The polar- orbiting environmental satellites (POES) and some military satellites orbit at a much lower level in order to obtain more detailed information. POES complete an Earth orbit 14.1 times per day. What are the orbital speed and the ltitude of the POES?
First get the distance R from the center of the Earth
GM/R^2 = V^2/R
Period: P = (1/14.1)*24 hours*3600 s/h = 6128 s
2 pi*R/P = V
Solve the two independent equations for V and R.
Once you have R, subtract the radius of the Earth for altitude.
To calculate the orbital speed and altitude of the POES, we can use Kepler's third law of planetary motion. This law states that the square of the orbital period of a satellite is directly proportional to the cube of its average distance from the center of the Earth.
Given that the POES completes an Earth orbit 14.1 times per day, we can first calculate the orbital period using the following formula:
Orbital Period = 24 hours / Number of Orbits per Day
Orbital Period = 24 hours / 14.1 orbits per day
Orbital Period ≈ 1.70 hours
Next, we need to find the average distance (radius) of the orbit from the center of the Earth. This can be obtained by converting the orbital period into seconds and using the following formula:
Radius = (G * M * Orbital Period^2 / (4 * π^2))^(1/3)
where G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2) and M is the mass of the Earth (5.972 × 10^24 kg).
Let's calculate the radius:
Radius = (6.67430 × 10^-11 * 5.972 × 10^24 * (1.70 * 3600)^2 / (4 * π^2))^(1/3)
Radius ≈ 8,550 km
Finally, we can calculate the orbital speed using the formula:
Orbital Speed = (G * M / Radius)^0.5
Let's calculate the orbital speed:
Orbital Speed = (6.67430 × 10^-11 * 5.972 × 10^24 / 8,550,000) ^ 0.5
Orbital Speed ≈ 7.62 km/s
Therefore, the orbital speed of the POES is approximately 7.62 km/s, and the altitude is approximately 8,550 km.