Calculating the dV needed to change orbits

[davidpsummers]

How do you calculate the dV needed to change orbits? I'm OK with assuming circular, but obviously a more general solution would be great.

I mean, once I'm in orbit, I can use maneuver nodes to see what it will take. But I would find it useful to calculate them while I'm designing my rocket.

Edited May 23, 2015 by davidpsummers

[NASAHireMe]

Easiest way is to consult a delta-V chart. Any accurate one will tell you the approximate dV for all of the orbits that are important: low orbit around Kerbin to Kerbin escape to interplanetary transfer to capture to low orbit around the target body.

For orbits NOT covered on the dV map, you can calculate the dV requirements yourself pretty easily. You will need to understand Kepler's laws of planetary motion and the related orbital period calculation. Read the Wiki here or here.

The most important equation you need to know is the vis-visa equation.

"For any Kepler orbit (elliptic, parabolic, hyperbolic, or radial), the vis-viva equation^[1] is as follows:

where:

• v is the relative speed of the two bodies
  
• r is the distance between the two bodies
  
• a is the semi-major axis (a > 0 for ellipses, a = ∞ or 1/a = 0 for parabolas, and a < 0 for hyperbolas)
  
• G is the gravitational constant
  
• M is the mass of the central body
  

The product of GM can also be expressed using the Greek letter μ."

You can find the gravitational constant and mass from the KSP wikis.

Edited May 22, 2015 by NASAHireMe

[Jonboy]

If you're simply changing orbits from one circular orbit to another within a planet's SOI via a Hohmann transfer orbit, the calculation is pretty simple. (A Hohmann transfer orbit, you probably know, is simple the where you burn to change your apoapsis or periapsis to the altitude of your intended final orbit, then burn to circularize once you get there.)

- r is the distance of the orbiting body from the center of the central body (this means you have to add the radius of the planet to your ship's altitude, in the case of Kerbin it's 600km)

- μ is the Standard Gravitational Parameter of the central body, which is the product of its gravitational constant and its mass. (Kerbin's is 3.5316x10^12 m^3/s^2)

The Delta-V for your first burn is calculated with this equation:

and the Delta-V for your second can be calculated with this equation:

and the sum of these two equations is the total Delta-V required to change from one circular orbit to another within a planet's (or sun's) SOI. R1 is your starting orbital radius and R2 is your destination orbital radius. To make the units work easily, use meters instead of kilometers (multiply by 1,000).

And just for fun, I threw together an Excel spreadsheet that allows you to easily calculate the Delta-V between two circular orbits in Kerbin's SOI. To use for another body's SOI, just look up the body's Standard Gravitation Parameter and Equatorial Radius on the wiki and plug those in to the left side of the spreadsheet:

https://www.dropbox.com/s/2i5g65ic0ck4ihi/Hohmann%20Transfer%20Delta-V.xlsx?dl=0

Edited May 22, 2015 by Jonboy

[OhioBob]

The following should help,

Orbital Mechanics

There may be more in that page then you need, but you can always skim through it until you find the parts that interests you. There are sample problems that show how to compute a wide variety of orbital maneuvers. If there is anything you don't understand, don't hesitate to ask specific questions.

[Anglave]

You guys are awesome. My vote for sticky.

[davidpsummers]

Well, I was going to do the calculation in a spreadsheet (mostly so I don't have to keep looking up the equaiton). But someone even makes up a nice formatted spreadsheet? :-)