Calculating Satellite Orbit Height: A Challenge

[Link]

A satellite is orbiting the Earth at an rate of 96 minutes. The radius of the Earth and the mass is known. How do I calculate how high above Earth the satellite is orbiting?

I tried to use formula a= 4*(3.14^2)*(r+6380)/t

But I don't have the acceleration, and If I would use Newtons law of universal gravitation, I don't know where to start. Can someone help me?

 

[Pseudo Statistic]

T = 2xPi SquareRoot(r^3/GM)
Where G = 6.67 x 10^-11 and M is the mass of the earth, use r = radius..
You have the time, 96 x 60 for seconds..
Now, you're solving for r.

 

[wais]

Calculating the orbit height of a satellite can be a challenging task, but with the right equations and information, it is possible to determine the approximate height. In this case, we have the orbital period (96 minutes) and the radius of the Earth, but we are missing the acceleration and the mass of the satellite.

To calculate the acceleration, we can use Newton's second law of motion, which states that force equals mass times acceleration (F=ma). Since we know the mass of the Earth and the radius, we can calculate the force of gravity acting on the satellite using Newton's law of universal gravitation (F=GmM/r^2).

By setting these two equations equal to each other, we can solve for the acceleration (a=GmM/r^2m). This will give us the acceleration of the satellite as it orbits the Earth.

Next, we can use the formula for centripetal acceleration (a=v^2/r) to find the velocity of the satellite. We know the orbital period (T) in minutes, so we can convert it to seconds (T=96 minutes x 60 seconds/minute = 5760 seconds). Then, we can plug in the values for the acceleration and radius of the Earth to solve for the velocity (v=sqrt(GmM/r)).

Finally, we can use the equation for orbital velocity (v=2πr/T) to determine the radius of the satellite's orbit (r=vT/2π). This will give us the height above Earth that the satellite is orbiting at.

In summary, to calculate the orbit height of a satellite, we need to use the equations for Newton's law of universal gravitation, centripetal acceleration, and orbital velocity. By setting these equations equal to each other and solving for the unknown variables, we can determine the height at which the satellite is orbiting. I hope this helps guide you in your calculations.