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A rendezvous usually takes place in orbit, e.g. when spacecrafts are travelling to a space station. If two spacecraft are close enough to each other (< 300m) and travel in similar orbits they are said to rendezvous. In such a situation, both spacecraft can stay close to the space station with minimal corrections (linear [[RCS]]). | A rendezvous usually takes place in orbit, e.g. when spacecrafts are travelling to a space station. If two spacecraft are close enough to each other (< 300m) and travel in similar orbits they are said to rendezvous. In such a situation, both spacecraft can stay close to the space station with minimal corrections (linear [[RCS]]). | ||
| − | There are two ways to | + | There are two possible ways to get to rendezvous: |
* direct insertion into the space station's orbit, or | * direct insertion into the space station's orbit, or | ||
* insertion into a catch-up orbit. | * insertion into a catch-up orbit. | ||
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===Catch-up orbit=== | ===Catch-up orbit=== | ||
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| − | + | The best launch window for a catch-up orbit is one that places the ship into the same orbital plane as the target but with a significantly lower orbit. The important measure is the difference between the [[large semiaxis|large semiaxes]], since the large semiaxis defines the time needed for one revolution around [[Earth]]. | |
| − | The best launch window for a catch-up orbit is one that places the ship into the same orbital plane as the target but with a significantly lower orbit. The important measure is the difference between the [[ | ||
The point at which the spacecraft should leave the (almost circular) catch-up orbit can be calculated using this formula: | The point at which the spacecraft should leave the (almost circular) catch-up orbit can be calculated using this formula: | ||
| − | <math>\Delta \varphi = | + | <math>\Delta \varphi = \pi \left [ 1 - ( 2 m - 1 ) \left ( \frac {a}{r_z} \right )^{\frac{3}{2}} \right ] </math> |
where | where | ||
* <math>\Delta \varphi</math> - the [[distance angle]] between the chasing spacecraft and the target spacecraft. | * <math>\Delta \varphi</math> - the [[distance angle]] between the chasing spacecraft and the target spacecraft. | ||
* <math>m</math> - the number of [[apoapsis|apogee]] passes on the [[transfer ellipse]]. | * <math>m</math> - the number of [[apoapsis|apogee]] passes on the [[transfer ellipse]]. | ||
| − | * <math>a</math> - the | + | * <math>a</math> - the large semiaxis of the transfer ellipse. |
* <math>r_z</math> - the radius of the target orbit (assumed circular). | * <math>r_z</math> - the radius of the target orbit (assumed circular). | ||
| − | When this angle is reached, the chasing spacecraft performs a prograde burn to enter the planned transfer ellipse. This is called the ''intercept burn''. | + | When this angle is reached, the chasing spacecraft performs a prograde burn to enter the planned transfer ellipse. This is called the ''intercept burn''. |
===Rendezvous burn=== | ===Rendezvous burn=== | ||
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When reaching the final apogee pass of the transfer ellipse, all possible errors will usually bring the spacecraft away from its desired course (including errors because the initial orbits have not been perfectly circular). Because of that influences, the next orbit is usually not the final target orbit, but again a less eccentric chasing orbit. The parameters of this orbit can be calculated using the following formula: | When reaching the final apogee pass of the transfer ellipse, all possible errors will usually bring the spacecraft away from its desired course (including errors because the initial orbits have not been perfectly circular). Because of that influences, the next orbit is usually not the final target orbit, but again a less eccentric chasing orbit. The parameters of this orbit can be calculated using the following formula: | ||
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* The target arrives at the target point before the chasing spacecraft: | * The target arrives at the target point before the chasing spacecraft: | ||
<math>a = r_z \cdot {}^3 \sqrt {\left ( 1 - \frac{1}{n} \cdot \frac{ \Delta \varphi}{2 \pi}\right )^2}</math> | <math>a = r_z \cdot {}^3 \sqrt {\left ( 1 - \frac{1}{n} \cdot \frac{ \Delta \varphi}{2 \pi}\right )^2}</math> | ||
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===Rendezvous=== | ===Rendezvous=== | ||
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When the other spacecraft is far away (such as on the other side of the planet), a more fuel-efficient way to get there may be via a ballistic trajectory. This can be thought of as "throwing" the spacecraft towards the target, and letting it fall close to it. On planets with no atmosphere the [[Map MFD]] can be used to estimate and adjust the ballistic trajectory and the landing point. | When the other spacecraft is far away (such as on the other side of the planet), a more fuel-efficient way to get there may be via a ballistic trajectory. This can be thought of as "throwing" the spacecraft towards the target, and letting it fall close to it. On planets with no atmosphere the [[Map MFD]] can be used to estimate and adjust the ballistic trajectory and the landing point. | ||
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