Tutorial: Basic Orbiting/fr

Aller dans l'espace est relativement simple, mais y rester sans retomber au sol ou dériver sans fin dans l'espace est une autre paire de manches. Ce tutoriel vous expliquera comment procéder à une mise en orbite et à y rester, comment circulariser votre orbite ou créer une orbite elliptique et comment diminuer ou augmenter votre orbite.

Stabiliser une orbite

Lors d'une orbite, votre vaisseau va atteindre une altitude maximale, l''apoastre, et une altitude minimale, le périastre, diamétralement opposés l'un à l'autre. En ces deux points, la vitesse verticale (par rapport à la surface) est nulle, on peut donc aisément calculer notre vitesse orbitale (qui est la même que la vitesse surface). C'est en ces deux endroits qu'il est le plus facile (et le moins coûteux en carburant) de faire des corrections de trajectoire afin de modifier l'orbite. La différence d'altitude entre périastre et apoastre est caractérisée par l'excentricité de l'orbite. Une orbite très circulaire a une excentricité nulle et une orbite très elliptique a une excentricité proche de 1.

Vous trouverez facilement des calculateurs qui vous permettent de calculer tous les paramètres orbitaux et le $\Delta v$ dont vous avez besoin pour vos manœuvres. que vous utilisiez un calculateur ou que vous calculiez vos orbites à la main, le mode opératoire est le même que celui explosé ci-dessous.

Afin de former une belle orbite bien ronde, vous devez déterminer à quelle vitesse vous allez. Les paramètres que vous devez connaître pour calculer votre vitesse est votre distance $r$ au centre du corps que vous orbitez (c'est-à-dire la somme du rayon de la planète et de votre altitude), le demi-grand axe $a$ de votre orbite, et la masse $M_{C}$ du corps orbité.

Vous pouvez calculer votre vitesse en tout point de l'orbite par la formule suivante :

$v={\sqrt {\mu \left({\frac {2}{r}}-{\frac {1}{a}}\right)}}$

First, in order to get into a nice, round orbit, you need to determine how fast to go. The mathematical basis for orbital speed is determined from your current distance from your central body ($r$), your semi-major axis from your central body ($a$), and the mass of the central body itself ($M$). These may be use to find the speed at an orbit around any body using the relation

$v={\sqrt {GM\left({\frac {2}{r}}-{\frac {1}{a}}\right)}}$

where $G$ is the gravitational constant $6.674\cdot 10^{-11}\mathrm {\frac {m^{3}}{kg\cdot s^{2}}}$. Keep in mind that distances to the central body must account not only for altitude but also for the radius ($R$) of whatever body you are orbiting. The exact values of $M$ and $R$ may be found on their respective pages.

Returning to our case, the higher your orbit, the less gravity you'll feel from Kerbin, so the slower you'll need to go to be in a circular orbit. Determine the proper speed for your altitude at apoapsis or periapsis either by hand, by calculator, or by table. You'll probably want to watch your altimeter as you near one of the critical points, remember the altitude, determine your desired speed, and make the correction on your next pass. If you want to "round out" your orbit from apoapsis, you need to speed up to avoid falling back down to periapsis. Point your craft in the exact direction of travel (use the green circular indicator on the gimbal to line up), and apply thrust until you've gained enough speed. To round out an orbit from periapsis, you need to slow down to avoid climbing back up to apoapsis. Point your craft in the opposite direction of travel (indicated on the gimbal by a green circle with an "X" through it), and apply thrust until you have slowed to the speed indicated by the table. You should then be in an orbit that is very close to circular! Depending on how eccentric your initial orbit was, you may need to make a large correction on your first pass followed by a small correction on a subsequent pass to get very stable.

If you have version 0.11 or better, adding a set of RCS thrusters to your craft can help make minute adjustments to an orbit easier. Version 0.11 also allows you to see the current trajectory (and read periapsis and apoapsis altitudes) by switching to the Map view (M key)

Transfer Orbits

The most efficient way to transfer from a lower circular orbit to a higher circular orbit (or vice-versa) is to use an elliptical transfer orbit, also known as a Hohmann transfer orbit. To transfer, we make the periapsis of the elliptical orbit the same as the radius of the lower orbit, and the apoapsis of the elliptical orbit the same as the radius of the higher orbit. If you are going from low to high, you make a burn in the direction of travel to elongate your orbit. You will climb in altitude as you travel around the planet to the apoapsis of your transfer orbit. Then, make a second burn to round out the new, higher orbit (as described above). To go from high to low, do the opposite: Burn in the opposite direction of travel, then fall down to the periapsis of your transfer orbit, and make a second burn to round out the lower orbit (again in the opposite direction of travel).

Target Speed

The key to transfer orbits is figuring out how much speed to add or subtract to reach a desired new orbital altitude. To do this, use the formula below to determine the target velocity for your initial burn:

$v=1,878,968\cdot {\sqrt {{\frac {2}{r_{i}}}-{\frac {2}{(r_{l}+r_{h})}}}}$

In this formula, r_l and r_h are the radii of the lower and higher orbits, respectively, and r_i is the radius of the initial orbit. If you are transferring to a higher orbit, r_i will be equal to r_l, and v will be faster than your current speed, so burn in the direction of travel to reach v. If you are transferring to a lower orbit, r_i will be equal to r_h, and v will be slower than your current speed, so burn in the opposite direction to reach v. Remember, v is the target speed for your initial burn that puts you into the elliptical transfer orbit. Once you reach your new orbital altitude, you need to make a second burn to round out your orbit, using the same technique described in the stabilizing your orbit section.

Details of where this formula comes from are in the technical section below. When using this formula, take care to remember that the radius of an orbit is equal to the orbital altitude plus Kerbin's radius (600 000 m).

