B Derivation for Aphelion and Perihelion Distances

  • B
  • Thread starter Thread starter bruhh
  • Start date Start date
  • Tags Tags
    Derivation
AI Thread Summary
The formulas for perihelion and aphelion distances in an orbit are derived from the definitions of semi-major axis (SMA) and eccentricity. The perihelion distance is given by a(1-e) and the aphelion distance by a(1+e). This relationship stems from the definition of eccentricity, where the focal points of an ellipse are located at a distance of ±ea from the center. The sum of the distances from any point on the ellipse to the two foci equals 2a. Understanding these concepts is essential for grasping the derivation of these distances.
bruhh
Messages
2
Reaction score
0
I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.
 
Astronomy news on Phys.org
Not sure what you mean by "why" here. The focus-directrix definition of an ellipse gives you this more or less instantly, but you may have to work harder with other definitions. Or are you trying to prove it from ##F=GMm/r^2##?

Basically, you have told us where you want to go but not where you are. That makes it tricky to give directions.
 
Last edited:
See any classical mechanics textbook
 
bruhh said:
I know the formulas for perihelion and aphelion distances in an orbit with SMA a and eccentricity e are a(1-e) and a(1+e), respectively. However, why is this? I can't seem to find any derivations for this anywhere and also cannot figure this out myself.
It follows from the definition of the eccentricity: the focal points of an ellipse are at a distance ## \pm e a ## from the center. And for perihelion and aphelion, as for any points on the ellipse, the sum of the distances to the foci must be ## 2a ##.
 
Is a homemade radio telescope realistic? There seems to be a confluence of multiple technologies that makes the situation better than when I was a wee lad: software-defined radio (SDR), the easy availability of satellite dishes, surveillance drives, and fast CPUs. Let's take a step back - it is trivial to see the sun in radio. An old analog TV, a set of "rabbit ears" antenna, and you're good to go. Point the antenna at the sun (i.e. the ears are perpendicular to it) and there is...
This thread is dedicated to the beauty and awesomeness of our Universe. If you feel like it, please share video clips and photos (or nice animations) of space and objects in space in this thread. Your posts, clips and photos may by all means include scientific information; that does not make it less beautiful to me (n.b. the posts must of course comply with the PF guidelines, i.e. regarding science, only mainstream science is allowed, fringe/pseudoscience is not allowed). n.b. I start this...
Back
Top