Design of the Recovery Trajectory for JAXA Venus Orbiter Akatsuki

Abstract

Akatsuki (“dawn” in Japanese) is the JAXA Venus orbiter that was scheduled to enter orbit around Venus on Dec. 7^th, 2010. Following the failure of the main engine during the orbit insertion maneuver, the spacecraft escaped Venus on a 200-day orbit around the Sun, only to return in early 2017. This paper presents the design and implementation of the recovery trajectory, which involves perihelion maneuvers to re-encounter Venus in late 2015. Relying only on the onboard propellant, the trajectory rescued the mission by (1) anticipating the beginning of the science phase within the nominal lifetime of the spacecraft, and (2) halving the Δv requirements for the orbit insertion maneuver. Several trajectories are designed with an innovative use of a technique called non-tangent V-Infinity Leveraging Transfers (VILTs). Candidate solutions are then recomputed in higher fidelity models, and one solution is finally selected for its low Δv requirements and for programmatic reasons. The results of the perihelion maneuver campaign are also presented.

Appendix: Non-tangent VILT Computation

This Appendix shows the expression of phasing constraint (Eq. 2) for AKATSUKI’s interior, non-tangent VILT (EI = −1). In this Appendix, non-dimensioal units are used in all the equations, where the lengths are normalized by a _VE , and the velocity are normalized by $v_{VE}=\sqrt {\mu _{SUN}/a_{VE}}$.

The leveraging apse is the pericenter of both legs of the transfer, and it is equal to $\bar {r}_{p}=9.150e7/a_{VE}$. The v _∞1 is also fixed by the exit flyby conditions, and is equal to $\bar {v}_{\infty }=2.653/v_{VE}$ (we assume coplanar motion). The apocenter of the first leg is computed with the formula

$$ \bar{v}_{p}(\bar{r}_{p},\bar{v}_{\infty})=\bar{r}_{p}+\sqrt{\bar{r}_{P}^{2}-3+\frac{2}{\bar{r}_{p}}+\bar{v}_{\infty}} $$

(4)

$$ \bar{r}_{a}(\bar{r}_{p},\bar{v}_{\infty})=\left( \frac{2}{\left( \bar{r}_{p}\bar{v}_{p}(\bar{r}_{p},\bar{v}_{\infty})\right)^{2}}-\frac{1}{\bar{r}_{p}}\right)^{-1} $$

(5)

The second vacant apse is the apocenter of the second leg r _a2, and is solution of the phasing constraint (Eq. 2) with

$$\begin{array}{@{}rcl@{}} f^{(s)}\left( \bar{r}_{p},r_{a2},\bar{v}_{\infty}\right) & \doteq & {\Delta}\theta\left( \bar{r}_{a}(\bar{r}_{p},\bar{v}_{\infty}),\bar{r}_{p},\sigma_{1},k_{1}\right)+{\Delta}\theta_{2}\left( r_{a2},\bar{r}_{p},\sigma_{2},k_{1}\right)+ \end{array} $$

(6)

$$\begin{array}{@{}rcl@{}} && -2\pi\left( k_{1}+k_{2}+1-n\right) \end{array} $$

(7)

and with

$$\begin{array}{@{}rcl@{}} &&{\Delta}\theta(r_{a},r_{p}\sigma,k)=2\pi k-\sigma\arccos\left( \frac{2r_{a}r_{p}-r_{a}-r_{p}}{r_{a}-r_{p}}\right)+\pi(1-\sigma)+\\ &&-\sqrt{\frac{\left( r_{a}+r_{p}\right)^{3}}{8}}\left( 2\pi k-\sigma\left( 2\arctan\left( \sqrt{\frac{1-r_{p}}{r_{a}-1}}\right)-2\sqrt{\frac{(r_{a}-1)(1-r_{p})}{r_{a}+r_{p}}}+\pi(1-\sigma)\right)\right) \end{array} $$

(8)

Deteails on the generic formulas and on the derivation of Eqs. 4–8 are found in [5].