De-orbiting

The most efficient way to de-orbit from any altitude is to initiate a transfer orbit with a periapsis below 70000 m, the edge of Kerbin's atmosphere. Note that the upper atmosphere is very thin so if you do not want to wait for several orbits of aerobraking, aim for under 35000 m and thicker air. As you approach periapsis, the atmospheric drag will start to slow your craft and eventually it can no longer maintain orbit.

R code snippet for planning Hohmann transfer

   hohmann <- function(from_alt,to_alt){
     # provides information needed to perform
     # a hohmann transfer from a circular ortbit
     # at from_alt (km) to a circular orbit at to_alt (km)
     mu  <- 3530.394     # Gravitational parameter (km^3/s^2)
     R   <- 600          # Kerbin radius (km)
     r1  <- from_alt+R   # radius 1 (km)
     r2  <- to_alt+R     # radius 2 (km)
     vc1 <- sqrt(mu/r1)  # circular orbit velocity 1 (km/s)
     vc2 <- sqrt(mu/r2)  # circular orbit velocity 2 (km/s)
     a   <- (r1+r2)/2    # semi-major axis of transfer orbit (km)
     T   <- 2*pi*sqrt((a^3)/mu)  # period of transfer orbit (s)
     dv1 <- (sqrt(r2/a)-1)*vc1   # delta v1 (km/s)
     dv2 <- (1-sqrt(r1/a))*vc2   # delta v2 (km/s)
     b1  <- list(from=vc1,to=vc1+dv1) # burn one from-to velocities (km/s)
     t   <- T/2          # time between burns (s)
     b2  <- list(from=vc2+dv2,to=vc2) # burn two from-to velocities (km/s)
     out <- list(from_alt=from_alt,b1=b1,t=t,b2=b2,to_alt=to_alt)
   return(out)}

Example usage

Produce a graph showing the speeds need to transfer from a range of circular orbit altitudes into a landing orbit.

plot(100*1:40,1000*hohmann(100*1:40,34)$b1$to,main="Landing speeds",xlab="altitude (km)",ylab="speed (m/s)")

R project Link [1]

Transfer Orbits

Coming soon!

Orbital Table

Note: The atmosphere previously had a sharp cutoff at 34.5 km, but now extends to approximately 68 km. Below this altitude, your orbit will gradually decay. The decay becomes quite rapid below about 45 km. The orbital parameters below 68 km are provided for reference, but understand that you will not be able to maintain these orbits without regular corrections to counteract the atmospheric drag.

Altitude (m)	Horizontal Speed (m/s)	Orbital Period (min)
40000	2348.7	28.54
50000	2330.6	29.21
60000	2312.8	29.88
70000	2295.5	30.56
80000	2278.6	31.25
85000	2270.3	31.60
90000	2262.0	31.94
100000	2245.8	32.64
110000	2229.9	33.34
120000	2214.4	34.05
130000	2199.2	34.76
140000	2184.3	35.48
150000	2169.6	36.20
160000	2155.3	36.93
170000	2141.3	37.66
180000	2127.5	38.39
190000	2114.0	39.13
200000	2100.7	39.88
210000	2087.7	40.63
220000	2075.0	41.38
230000	2062.4	42.14
240000	2050.1	42.91
250000	2038.0	43.68
260000	2026.1	44.45
270000	2014.5	45.23
280000	2003.0	46.01
290000	1991.7	46.79
300000	1980.6	47.59
310000	1969.7	48.38
320000	1959.0	49.18
330000	1948.4	49.98
340000	1938.0	50.79
350000	1927.8	51.61
360000	1917.7	52.42
370000	1907.8	53.24
380000	1898.0	54.07
390000	1888.4	54.90
400000	1879.0	55.73
410000	1869.6	56.57
420000	1860.5	57.41
430000	1851.4	58.26
440000	1842.5	59.11
450000	1833.7	59.96
460000	1825.0	60.82
470000	1816.5	61.69
480000	1808.0	62.55
490000	1799.7	63.42
500000	1791.5	64.30
510000	1783.4	65.18
520000	1775.5	66.06
530000	1767.6	66.95
540000	1759.8	67.84
550000	1752.1	68.73
560000	1744.6	69.63
570000	1737.1	70.53
580000	1729.7	71.44
590000	1722.4	72.35
600000	1715.3	73.26
610000	1708.2	74.18
620000	1701.1	75.10
630000	1694.2	76.03
640000	1687.4	76.96
650000	1680.6	77.89
660000	1673.9	78.83
670000	1667.3	79.77
680000	1660.8	80.71
690000	1654.3	81.66
700000	1648.0	82.61
710000	1641.7	83.56
720000	1635.4	84.52
730000	1629.3	85.48
740000	1623.2	86.45
750000	1617.2	87.42
760000	1611.2	88.39
770000	1605.3	89.37
780000	1599.5	90.35
790000	1593.7	91.33
800000	1588.0	92.32
810000	1582.4	93.31
820000	1576.8	94.31
830000	1571.3	95.30
840000	1565.8	96.31
850000	1560.4	97.31
860000	1555.0	98.32
870000	1549.7	99.33
880000	1544.5	100.35
885000	1541.9	100.86
890000	1539.3	101.37
900000	1534.2	102.39
910000	1529.1	103.41
920000	1524.0	104.44
930000	1519.1	105.47
940000	1514.1	106.51
950000	1509.2	107.55
960000	1504.4	108.59
970000	1499.6	109.64
980000	1494.8	110.69
990000	1490.1	111.74
1000000	1485.5	112.79
2 868 378	1008.910	6 hours
8 140 000	635.4	24 hours