text: Finding Delta V to circularize orbit after a transfer orbit.
  
  I have been working on calculating all the the delta V needed to fly a rocket from one planet to another. I have worked out the delta V needed to raise the orbit to intercept the second planet, but once there, I cannot figure out how much delta V I would need to then circularize the orbit around the new planet.
  
  • What have you tried? Do you know the velocity at periapsis? Do you know the circular orbital velocity? May 17 '17 at 16:06
  • I can get all of those. I am looking more for a general fourmula. May 17 '17 at 16:29
  • It should be clear that subtracting the circular velocity from the periapsis velocity is the delta-v required to change from flyby to circular orbit. May 17 '17 at 17:02
  • @RussellBorogove Is that it? Sweet, thats all I need. May 17 '17 at 17:35
  • Sometimes the vis-viva equation is very helpful for this. $v^2 \ = \ GM(2/r-1/a)$ see article for more info: en.wikipedia.org/wiki/Vis-viva_equation#Equation
  – uhoh
  May 18 '17 at 1:42
  
  I'll use Earth to Mars as an example.
  
  Here's a quick and dirty pic of an Earth to mars Hohmann:
  
  For sake of simplicity I'm rounding quite a bit here.
  
  At Mars rendezvous you can see the speed difference is about 2.5 km/s. We'll call this 2.5 km/s Vinfinity.
  
  When the ship enters Mars sphere of influence, the path is better modeled by a hyperbola about Mars rather than an ellipse about the sun.
  
  A hyperbola's velocity:
  
  $V_{hyperbola}=\sqrt{V_{infinity}^2 + V_{escape}^2}$
  
  A good memory device for remembering hyperbola's speed is thinking of Vinf and Vesc as the legs of a right triangle and the hyperbola's speed as the hypotenuse.
  
  Vescape, a.k.a. escape velocity varies depending on distance from planet. The 11 km/s earth escape velocity near earth perigee. The 5 km/s Mars escape velocity also assumes a periapsis near Mars' surface.
  
  Low Mars orbit is about 3.5 km/s. So to enter low Mars orbit, you subtract 3.5 from 5.6 km/s. You'd need about a 2 km/s burn.
  
  Now the periapsis speed of a 300 x 574,000 km Mars capture orbit is about 4.8 km/s. So if a capture orbit is all you need, .8 km/s would suffice.
  
  To calculate speeds at different points of various orbits, use the vis viva equation
  
  $V=\sqrt{\mu (2/r - 1/a)}$
  
  Where a is semi major axis of an orbit, mu is GM and r is distance from center of gravitating body.
  
  If you don't want to look up different quantities and work out equations, you can use my Hohmann spreadsheet
explanation: The document is a discussion thread about calculating the delta V required to circularize an orbit around a new planet after a transfer orbit. It starts with a user asking for help with the specific calculation and includes responses from other users providing guidance and formulas. The thread contains a question and multiple answers or suggestions.
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distilabel_metadata.content: Finding Delta V to circularize orbit after a transfer orbit.
  
  I have been working on calculating all the the delta V needed to fly a rocket from one planet to another. I have worked out the delta V needed to raise the orbit to intercept the second planet, but once there, I cannot figure out how much delta V I would need to then circularize the orbit around the new planet.
  
  • What have you tried? Do you know the velocity at periapsis? Do you know the circular orbital velocity? May 17 '17 at 16:06
  • I can get all of those. I am looking more for a general fourmula. May 17 '17 at 16:29
  • It should be clear that subtracting the circular velocity from the periapsis velocity is the delta-v required to change from flyby to circular orbit. May 17 '17 at 17:02
  • @RussellBorogove Is that it? Sweet, thats all I need. May 17 '17 at 17:35
  • Sometimes the vis-viva equation is very helpful for this. $v^2 \ = \ GM(2/r-1/a)$ see article for more info: en.wikipedia.org/wiki/Vis-viva_equation#Equation
  – uhoh
  May 18 '17 at 1:42
  
  I'll use Earth to Mars as an example.
  
  Here's a quick and dirty pic of an Earth to mars Hohmann:
  
  For sake of simplicity I'm rounding quite a bit here.
  
  At Mars rendezvous you can see the speed difference is about 2.5 km/s. We'll call this 2.5 km/s Vinfinity.
  
  When the ship enters Mars sphere of influence, the path is better modeled by a hyperbola about Mars rather than an ellipse about the sun.
  
  A hyperbola's velocity:
  
  $V_{hyperbola}=\sqrt{V_{infinity}^2 + V_{escape}^2}$
  
  A good memory device for remembering hyperbola's speed is thinking of Vinf and Vesc as the legs of a right triangle and the hyperbola's speed as the hypotenuse.
  
  Vescape, a.k.a. escape velocity varies depending on distance from planet. The 11 km/s earth escape velocity near earth perigee. The 5 km/s Mars escape velocity also assumes a periapsis near Mars' surface.
  
  Low Mars orbit is about 3.5 km/s. So to enter low Mars orbit, you subtract 3.5 from 5.6 km/s. You'd need about a 2 km/s burn.
  
  Now the periapsis speed of a 300 x 574,000 km Mars capture orbit is about 4.8 km/s. So if a capture orbit is all you need, .8 km/s would suffice.
  
  To calculate speeds at different points of various orbits, use the vis viva equation
  
  $V=\sqrt{\mu (2/r - 1/a)}$
  
  Where a is semi major axis of an orbit, mu is GM and r is distance from center of gravitating body.
  
  If you don't want to look up different quantities and work out equations, you can use my Hohmann spreadsheet
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a discussion thread about calculating the delta V required to circularize an orbit around a new planet after a transfer orbit. It starts with a user asking for help with the specific calculation and includes responses from other users providing guidance and formulas. The thread contains a question and multiple answers or suggestions.
  
  Label: question-and-answer