Math Help

[arobie]

If I have the equation:<br /><br />mass fraction = e ^ ( dV / Ve ),<br /><br />How would I rearrange that to solve for dV?

 

[kmarinas86]

<font color="yellow"><br />If I have the equation: <br /><br />mass fraction = e ^ ( dV / Ve ), <br /><br />How would I rearrange that to solve for dV?</font><br /><br />log (mass fraction) = log (e) * (dV / Ve)<br />log (mass fraction) / log (e) = (dV / Ve)<br />Ve * log (mass fraction) / log (e) = dV<br />

 

[arobie]

Thank You!<br /><br />I've been sitting here trying to figure that out for a while now. Thanks for the help.

 

[mrmorris]

Looks like:<br /><br />dv = -Ve * ln (Mf / Mi) <br /><br />Mf = Final mass<br />Mi = Initial mass

 

[arobie]

Thank you also mrmorris. I did the same calcs using both yours and kmarinas equation and came up with the same thing. You'll see these calculations on another thread soon.

 

[spacester]

<img src="/images/icons/cool.gif" /> <div class="Discussion_UserSignature"> </div>

 

[propforce]

Go ahead Spacester.... I know you're just DYING to jump in here <img src="/images/icons/smile.gif" /> <div class="Discussion_UserSignature"> </div>

 

[arobie]

Actually Spacester, I have a question for you. (or anyone who knows) I was looking over your post on the XCOR Aerospace News thread about gravity losses, and I had a question.<br /><br />You have:<br /><br />Earth's GM = 398600.44 km^3 / s^2<br /><br />and you used it in the formula:<br /><br />g, end of flight = Earth's GM / Rb^2<br /><br />g, end of flight = 3.986E5 / 6473^2 = .009514 km/s^2 <br /><br />Why were you able to write 398600.44 as 3.986E5?<br /><br />Sorry for bothering you about your old posts. Thank you.

 

[spacester]

Hey, when have I ever been bashful? <img src="/images/icons/laugh.gif" /><br /><br />There's nothing to correct, and it seems too egotistical for me to post just to confirm that the smart people here are correct. Thankfully, I am not the only one here with math skills, and certainly guys like you have much more real-world experience with the rocket equation. And mrmorris is reliable as well.<br /><br />I just wanted to indicate that I think Arobie is cool and that I'm looking forward to his post.<br /> <div class="Discussion_UserSignature"> </div>

 

[spacester]

Hey Arobie, no bother at all . . . it's fun, I'm at work and I sneak over to look at threads from time to time. But sometimes it takes me a while to write the simplest posts 'cuz my boss keeps walking by. <img src="/images/icons/laugh.gif" /> The quiet rebel doncha know . . .<br /><br />Scientific notation, as said . . .<br /><br />the 'E' in this case is short for 10^<br /><br />10^ means "Ten raised to the power of . . . "<br /><br />So E3 equals 10^3 equals 10*10*10 equals 1000<br /><br />So 2.35E3 equals 2.35 * 10^3 equals 2350<br /><br />When you get into really big numbers you have little choice but to use scientific notation.<br /><br />The trick is to count the number of places the decimal moves, that's your power of ten.<br /><br />So to convert<br />398600.44<br />to Scientific Notation, we're going to move the decimal until there's just one digit before the decimal.<br />We move the decimal 5 places to change it to<br />3.9860044<br />so we have converted<br />398600.44 to 3.9860044E5<br /><br />The next lesson is "significant digits" . . . <img src="/images/icons/laugh.gif" /> <div class="Discussion_UserSignature"> </div>

 

[arobie]

Thanks Sluggah and Spacester. I had never heard of 'E' being used instead of the 10 before. 2.35E3 is easier to type than 2.35*10^3. <img src="/images/icons/smile.gif" /><br /><br />Spacester,<br /><br />Here is my post on the Gemini: We can rebuild it, we have the technology thread if your interested.

 

[najab]

And once again we have to conclude that HTML (or UBBCode for that matter) makes a lousy medium for technical/scientific discussion.

 

[arobie]

Oh yea! And what is Earth's GM anyways...it's mass?

 

[spacester]

GM is G * M<br /><br />G is the universal gravitational constant. It's the same number for everything.<br /><br />M is the mass of the planet.<br /><br />It turns out to be easier to measure GM for a planet than to measure M directly. So that's what gets published: GM instead of just M.<br /><br />In practice, you rarely use M all by itself. In most equations, you see GM together. <div class="Discussion_UserSignature"> </div>

 

[arobie]

Ok, Thanks. <img src="/images/icons/smile.gif" />