# [spacefight mechanics]how to find true anomaly and eccentricity?

• smalllittle
In summary, the problem involves finding the true anomaly and eccentricity of an Earth satellite with a speed of 7km/s, a flight path angle of 15 degrees, and a radius of 9000km. The solution involves using lagrange coefficients and expressing r and v in a non-rotating reference frame, then transferring them to the perifocal frame. The eccentricity can be found using the equation e = 1/u * (r x v) - r/r, with the given answer being a true anomaly of 83.35 degrees and an eccentricity of 0.2785.
smalllittle

## Homework Statement

An Earth satellite has a speed of 7km/s and a flight path angle of 15 degree when its radius is 9000km calculate the true anomaly and eccentricity of the orbit.

## Homework Equations

r=h^2/u(1+ecostheta)

## The Attempt at a Solution

The problem statement just doesn't seem provided enough information. The direction to the solution should deal with lagrange coefficients. Express r and v in the standard Earth refrence frame using flight pitch angle, then transfer them to the perifocal fame.
Then in perifocal fame:
h=r cross v (in perifocal fame)
e=1/u*(r cross v) -r(vector)/r
But i don't know how to find the r and v vectors in the standard Earth ref frame :(
correct me if my approach is incorrect >.>

the answer given is theta=83.35degree, e=0.2785

smalllittle said:

## The Attempt at a Solution

The problem statement just doesn't seem provided enough information. The direction to the solution should deal with lagrange coefficients. Express r and v in the standard Earth refrence frame using flight pitch angle, then transfer them to the perifocal fame.
Then in perifocal fame:
h=r cross v (in perifocal fame)
e=1/u*(r cross v) -r(vector)/r
But i don't know how to find the r and v vectors in the standard Earth ref frame :(
correct me if my approach is incorrect >.>

the answer given is theta=83.35degree, e=0.2785
The problem does provide all the information needed. You do not need to find the r and v vectors in "the standard Earth ref frame", just some earth-centered non-rotating reference frame.

BTW, your equation for the eccentricity vector is incorrect.

I would first clarify the problem statement to make sure all the necessary information is provided. In this case, it seems like the problem is asking for the true anomaly and eccentricity of an Earth satellite with a given speed, flight path angle, and radius at a specific point in its orbit. However, more information is needed, such as the position of the satellite in its orbit (i.e. its longitude or time since periapsis) and the mass of the Earth.

Assuming this information is known, the approach provided in the attempt at a solution seems correct. The r and v vectors can be found by converting the given speed and flight path angle into Cartesian coordinates in the Earth reference frame. From there, they can be transformed into the perifocal frame and the true anomaly and eccentricity can be calculated using the provided equations.

It would also be helpful to provide a diagram or figure to better visualize the situation and to make sure all the calculations are being done correctly. it is important to double check all calculations and make sure all assumptions are valid before arriving at a final answer.

## 1. What is true anomaly and eccentricity in spaceflight mechanics?

True anomaly and eccentricity are two important parameters used to describe the orbit of a spacecraft. True anomaly is the angle between the current position of the spacecraft and its closest approach to the central body (usually a planet or star) in its orbit. Eccentricity, on the other hand, is a measure of how elliptical the orbit is, with a value of 0 indicating a perfect circle and a value of 1 indicating a highly elongated orbit.

## 2. How do you calculate true anomaly and eccentricity?

True anomaly and eccentricity can be calculated using mathematical equations that take into account the position, velocity, and gravitational forces acting on the spacecraft. These equations involve the use of Kepler's laws of planetary motion and can be solved using specialized software or through manual calculations.

## 3. What is the importance of knowing true anomaly and eccentricity in spaceflight mechanics?

Knowing the true anomaly and eccentricity of a spacecraft's orbit is crucial for accurately predicting its trajectory and ensuring a successful mission. These parameters are used to calculate the spacecraft's position and velocity at any given time, and can also help determine the amount of fuel needed for maneuvers and the potential for orbital changes.

## 4. How do you measure true anomaly and eccentricity in real-time during a spaceflight?

During a spaceflight, true anomaly and eccentricity can be measured using onboard instruments such as gyroscopes, accelerometers, and radar. These instruments gather data on the spacecraft's position and velocity, which can then be used to calculate the true anomaly and eccentricity in real-time.

## 5. Can true anomaly and eccentricity change over time during a spaceflight?

Yes, true anomaly and eccentricity can change over time during a spaceflight due to various factors such as gravitational forces from other bodies, atmospheric drag, and thrust from onboard engines. These changes can be predicted and accounted for in mission planning to ensure the spacecraft remains on its desired trajectory.

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