tag:blogger.com,1999:blog-2675974463524895416.post961619284408001564..comments2024-03-28T01:06:18.986-05:00Comments on An Ex Rocket Man's Take On It: Fundamentals of Elliptic OrbitsGary Johnsonhttp://www.blogger.com/profile/06723964751681093047noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-2675974463524895416.post-24254842902883366122021-03-17T12:25:32.361-05:002021-03-17T12:25:32.361-05:00I'm not sure how to respond to your comment or...I'm not sure how to respond to your comment or question. My reasoning was very simple: orbital velocities are higher nearer periapsis than near apoapsis. Higher velocities over the same distance means shorter transit times. I was looking at shortest transit time, not min delta-vee for a fixed transit time (I have no way to do that). As for the difference in numbers, your input numbers are not identical to mine. So you should not be surprised when you answer differs from mine. -- GWGary Johnsonhttps://www.blogger.com/profile/06723964751681093047noreply@blogger.comtag:blogger.com,1999:blog-2675974463524895416.post-26486995952932496712021-03-15T20:05:04.200-05:002021-03-15T20:05:04.200-05:00Dear Mr. Johnson,
“The faster trajectories to o...Dear Mr. Johnson, <br /><br />“The faster trajectories to outer planets all have perihelion points located at the Earth’s orbit, and so are tangent there, for an arithmetic calculation of departure delta-vee.”<br /><br /> I saw a similar statement in Bate (Fundamentals of Astrodynamics, page 362). Checking empirically, using<br /><br /> rTerra =149600000000 m, rMars = 227900000000 m, and Msol*G = 1.3274E20, I found <br /><br /><br />Perihelion 149600000000 m 1480000000 m 149600000000 m 148800000000 m<br /><br />Aphelion 247000000000 m 2377250000 m 237122000000 m 232992000000 m<br /><br />Transit time<br />rT to rM 180 days 180 days 200 days 200 days <br /><br />total delta V 8419 m/s 7486 m/s 7161 m/s 6836 m/s<br /><br /><br /> showing that for a required transit time, there is a savings in delta vee if perihelion is smaller than rTerra. Have I misunderstood the situation? <br /><br /> I tried to check my calculations against your Figure 10. Assuming a circular orbit and deriving <br /><br />Msol*G = VE2 * rE = (29771 m/s)^2 *149570000000 m = 1.3257E20 m^3/s^2 , <br /><br />then perihelion speed for the Holmann orbit would be 32716 m/s, not 33378 m/s. Again, have I misunderstood? <br /><br /> Thank you, MBMelcon <br />Melcon37https://www.blogger.com/profile/11220458377451730966noreply@blogger.com