Calculating Sputnik I's Orbital Period

[uno]

1.Sputnik I, the first artificial satellite to circle the planet (October 1957) had a mean orbital radius of 6957 km. Compute its period in seconds



2. I am using the equation T^2 = R^3/C



3. I converted 6957 km to AU's which equals 4.638 E-5. When I plug in the numbers, and convert it to seconds, I come up with 9.96 seconds. Am I using the correct formula?

Thanks for your help.

 

[Rake-MC]

Use:

$$T^2 = (\frac{4\pi^2}{GM})r^3$$

G = 6.67E-11 (metres-cubed per kilogram per second-squared)
M = 5.98E24 (kilograms)
r = 6.957E6 (metres)

 

[alphysicist]

Hi Rake-MC,

Use:

$$T^2 = (\frac{4\pi^2}{GM})r^3$$

G = 6.67E-11 (metres-cubed per kilogram per second-squared)
M = 5.98E24 (kilograms)
r = 6.37E6 + 6.957E6 (metres)

The way I read the problem, I think the radius of the Earth is included in the 6957km given. Does that sound right to you?

 

[Rake-MC]

Hmm it's a bit ambiguous, but thinking logically I would entirely agree that the radius of the Earth is included in the 6957km. Clearly I was thinking purely mathemtically and not realistically.

 

[uno]

My professor told me to use formulas V=2 pi r/T and V^2 = GM/R, but my answer is still incorrect. Any suggestions?

Thanks

 

[Rake-MC]

Using either:

$$T^2 = (\frac{4\pi^2}{GM})r^3$$

Or the formula your professor gave you will yield the same answer.

It looks like it'll be approximately 90 minutes.