Centripetal acceleration on Earth

daysrunaway

1. The problem statement, all variables and given/known data
An object orbits the earth at a constant speed in a circle of radius 6.38 x 10⁶ m, very close to but not touching the earth's surface. What is its centripetal acceleration?


2. Relevant equations
a = v²/r = 4[tex]\pi[/tex]²v/T²
v = 2[tex]\pi[/tex]r/T

3. The attempt at a solution
I plugged in r = 6.38 x 10⁶ m and T = 24.0 h = (24.0 h x 3600 s / 1 h) = 86,400 s into the equation above and found a = 3.37 x 10^-2 m/s². However, I looked up the centripetal acceleration on the earth's surface and found out it is 0.006 m/s². I can't understand why my answer is wrong. Can anyone point out the error in my logic?

Thanks!

RoughRoad

Try using this formula- 2[tex]\pi[/tex]/[tex]\omega[/tex]

[tex]\omega[/tex]= 360/24*3600


Let me know if you got the answer.

daysrunaway

Thanks for the suggestion RoughRoad but I don't really understand how I am supposed to use this equation.

I found that my calculation for the angular velocity (2piR/T) is approximately equal to the wikipedia value for angular velocity, so I really am confused now because I can't see what I'm doing wrong in just squaring that value and dividing by 6.38 x 10⁶.

RoughRoad

Is the mass of the satellite given?

daysrunaway

No, it isn't.

jyothsna pb

try using the equation GMm/r^2=mv^2/r
m-mass of satellite
M-mass of earth
r-radius of orbit
v^2/r is the centripetal acceleration

jyothsna pb

gravitational frce of earth is utilised for centripetal force

RoughRoad

You are right. But what about the velocity?

jyothsna pb

you are asked to find the centripetal acceleration you just have to find the value of v^2/r which gives the centripetal acceleration

RoughRoad

Oh yeah! How can I be so foolish. Thanks for helping!

jyothsna pb

hope you got the answer

jyothsna pb

u r welcome

RoughRoad

And reply to my visitor msg pls

daysrunaway

I didn't, though, and that's the source of my confusion. I know I have the right value for v but when I plug it in to v^2/r, I get 3.37 x 10^-2 m/s^2. This answer is not equal to the answer I found for the actual acceleration, which is 0.006 m/s^2. My question is why is my answer different from the real value?

jyothsna pb

what is the value of v?

daysrunaway

465.1 m/s

jyothsna pb

there is some error in the velocity value