please help to convert this formula into linear form

kukidog

New member
Joined
Jun 3, 2014
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Hi everbody,
Can you please help me to convert this formula into linear form.

a8457a2a56ba9cc0417aa306f65ac101.png


Where:
b72bb92668acc30b4474caff40274044.png
= Gravitational parameter of parent body 3530.461 km³/s²
4d554a7e92878e1fcb95a1aa3d1186a4.png
= The altitude of first orbit (100 km in this case)
acb7bc85ecad9b0a5ba463144b229605.png
= The altitude of second orbit (200 km in this case)
e1e1d3d40573127e9ee0480caf1283d6.png
= The radius of parent body (600 km in this case).

Thanks in advance.
 

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If I'm not mistaken, you want to put dV = f(r1, r2, R) into a linear form.
dV1 = f(r1 sub 0, r2 sub 0, R sub 0) + f sub r1 * (r1 - r1 sub 0) + f sub r2 * (r2 - r2 sub 0) +
f sub R * (R - R sub 0).
where "r1 sub 0" is const you provide for r1, same for "r2 sub 0" and "R sub 0"
"f sub r1" is the partial derivative with respective to r1, same for "f sub r2" and "f sub R".
sorry I can not write these symbols.
 
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