What is the relationship between orbital semi latus rectum and angular momentum?

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SUMMARY

The relationship between the semi latus rectum (P) and angular momentum (h) in orbital mechanics is defined by the equation P = h² / (GM), where G is the gravitational constant and M is the mass of the central body. Users in the discussion highlighted discrepancies in derived values of P from various equations, suggesting potential rounding errors or measurement uncertainties. The conversation emphasized the importance of understanding these concepts for calculating elliptic orbits accurately, particularly when using equations for apoapsis and periapsis.

PREREQUISITES
  • Understanding of orbital mechanics principles
  • Familiarity with the equations for apoapsis and periapsis
  • Knowledge of angular momentum in celestial mechanics
  • Basic proficiency in mathematical derivations related to orbits
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  • Study the derivation of the semi latus rectum from angular momentum equations
  • Learn about the implications of measurement uncertainties in orbital calculations
  • Explore the relationship between eccentricity and the semi latus rectum in elliptic orbits
  • Investigate the effects of mass limitations on orbital dynamics
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Astronomy students, astrophysicists, and anyone involved in orbital mechanics or celestial navigation will benefit from this discussion.

Penguinluons
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Hi. I have recently been trying my hands at calculating a few orbits but have encountered difficulties in trying to 'understand' the semi latus rectum.

P=h^2/GM

What does it have to do with the orbiting object's angular momentum? How come I get different values when I derive it from other equations? Please help me as I need to understand this to move on to elliptic orbits.

(Note: When I derived P from other equations, I got different values but they were all quite close to each other.)
 
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Which numbers and formulas do you use to calculate the values and what are the results?
Penguinluons said:
(Note: When I derived P from other equations, I got different values but they were all quite close to each other.)
Could that come from rounding errors or measurement uncertainties?
Penguinluons said:
What does it have to do with the orbiting object's angular momentum?
Both describe some aspect of the orbital motion, what is surprising about equations involving both?
 
mfb said:
Which numbers and formulas do you use to calculate the values and what are the results?
Could that come from rounding errors or measurement uncertainties?
Both describe some aspect of the orbital motion, what is surprising about equations involving both?

I used the equations for apoapsis and periapsis as well as the general equation r=P/1+e cosθ. I tried deriving p from the semi major axis as well.e had an accuracy of about 10 digits. It was an elliptic orbit. Does this therefore place limitations on the mass of my orbiting object?
 
That does not answer my questions.

And I don't understand how you want to get limitations on a mass.
 

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