Why Don't My Patched Conics Calculations for Orbital Mechanics Match the Text?

In summary, the conversation discusses the challenges of self-teaching the patched conics approach for orbital mechanics, particularly for a visual learner. The person is struggling to find text that caters to their needs and faces difficulty in understanding calculations for an interplanetary transfer. They share a problem from a specific textbook page and their solution, which does not match the text. The response explains that the given answer is based on specific assumptions and provides an alternative approach for solving the problem using numerical methods. The conversation ends with a helpful resource for further information on numerical orbit propagation.
  • #1
Orbiter9
1
0
I'm working on self teaching the patched conics approach for orbital mechanics. I am a very visual learner and I am having difficulty finding text that tailors to my need. Recently I have been working on the calculations for an interplanetary transfer and I seem to be getting pieces of the whole, but I am still missing the big picture. One problem I came across was from this http://lnk.nu/books.google.com/1cjvq page 423 problem (b).

I am pretty rusty with math, but up to this point I have been able to match the calculations required for this an other problems. Having little to no understanding how to calculate the angle for when to begin a departure burn, this is the only text I have found to lay it out so neatly. The problem is my calculations for the solution do not match the text.

Here is my solution which is off by almost a degree. I have reworked the same problem on different calculators on different days and still have arrived at the same number. If anyone can help me understand why my calculation does not match the text I can continue my quest to learn this complicated field. Thank you in advance
 
Astronomy news on Phys.org
  • #2
. The problem at page 423 is a bit more complicated than the standard patched conics approach to orbital mechanics. The answer given in the text is based on the assumption that the Sun is fixed, and the orbits of the Earth and Mars are both circular and have the same semi-major axis. Under this assumption, the answer given in the text is correct. In the general case, however, when the orbits are elliptical and have different semi-major axes, the answer will be slightly different. To solve the problem without assuming circular orbits, you will need to use a numerical approach. This means that you will need to set up an equation that describes the orbits of the Earth and Mars, and then use numerical methods to solve for the desired angle. You can find more information about numerical orbit propagation here: https://en.wikipedia.org/wiki/Orbit_propagationI hope this helps!
 

FAQ: Why Don't My Patched Conics Calculations for Orbital Mechanics Match the Text?

What are patched conics calculations?

Patched conics calculations are a method used in orbital mechanics to approximate the trajectory of an object moving in space using a series of conic sections (such as circles, ellipses, and hyperbolas). This method is based on the laws of gravity and allows for simplified calculations of a spacecraft's trajectory.

How are patched conics calculations used in space exploration?

Patched conics calculations are used in space exploration to plan and execute space missions. They are used to determine the most efficient trajectory for a spacecraft to reach its destination, and to predict the spacecraft's path and position in space at any given time. They are also used to calculate the necessary velocity and direction for a spacecraft to enter and exit orbit around a celestial body.

What factors are taken into account when performing patched conics calculations?

When performing patched conics calculations, factors such as the mass, velocity, and direction of the spacecraft, as well as the gravitational forces of celestial bodies, are taken into account. These calculations also consider the shape and size of the orbits of the celestial bodies involved, as well as the relative positions of these bodies in space.

What are the limitations of patched conics calculations?

Patched conics calculations have some limitations, one of which is that they assume the spacecraft is only affected by the gravitational forces of one celestial body at a time. This can lead to errors in the trajectory calculation if the spacecraft is close to multiple celestial bodies. Additionally, patched conics calculations do not take into account external forces such as atmospheric drag or solar radiation pressure, which can affect the spacecraft's trajectory.

How accurate are patched conics calculations?

The accuracy of patched conics calculations depends on the complexity of the space mission and the precision of the initial data. For simpler missions, patched conics calculations can be highly accurate. However, for more complex missions with multiple gravitational influences and precise trajectories, additional calculations and adjustments may be necessary to ensure accuracy. Overall, patched conics calculations are a reliable and widely used method for approximating spacecraft trajectories in space exploration.

Similar threads

Patched Conics Trajectory from Initial Orbit State
Replies
9
Views
10K
B Calculating g with a Conical Pendulum
Replies
3
Views
2K
I Changing the ISS's orbital inclination to match the Moon
Replies
4
Views
2K
B How to calculate a star's luminosity/radius
Replies
15
Views
8K
Mass of orbiting body calculations
Replies
8
Views
5K
Textbook recommendations for second year physics (UK university)
Replies
5
Views
3K
Compute the useable power in a simple circuit with resistive vs. reactive loads
Replies
15
Views
2K
Orbital mechanics: is ballistic capture possible without acceleration?
Replies
7
Views
1K
Why low precision of the radius of Sun's orbit in MW?
Replies
15
Views
2K
A Regular vs stable orbits in spherically symmetric potentials
Replies
4
Views
967

Hot Threads

Recent Insights

Back
Top