Calculating Circular Polar Orbit Parameters and Fractional Doppler Shift

[firdano]

Hii guys.I have this problem.Can anybody help me on this.tq

Homework Statement

A satellite is in a circular polar orbit at a height of 870 km, the orbital period being approximately 102 min. The satellite orbit passes directly over a beacon at sea level. Assuming an average value of earth’s radius of 6371 km determine approximately the fractional Doppler shift at the instant the satellite is first visible from the beacon.

A satellite is in a 400-Km high circular orbit.
Determine:
a) The orbital angular velocity in radians per second.
b) The orbital period in minutes.
c) The orbital linear velocity in meters per second.
d) There is a very important satellite orbiting the Earth doing astronomical research with a similar orbit. Which one is it?
f) Why it uses such a low orbit?

Homework Equations

maybe V = squareroot u/R.

The Attempt at a Solution

I'm using f = ( v/v+vs) fo.

 

[Filip Larsen]

Try make a diagram of the situation that includes the position of the centre of earth, the observer and the satellite. Take note of which geometric distances and angles you know about. Then think about which direction of relative motion of the satellite relative to the observer that contributes to Doppler shift and see if you can relate that to the sketch you made.

The above hint is based on the assumption that you are supposed to utilize the special geometry that are present in the situation specified by the problem text. To calculate the Doppler shift for general satellite orbits and positions you would need some more complicated equations.

 

[firdano]

TQ for the solutions.

Anything for the next question?

 

[Filip Larsen]

Please explain which question you are stuck on and what you have tried already.

 

[paranormal]

I would like to provide a comprehensive response to the problem at hand. Firstly, in order to calculate the circular polar orbit parameters, we need to understand the basic principles of circular orbits. A circular orbit is an orbit in which the satellite maintains a constant distance from the center of the Earth, resulting in a circular path. In this problem, the satellite is at a height of 870 km, which means its distance from the center of the Earth is 6371 km + 870 km = 7241 km.

The orbital period of the satellite is given as 102 min, which means it takes 102 min for the satellite to complete one full orbit around the Earth. Using Kepler's third law, we can calculate the orbital angular velocity (ω) in radians per second as ω = 2π/T, where T is the orbital period. Substituting the values, we get ω = 2π/102 min = 0.0612 radians per second.

To determine the fractional Doppler shift, we need to use the formula f = (v/v+vs)fo, where v is the velocity of the satellite, vs is the velocity of the beacon, and fo is the original frequency. Since the satellite is in a circular orbit, its velocity (v) can be calculated using the formula v = √(μ/r), where μ is the gravitational parameter of the Earth and r is the distance from the center of the Earth. Substituting the values, we get v = √(3.986×10^14/7241000) = 7503.8 m/s.

The velocity of the beacon (vs) can be assumed to be negligible compared to the velocity of the satellite, and thus we can approximate the value of f as f = v/vo, where vo is the original velocity. The fractional Doppler shift can then be calculated as f = 7503.8/7500 = 1.0005.

Moving on to the second part of the problem, we are given the height of a satellite (400 km) and need to determine its orbital angular velocity, orbital period, and orbital linear velocity. Using the same formula as before, we can calculate the orbital angular velocity as ω = 2π/400 km = 0.0157 radians per second.

The orbital period can be calculated using the formula T = 2π/ω, where