular motion.

The Attempt at a Solution

http://prntscr.com/9huloh
http://prntscr.com/9hulwt

I feel like I'm being thrown off either by the units being in km/s or by not accounting for the fact that the acceleration vector points in the -x direction, but I don't see why that would affect the magnitude of the velocity. Can anyone point me in the right direction as to what I may be neglecting, because these problems are usually pretty easy for me.
*ps. sorry if my writing is not legible enough to read!

 

[SteamKing]

Homework Statement

http://prntscr.com/9huihp
Given,
Mass of the Earth = 6*10²⁴
Mass of Satellite = 45 kg
Radius of Satellite's orbit = 4.2*10⁷
G = 6.67*10^-11
Find the velocity of the satellite.

Homework Equations

Gravitational Force F_g = (G*M_e*M_s)/(R_s²)
Newton's second law:
F_g = M_s*a where a = v²/R_s due to uniform circular motion.

The Attempt at a Solution

http://prntscr.com/9huloh
http://prntscr.com/9hulwt

I feel like I'm being thrown off either by the units being in km/s or by not accounting for the fact that the acceleration vector points in the -x direction, but I don't see why that would affect the magnitude of the velocity. Can anyone point me in the right direction as to what I may be neglecting, because these problems are usually pretty easy for me.
*ps. sorry if my writing is not legible enough to read!

Well, you have the correct formula for the orbital speed of the satellite. Did you check your arithmetic? That's a good place to start.

I checked your calculations, and I come up with a different result.

 

[Thewindyfan]

Well, you have the correct formula for the orbital speed of the satellite. Did you check your arithmetic? That's a good place to start.

I checked your calculations, and I come up with a different result.

WOW.

Last time I did this problem I remembered making sure to take the square root of my answer but I still ended up not getting the correct answer, but now I did. Forgot to do the last step! Thank you.

 

[Buzz Bloom]

Hi windyfan:

*ps. sorry if my writing is not legible enough to read!

I confess that I do have trouble with the illegibility.

Re http://prntscr.com/9huloh
The equation that you derive looks OK.

Re http://prntscr.com/9hulwt
There is a need to keep track of units. I can't tell if you are doing that right or not since you don't include the units in your work. You are also not mentioning in section (1) the units for G and R_s. I suggest you do the work again writing all the units for each expression.

Hope this helps.

Regards,
Buzz

 

[Thewindyfan]

Hi windyfan:I confess that I do have trouble with the illegibility.

Re http://prntscr.com/9huloh
The equation that you derive looks OK.

Re http://prntscr.com/9hulwt
There is a need to keep track of units. I can't tell if you are doing that right or not since you don't include the units in your work. You are also not mentioning in section (1) the units for G and R_s. I suggest you do the work again writing all the units for each expression.

Hope this helps.

Regards,
Buzz

Thank you, because I realized it was because of the unorganized way I did my work that I forgot to complete the arithmetic!

This thread can be closed. Thank you guys for pointing my errors out!