(This corresponds to a flight time of 200 days.) The ephemeris data of Earth at launch
and Mars at arrival can be found on page 151 of the text. Note that there may be an error in
Earth\u2019s orbital radius, however.
(a) Design the transfer ellipse; determine the longitude of the line of apsides, the eccentricity,
and the semimajor axis.
(b) Calculate the inclination of the transfer ellipse with respect to the ecliptic plane.
(c) Calculate C3.
(d) Calculate the inclination of the transfer ellipse relative to the Mars orbital plane.
(e) Calculate velocity at infinity on the arrival hyperbola.
(f) Calculate the elements of the arrival hyperbola for a periapsis altitude of 378 km.
These are my answers. A looks okay but the rest seems really off. Not sure what I am missing. Can anyone help?
Earth Mars Longitute. Deg 181.444 333.221 Eccentricity 0.0167084 0.0934025 Semimajor Axis. km 149,598,020 227,939,133 Inclination. deg 0 1.8497 Long. of Perihelion. Deg 102.958 336.093 Long. of Ascending Node. Deg 0 49.572 Radius 1.496E 08 2.067E 08 Velocity 29.892 26.4964 True Anomaly. Deg 78.4854 357.128 Flight Path Angle, Deg 0.93486 -0.24524 Guess: Line of Apsides, Deg guess 168.861 True Anomaly. Deg 12.583 164.360 0.220 2.867 theta e theta m Transfer Ellipse: eccentricity (e) = 0.1655 rp 1.496E 08 a 1.793E 08 n (days)^-1 0.0131 Ee 0.186 Em 2.818 Tpe 11.85 Tpm 210.86 Flight time (days) = 199.018 a=(\u03a9 180) – Le (deg) 48.128 0.840 b=Lm – (\u03a9 180) (deg) 103.649 \u03b1 (deg) 178.150 3.108 cosc = cosacosb sinasinbcos\u03b1 0.549 c 56.7493726 0.990 Inclination of the transfer plane (deg) 5.391 0.094 rp 1.50E 08 Ve\/s 29.892 \u03d2e 0.935 ra 2.07E 08 Vs\/s r1V1=r2V2 21.637 \u03d2t -1.04 cos\u03b1 = cosit*cos(\u03d2e \u03d2t) 0.990 \u03b1 0.141 C3 = Ve^2 Vs^2 – 2*Ve*Vs*cos\u03b1 80.975 VHE Itp (deg) sin\u03b1sina\/sinc 1.728 Vp\/s 26.496 Vs\/a 19.179 \u03d2p -0.24524 \u03d2t-\u03d2p -0.795 cositp 0.156 cos\u03b1a = cositp*cos(\u03d2t-\u03d2p) 1.461 Vinfinity=b^2 c^2-2bccosA 30.96 zp 378 mu 42828.3 rp=rm Zp 3775 Vp=sqrt(Vinfinity^2 2mu\/rp) 31.324 Beta<\/p>\n","protected":false},"excerpt":{"rendered":"
(This corresponds to a flight time of 200 days.) The ephemeris data of Earth at launch and Mars at arrival can be found on page 151 of the text. Note that there may be an error in Earth\u2019s orbital radius, however. (a) Design the transfer ellipse; determine the longitude of the line of apsides, the […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[24],"class_list":["post-62041","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-engineering"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/62041","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=62041"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/62041\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=62041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=62041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=62041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}