Design of Gravity Assist trajectory from Earth to Jupiter

M. K. Ammar; D. A. Oda

Open Access

Design of Gravity Assist trajectory from Earth to Jupiter

M. K. Ammar

and

D. A. Oda

| Oct 03, 2018

Applied Mathematics and Nonlinear Sciences

Volume 3 (2018): Issue 1 (June 2018)

About this article

Cite

Page range: 151 - 160

Received: Feb 24, 2018

Accepted: May 08, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00011

Keywords
Interplanetary trajectories, Gravity Assist, Flyby, Departure and arrival trajectories

© 2018 HM.K. Ammar, D.A. Oda, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Description of the mission from Earth to fly by with Mars

Calculations of Lambert problems

	lambert earth - Mars		Lambert Mars -Jupiter
r_0x (km)	-1.280952970127814 × 10⁸	r_2x = r_1x (km)	1.588109522284044 × 10⁸
r_0y (km)	-7.873040871488884 × 10⁷	r_2y = r_1y (km)	-1.331196049556935 × 10⁸
r_0z (km)	4241.23706297353500	r_2z = r_1z (km)	-6690470.129802731
r_1x (km)	1.588109522284044 × 10⁸	r_3x (km)	5.331461279416993 × 10⁸
r_1y (km)	-1.3311960495569350 × 10⁸	r_3y (km)	5.392020271071861 × 10⁸
r_z (km)	-6690470.12980273100	r_3z (km)	-9671957.471152349
Δ t₁(s)	1.054080811623402 × 10⁷	Δ t₂(s)	8.25504364820473 × 10⁷
μ_s (km³/s²)	1.32712428000 × 10¹¹	μ_s (km³/s²)	1.32712428 × 10¹¹
V_0x (km/s)	18.61716546638244600	V_2x (km/s)	30.823073404118684
V_0y (km/s)	-28.29950136444239000	V_2y (km/s)	4.934176592416298
V_0z (km/s)	-1.152116764359739900	V_2z (km/s)	-0.8994633203622276
V_1x (km/s)	21.7254264303175400	V_3x (km/s)	-5.888427200446674
V_1y (km/s)	13.84469939965363100	V_3y (km/s)	3.2105733597573787
V_1z (km/s)	0.013528429195021072	V_3z (km/s)	0.22569580208145187

Capture from Jupiter at T2V⃗3 = {-5.888427200446674, 3.2105733597573787, 0.22569580208145187}V⃗J = {9.130213923868334, 9.803076409849977, -0.2456201552966279}JD (Julian day No) of T2 = 0.21253784951961086V⃗∞3 = {-15.0186, -6.5925, 0.471316}

V_∞2 (km/s)	μ_J (km³/s²)	r_p1 (km)	e₂	Δ (km)	V_p3 (km/s)	Δ V₃ (km/s)
16.4086	1.26675 × 10⁸	69911	1.14859	265842	62.3951	-62.3951

Escape from Earth at T0V⃗E0 = {15.113446216468128, -25.49053048920682, 0.0008860019561318039}V⃗0 = {18.617165466382446, -28.29950136444239, -1.1521167643597399}V⃗∞1 = {3.50372, -2.80897, -1.153}JD (Julian day No) of T0 = 2458230.5V(parking orbit) = 11.8689(km/s)

V_∞1 (km/s)	μ_E (km³/s²)	r_p1 (km)	e₁	h₁	β(red)	V_p1 (km/s)	Δ V₁ (km/s)
4.63635	3.986004415 × 10⁵	6678.1363	1.36014	79262.1	.744807	7.72576	4.14313

Fly by Mars at T1V⃗in = V⃗1 = {21.72542643031754, 13.844699399653631, 0.013528429195021072}V⃗out = V⃗2 = {30.823073404118684, 4.934176592416298, -0.8994633203622276}V⃗M = {16.48592538172737, 20.64382791494634, 0.02774276866812586}JD (Julian day No) of T1 = 2458230.5

V_∞2 (km/s)	μ_M (km³/s²)	r_p1 (km)	e₂	Δ (km)	V_out/M (km/s)	δ (red)	Δ V₂ (km/s)
8.58375	4.305 × 10⁴	11968.6	21.4844	12539.3	21.2887	0.0931244	12.7049

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Design of Gravity Assist trajectory from Earth to Jupiter

Published Online: Oct 03, 2018

Page range: 151 - 160

Received: Feb 24, 2018

Accepted: May 08, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00011

Keywords
Interplanetary trajectories, Gravity Assist, Flyby, Departure and arrival trajectories

© 2018 HM.K. Ammar, D.A. Oda, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Calculations of Lambert problems

Capture from Jupiter at T2V⃗3 = {-5.888427200446674, 3.2105733597573787, 0.22569580208145187}V⃗J = {9.130213923868334, 9.803076409849977, -0.2456201552966279}JD (Julian day No) of T2 = 0.21253784951961086V⃗∞3 = {-15.0186, -6.5925, 0.471316}

Escape from Earth at T0V⃗E0 = {15.113446216468128, -25.49053048920682, 0.0008860019561318039}V⃗0 = {18.617165466382446, -28.29950136444239, -1.1521167643597399}V⃗∞1 = {3.50372, -2.80897, -1.153}JD (Julian day No) of T0 = 2458230.5V(parking orbit) = 11.8689(km/s)

Fly by Mars at T1V⃗in = V⃗1 = {21.72542643031754, 13.844699399653631, 0.013528429195021072}V⃗out = V⃗2 = {30.823073404118684, 4.934176592416298, -0.8994633203622276}V⃗M = {16.48592538172737, 20.64382791494634, 0.02774276866812586}JD (Julian day No) of T1 = 2458230.5

Design of Gravity Assist trajectory from Earth to Jupiter

Published Online: Oct 03, 2018

Page range: 151 - 160

Received: Feb 24, 2018

Accepted: May 08, 2018

DOI: https://doi.org/10.21042/AMNS.2018.1.00011

KeywordsInterplanetary trajectories, Gravity Assist, Flyby, Departure and arrival trajectories

© 2018 HM.K. Ammar, D.A. Oda, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fig. 1

Fig. 2

Fig. 3

Calculations of Lambert problems

Capture from Jupiter at T2V⃗3 = {-5.888427200446674, 3.2105733597573787, 0.22569580208145187}V⃗J = {9.130213923868334, 9.803076409849977, -0.2456201552966279}JD (Julian day No) of T2 = 0.21253784951961086V⃗∞3 = {-15.0186, -6.5925, 0.471316}

Escape from Earth at T0V⃗E0 = {15.113446216468128, -25.49053048920682, 0.0008860019561318039}V⃗0 = {18.617165466382446, -28.29950136444239, -1.1521167643597399}V⃗∞1 = {3.50372, -2.80897, -1.153}JD (Julian day No) of T0 = 2458230.5V(parking orbit) = 11.8689(km/s)

Fly by Mars at T1V⃗in = V⃗1 = {21.72542643031754, 13.844699399653631, 0.013528429195021072}V⃗out = V⃗2 = {30.823073404118684, 4.934176592416298, -0.8994633203622276}V⃗M = {16.48592538172737, 20.64382791494634, 0.02774276866812586}JD (Julian day No) of T1 = 2458230.5

Keywords
Interplanetary trajectories, Gravity Assist, Flyby, Departure and arrival trajectories