Centripetal acceleration on Earth

[daysrunaway]

Homework Statement

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?

Homework Equations

a = v²/r = 4$$\pi$$²v/T²
v = 2$$\pi$$r/T

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$$\pi$$/$$\omega$$

$$\omega$$= 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]

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

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]

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

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 into 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

 

[jyothsna pb]

we get acceleration value almost equal to g

 

[jyothsna pb]

velocity in dis orbit must b approximately equal to 7.9*10^3m/s

 

[daysrunaway]

I don't understand why that is, especially since Wikipedia says it is 451 m/s
en.wikipedia.org/wiki/Earth

 

[jyothsna pb]

it wud b easy if u jus show me dat particular part from d article

 

[daysrunaway]

It's on the sidebar, under "Physical Characteristics".

 

[jyothsna pb]

it is equatorial rotation velocity of Earth while that mentioned here is the velocity of a satellite of Earth in an orbit very close to it both r different

 

[EngineerHead]

The centripetal acceleration must balance out the acceleration due to gravity (it is essentially at ground level, so 9.8 m/s^2).

*Force of gravity = mg
*Centripetal acceleration = a (not v^2/r, because you are solving for this total value, not any sub-values within a)

The centripetal acceleration when traveling in a constant circular orbit at ground level on Earth should be equal to gravity, or 9.8. You don't necessarily need velocity, radius, mass, time, etc.

 

[RoughRoad]

Try this-

Centripetal acceleration= $$\omega$$^2*r= (2$$\pi$$/T)*r

Let me know if you got the answer.

 

[Jokerhelper]

Try this-

Centripetal acceleration= $$\omega$$^2*r= (2$$\pi$$/T)*r

Let me know if you got the answer.

but the problem is that the period is unknown, i think

 

[RoughRoad]

but the problem is that the period is unknown, i think

The body moves with a constant speed, so it's T should be 24*3600. I may be wrong though.