Editing Spacecraft flight dynamics (section)

===Simplifying assumptions===
{| {{Table|class=floatright}}
|-
! Body
! Eccentricity<ref name=ssd-mean>{{cite web | title=Keplerian elements for 1800 A.D. to 2050 A.D. | publisher=JPL Solar System Dynamics | url=http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt | archive-url=https://web.archive.org/web/20090723033252/http://ssd.jpl.nasa.gov/txt/p_elem_t1.txt | archive-date=2009-07-23  | access-date=17 December 2009}}</ref>
! Mean<br />distance<br />(10<sup>6</sup> km){{sfnp|Bate| Mueller| White|1971| p=361}}
! Orbital<br />speed<br />(km/sec){{sfnp|Bate| Mueller| White|1971| p=361}}
! Orbital<br />period<br />(years){{sfnp|Bate| Mueller| White|1971| p=361}}
! Mass<br />Earth = 1{{sfnp|Bate| Mueller| White|1971| p=361}}
! <math>\mu</math><br/>(km<sup>3</sup>/sec<sup>2</sup>){{sfnp|Bate| Mueller| White|1971| p=361}}
|-
| Sun || --- || --- || --- || ---  || 333,432 || {{val|1.327e11}}
|-
| Mercury || .2056 || 57.9 || 47.87 || .241 || .056 || {{val|2.232e4}}
|-
| Venus || .0068 || 108.1 || 35.04 ||  .615 || .817 || {{val|3.257e5}}
|-
| Earth || .0167 || 149.5 || 29.79 || 1.000 || 1.000 || {{val|3.986e5}}
|-
| Mars || .0934 || 227.8 || 24.14 || 1.881 || .108 || {{val|4.305e4}}
|-
| Jupiter || .0484 || 778 || 13.06 || 11.86 || 318.0 || {{val|1.268e8}}
|-
| Saturn || .0541 || 1426 || 9.65 || 29.46 || 95.2 || {{val|3.795e7}}
|-
| Uranus || .0472 || 2868 || 6.80 || 84.01 ||  14.6 || {{val|5.820e6}}
|-
| Neptune || .0086  || 4494  || 5.49 || 164.8 || 17.3 || {{val|6.896e6}}
|}
For the purpose of preliminary mission analysis and feasibility studies, certain simplified assumptions may be made to enable delta-v calculation with very small error:{{sfnp|Bate| Mueller| White| 1971| pp=359, 362}}
*All the planets' orbits except [[Mercury (planet)|Mercury]] have very small eccentricity, and therefore may be assumed to be circular at a constant orbital speed and mean distance from the Sun.
*All the planets' orbits (except Mercury) are nearly coplanar, with very small inclination to the [[ecliptic]] (3.39 degrees or less; Mercury's inclination is 7.00 degrees).
*The perturbating effects of the other planets' gravity are negligible.
*The spacecraft will spend most of its flight time under only the gravitational influence of the Sun, except for brief periods when it is in the [[sphere of influence (astrodynamics)|sphere of influence]] of the departure and destination planets.

Since interplanetary spacecraft spend a large period of time in [[heliocentric orbit]] between the planets, which are at relatively large distances away from each other, the patched-conic approximation is much more accurate for interplanetary trajectories than for translunar trajectories.{{sfnp|Bate| Mueller| White| 1971| pp=359, 362}} The patch point between the hyperbolic trajectory relative to the departure planet and the heliocentric transfer orbit occurs at the planet's sphere of influence radius relative to the Sun, as defined above in [[#Orbital flight|Orbital flight]]. Given the Sun's mass ratio of 333,432 times that of Earth and distance of {{convert|149,500,000|km|nmi|sp=us|abbr=off}}, the Earth's sphere of influence radius is {{convert|924,000|km|nmi|sp=us|abbr=off}} (roughly 1,000,000 kilometers).{{sfnp|Bate| Mueller| White|1971|p=368}}