Calculating delta/V for a Hohmann transfer orbit

[kirbo]

So I've got a scenario in which I have a craft in a stable orbit around Kerbin at near as makes no difference 100km. I want to raise the orbit from 100km to 600km, and I want to be able to calculate the delta/V for both burns of the Hohmann transfer. I know the equations are and for the second, where μ is the gravitational parameter of Kerbin, which the wiki states is 3530.461m/s, r1 is the starting radius, and r2 is the ending radius.

So if I plug this in, I get v1=sq(3530.461/100)*sq((2*600)/(100+600) - 1.

First step, v1=sq(35.3046) * sq(1200/700)-1

Second step, v1= 5.9417* (1.3092 - 1)

Third step, v1= 5.9417*.3092

Fourth step, v1= 1.837km/s

Now if I convert that to m/s by multiplying by 1000, I get v1=1837m/s.

For the second formula, I can plug in to get v2= sq(3530.461/600)*(1-sq((2*100)/(100+600)))

First step, v2=sq(5.8841*(1-sq((200/700))

Second step, v2=sq(5.8847*(1-sq(.2857))

Third step, v2=2.4257(1-.5345)

Fourth step, v2= 2.4257*.4655

so v2=1.128km/s or 1128m/s.

So, if I add v1 and v2, if will give me the total delta/V for the Hohmann, but when I add them up, I'm left with a delta v of 2965m/s, which sounds waaaaay, waaaaaaay to high if I'm just trying to go from 100km to 650km. What am I doing wrong?

I'm thinking maybe it's because I'm using the wrong μ. I know that μ = GM, with g being the gravitational constant and M being the mass of the planet. So, if the constant of gravity at Kerbin's surface is 9.81, perhaps I should send a probe up to 100,000m and re-measure the gravitational constant so that I can recalculate the new, lower μ and get a more accurate delta/V equations?

Thanks! Kirbo

[purpletarget]

9.81 is the standard acceleration of gravity at sea level and is sometimes referred as small g in equations and also enumerated as 1G's as a unit of measurement.

But that isn't the droid you are looking for. Go to wiki and look up *gravitational constant* to find big G. Its a really small number used to scale the huge masses required for moderate gravitational forces.

[kirbo]

9.81 is the standard acceleration of gravity at sea level and is sometimes referred as small g in equations and also enumerated as 1G's as a unit of measurement.

But that isn't the droid you are looking for. Go to wiki and look up *gravitational constant* to find big G. Its a really small number used to scale the huge masses required for moderate gravitational forces.

Ah! Great info! Thanks!

But when I do my delta/V equations, I plugged in the proper μ for Kerbin of 3530.461 I found on the wiki, and it seems like the delta/V is still too high. Any advice?

[gigaforce90]

Im pretty sure i figured out your mistake since I got a v1 of 278m/s and a v2 of 242m/s

first off your μ is wrong according to the wiki the gravitational parameter of Kerbin is 3.5316000*10^12 m^3/s^2 which will throw things off

second and im not sure if this will really cause too much error but i also added the radius of Kerbin which is 600,000m to r1 and r2 so they are r1 = 700,000m and

r2 = 1,200,000m

I also kept everything in terms of meters instead of converting to km then back to meters

[capi3101]

Gigaforce90's figures are correct - the problems are that you've got a bad figure for the gravitational parameter, that the formulas apply for the distance from the center of mass (so yes, adding the surface radius - 600,000 meters in this case - is essential), and that you've got make sure you're working with the same set of units in all cases (i.e. you can't cancel out kilometers with meters; you've got to have either kilometers or meters, not both).

That's the only beef I have with the Advanced Rocket tutorial; I genuinely wish whoever had wrote that had kept all the figures in the base units of measurement. I mean, the game uses meters per second; why confuse folks by attempting to use kilometers per second?

(Not attempting to start a flame war, in case whoever wrote the tutorial reads this. Just registering an honest gripe.)

In any case, the total delta-V you need is 520 m/s. Not much at all.

[kirbo]

Gentlemen! Thank you so much for you answers! I've got it worked out now. Many thanks!

[pdxjjb]

Is there any way to get this thread to be marked "answered"? It's really useful, but I skipped it several times because it currently shows in search results as "not answered". Really I don't think you'll find an answer better than this - complete with corrections to worked examples.

[capi3101]

OP would have to edit the original post, go into advanced mode and change the header there.