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Mikael17
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Is it possible to calculate the Aphelion distance, - when I only know the Perihelion distance and perihelion speed ?
What is your question?Mikael17 said:Is it possible to calculate the Aphelion distance, - when I only know the Perihelion distance and perihelion speed ?
Very much this. However, given the mass of the primary and (indirectly) the angular momentum the full effective potential is known as well as thd classical turning point. It is then just a matter of finding the other classical turning point, which amounts to finding the roots of a second degree polynomial.Ibix said:I don't see how you can do it without the mass of the primary (the ##M## in post #2).
If the OP was asking a well-defined question one could assume that "perihelion" and "aphelion" is a reference to the Sun as primary mass.Ibix said:I don't see how you can do it without the mass of the primary (the ##M## in post #2).
If you know the primary mass (e.g. Sun) then yes. It follows more or less directly from the vis-viva equation that holds for all two-body keplerian orbits.Mikael17 said:Is it possible to calculate the Aphelion distance, - when I only know the Perihelion distance and perihelion speed ?
Indeed. Using vis-viva and solving for one apsis distance gives a direct "symmetric" relationship of this distance as a function of the other apsis distance and speed. This distance is then either positive, infinite or negative for elliptic, parabolic or hyperbolic orbits, respectively, so one equation covers all cases.snorkack said:When you know the distance and speed at one apse, and GM, you may find apoapse distance. But this is only one possibility. You may instead find out that there is only one apside (the given apside that was a periapse); or that the given apside was the apoapside; or that there is no apside line.
The case of positive distance further divides into the cases where the found apsis distance was bigger than given apsis distance (found was apoapsis), found apsis distance was equal to given apsis distance (neither was apsis after all because the orbit was not elliptic) or the found apsis distance was smaller than given apsis distance (found apsis was periapsis).Filip Larsen said:Using vis-viva and solving for one apsis distance gives a direct "symmetric" relationship of this distance as a function of the other apsis distance and speed. This distance is then either positive, infinite or negative for elliptic, parabolic or hyperbolic orbits, respectively, so one equation covers all cases.
Yes, but my point is that since you end up with an equation that is valid for all cases you don't really need to "worry" about the orbit classification unless you specifically want to know or verify that too. Also, the full orbit classification is more of a mathematical thing since in practice there are only either elliptical or hyperbolic orbits with the rest being "degenerate" (i.e. only approximately true) cases.snorkack said:The case of positive distance further divides into the cases where the found apsis distance was bigger than given apsis distance (found was apoapsis), found apsis distance was equal to given apsis distance (neither was apsis after all because the orbit was not elliptic) or the found apsis distance was smaller than given apsis distance (found apsis was periapsis).
To elaborate on this with the teeniest amount of math. The two-body problem with a Kepler potential separates into the motion of the barycenter (free motion so rectilinear) and a Kepler potential problem for the separation vector of the masses with gravitational potential ##- GM/r## with ##M = m_1 + m_2## being the total mass of the system (the potential energy is obviously ##- Gm_1m_2/r##, but the mass entering in the kinetic energy for the problem for the separation vector is the reduced mass ##m_1 m_2/M##).Ibix said:One caveat that's probably worth mentioning is that these approaches are assuming that the satellite has negligible mass in comparison to the primary. Depending on how precise you need to be, "negligible" could mean anything up to planetary masses if the primary is indeed the Sun.
The maths is actually no worse if the satellite mass is non-negligible, but you do need to know the satellite mass and you do need to take care about how you defined perihelion distance. You want to use the satellite-to-barycenter distance, and this will be significantly different from the satellite-to-primary distance in this case.
Filip Larsen said:If the OP was asking a well-defined question one could assume that "perihelion" and "aphelion" is a reference to the Sun as primary mass.
| Star | periastron, apoastron | -astrons |
What is wrong with the one we have?sophiecentaur said:I'd like a general term for apo and peri points of an orbit.
Oh for a content addressable memory. Thanks! I promise to use it whenever possible .Orodruin said:What is wrong with the one we have?
The Aphelion distance (A) can be calculated using the formula: A = a * (1 + e), where 'a' is the semi-major axis of the orbit and 'e' is the eccentricity of the orbit.
The semi-major axis (a) is the longest radius of an elliptical orbit, representing half of the longest diameter. It is a key parameter in orbital mechanics and is essential for calculating the Aphelion distance.
The eccentricity (e) of an orbit is a measure of its deviation from a perfect circle. It ranges from 0 (a circular orbit) to 1 (a parabolic trajectory). Eccentricity can be determined using the formula e = sqrt(1 - (b^2/a^2)), where 'b' is the semi-minor axis and 'a' is the semi-major axis.
Aphelion distance specifically applies to elliptical orbits. For circular orbits, the distance remains constant, and for hyperbolic trajectories, the concept of Aphelion does not apply as the object does not return.
The units used in the Aphelion distance formula are consistent with those used for the semi-major axis. Common units include astronomical units (AU) for celestial bodies, kilometers (km), or meters (m) for more precise measurements.