Sputnik's period around the earth

[rainbowtits]

Homework Statement

Sputnik I, the first artificial satellite to circle the planet (October 1957) had a mean orbital radius of 6953 km. Compute its period

Homework Equations

How do I compute the period?

The Attempt at a Solution

I thought that the radii of the sputnik could be compared to that of the moon, and same tih the period.

 

[Delphi51]

All satellite/orbit solutions begin with
Centripetal Force = Force of gravity
Then put in the two force formulas. If you are interested in the period use the centripetal force formula that has period instead of velocity - something like F = 4(pi)mr^2/T (I probably have not remembered that exactly right!)

As usual, solve for the quantity you want to find.

 

[nlightner]

I could use the formula for the period of a satellite, T= 2π√(r^3/GM), where r is the orbital radius, G is the gravitational constant, and M is the mass of the Earth. Plugging in the given values, the period of Sputnik I is approximately 96.2 minutes. This is significantly shorter than the average period of the moon, which is about 27 days. This highlights the difference between a low Earth orbit and a more distant orbit like that of the moon. Additionally, the period of Sputnik I also demonstrates the incredible speed at which it was traveling, completing a full orbit around the Earth in just over an hour and a half. This was a groundbreaking achievement in space exploration and marked the beginning of the Space Race between the United States and the Soviet Union.