Difference between revisions of "Tutorial: Basic Orbiting (Math)/zh-cn"

Revision as of 03:42, 3 June 2013

在基础轨道飞行指南篇中，你了解了轨道飞行的概念以及基本的轨道稳定调整，还拿到了一个轨道列表，可以籍此了解某轨道的重要参数。现在，假如你的轨道并不在这个表里该怎么办？假如你需要一个特定周期的轨道呢？下面这些公式会在这些场合起作用。

Orbital Speed

The relation between orbital speed and acceleration is given by the formula:

${\displaystyle a={\frac {v^{2}}{r}},}$

where a is the acceleration due to gravity, v is the horizontal speed, and r is the radius of orbit.

Of course, gravity varies depending on your distance from the planet, so we also need the following formula to determine a based on your altitude:

${\displaystyle a=g\left({\frac {R}{R+h}}\right)^{2},}$

where g is the acceleration due to gravity at sea level (9.807 m/s²), R is the radius of Kerbin (600 km), and h is the altitude of your orbit.

Note: Since the radius of your orbit r is equal to the radius of Kerbin R plus your altitude h, we can substitute R + h for r.

Now we have two expressions for a, so we set them on opposite sides of an equation and simplify:

${\displaystyle {\begin{aligned}g\left({\frac {R}{(R+h)}}\right)^{2}&={\frac {v^{2}}{r}}\\g\left({\frac {R}{(R+h)}}\right)^{2}&={\frac {v^{2}}{R+h}}\\g{\frac {R^{2}}{(R+h)^{2}}}&={\frac {v^{2}}{R+h}}\\g{\frac {R^{2}}{R+h}}&=v^{2}\\v^{2}&=g{\frac {R^{2}}{R+h}}\\v&={\sqrt {g{\frac {R^{2}}{R+h}}}}\\v&=R{\sqrt {\frac {g}{R+h}}}\\\end{aligned}}}$

Finally, substituting known values for g and R,

${\displaystyle v=600\ 000\ \mathrm {m} {\sqrt {\frac {9.807\ \mathrm {m} /\mathrm {s} ^{2}}{600\ 000\ \mathrm {m} +h}}}}$

Orbital Period

From the basic mechanics formula:

${\displaystyle d=vt}$

We know v from the above, and d is simply the circumference of a circle with a radius equal to your orbital altitude plus the radius of Kerbin:

${\displaystyle t=2\pi {\frac {600\ 000\ \mathrm {m} +h}{v}}}$