Tutorial: Basic Orbiting (Technical)

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Orbiting Tutorial

Getting into space is relatively easy, but staying there without drifting endlessly into space or falling back down to Kearth can be challenging. This tutorial will teach you how to get into and remain in orbit, how to adjust your orbit to be circular or elliptical, and how to adjust to a higher or lower orbit.

Your first orbit

A good procedure for getting into orbit was posted by HarvesteR on the KSP forums (edited with a better horizontal speed based on the orbital tables below):

  1. Launch straight up, and continue to climb up to about 10000 meters.
  2. Then, gradually start leveling off. You will start gaining horizontal speed.
  3. Now you're basically trading vertical speed for horizontal speed. The idea is to get to 0 vertical speed at about 40000 meters up, and be moving horizontally at about 2350 m/s.

This will put you in a stable orbit. The altitude at which you start leveling off and the altitude at which you reach orbital velocity will depend a lot on how your rocket is designed. The idea, however, is to get out of the thickest part of the atmosphere before you start adding horizontal speed, so that you aren't wasting energy adding horizontal speed which will just bleed off due to air resistance.

It is likely that you will overshoot or undershoot these figures by a wide margin on your first couple attempts. Don't worry! Manual orbit insertion is difficult, that's why NASA uses computer guidance! When you finally do get into a stable orbit, you'll probably be on an elliptical trajectory; that is, your ship will coast away from the planet, gradually losing speed. When it reaches its maximum altitude, it will start to fall back toward Kearth, picking up speed again. If you're going fast enough, you'll fall "past" Kearth instead of into it, and that's orbiting.

Controlling your orbit

During each orbit, your craft will reach maximum altitude, called apokee, and on the opposite side of the planet, it will reach minimum altitude, called perikee. At both apokee and perikee, your vertical speed will be zero. These points are the easiest points to make orbital corrections, because you can easily determine how fast to go when your vertical speed is zero. Note: The relative difference between your orbit's apokee and perikee is called its eccentricity. Orbits that are exactly circular have zero eccentricity, and highly "flattened-out" orbits have eccentricity close to 1.

First, in order to get into a nice, round orbit, you need to determine how fast to go. The higher your orbit, the less gravity you'll feel from Kearth, so the slower you'll need to go to be in a circular orbit. Consult the table below to determine the proper speed for your altitude at apokee or perikee. You'll probably want to watch your altimiter as you near one of the critical points, remember the altitude, look up the speed in the table, and make the correction on your next pass. If you want to "round out" your orbit from apokee, you need to speed up to avoid falling back down to perikee. 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 perikee, you need to slow down to avoid climbing back up to apokee. 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.

Video Tutorial

Video Example Of Building A Rocket And Taking It To Orbit

Technical Details

Below are the formulae used to determine orbital speeds, and a table of orbital speeds up to 1000 km.

Formulae

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

a = v2 / 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:

a = g * (R / (R + h))2,

where g is the acceleration due to gravity at sea level (9.81 m/s2), R is the radius of Kearth (600 km), and h is the altitude of your orbit.

Note: From here, we will substitute R + h for r, since the radius of your orbit is equal to the radius of Kearth plus your altitude.

Substituting for a and simplifying, we get:

g * (R / (R + h))2 = v2 / (R + h)

g * R2 / (R + h) = v2

v = R * sqrt(g / (R + h))

Finally, substituting known values for g and R,

v = 600 000 m * sqrt(9.81 m/s2 / (600 000 m + h))

From this formula, we can produce the table below.

Orbital Table

Note: Altitudes below 35 km are listed for reference, but the atmosphere will quickly drag you out of orbit at these altitudes.

Altitude Horizontal Speed
0 km 2425.56 m/s
5 km 2415.52 m/s
10 km 2405.60 m/s
15 km 2395.80 m/s
20 km 2386.12 m/s
25 km 2376.56 m/s
30 km 2367.11 m/s
35 km 2357.77 m/s
40 km 2348.54 m/s
45 km 2339.42 m/s
50 km 2330.41 m/s
55 km 2321.49 m/s
60 km 2312.68 m/s
65 km 2303.97 m/s
70 km 2295.36 m/s
75 km 2286.84 m/s
80 km 2278.42 m/s
85 km 2270.09 m/s
90 km 2261.85 m/s
95 km 2253.70 m/s
100 km 2245.64 m/s
105 km 2237.66 m/s
110 km 2229.77 m/s
115 km 2221.96 m/s
120 km 2214.23 m/s
125 km 2206.58 m/s
130 km 2199.01 m/s
135 km 2191.52 m/s
140 km 2184.10 m/s
145 km 2176.76 m/s
150 km 2169.49 m/s
155 km 2162.29 m/s
160 km 2155.17 m/s
165 km 2148.12 m/s
170 km 2141.13 m/s
175 km 2134.21 m/s
180 km 2127.36 m/s
185 km 2120.57 m/s
190 km 2113.85 m/s
195 km 2107.20 m/s
200 km 2100.60 m/s
205 km 2094.07 m/s
210 km 2087.59 m/s
215 km 2081.18 m/s
220 km 2074.82 m/s
225 km 2068.53 m/s
230 km 2062.29 m/s
235 km 2056.10 m/s
240 km 2049.98 m/s
245 km 2043.90 m/s
250 km 2037.88 m/s
255 km 2031.91 m/s
260 km 2026.00 m/s
265 km 2020.13 m/s
270 km 2014.32 m/s
275 km 2008.56 m/s
280 km 2002.84 m/s
285 km 1997.18 m/s
290 km 1991.56 m/s
295 km 1985.99 m/s
300 km 1980.46 m/s
305 km 1974.99 m/s
310 km 1969.55 m/s
315 km 1964.16 m/s
320 km 1958.82 m/s
325 km 1953.52 m/s
330 km 1948.26 m/s
335 km 1943.04 m/s
340 km 1937.87 m/s
345 km 1932.74 m/s
350 km 1927.64 m/s
355 km 1922.59 m/s
360 km 1917.58 m/s
365 km 1912.60 m/s
370 km 1907.67 m/s
375 km 1902.77 m/s
380 km 1897.91 m/s
385 km 1893.09 m/s
390 km 1888.30 m/s
395 km 1883.55 m/s
400 km 1878.83 m/s
405 km 1874.15 m/s
410 km 1869.51 m/s
415 km 1864.90 m/s
420 km 1860.32 m/s
425 km 1855.78 m/s
430 km 1851.27 m/s
435 km 1846.79 m/s
440 km 1842.35 m/s
445 km 1837.94 m/s
450 km 1833.55 m/s
455 km 1829.20 m/s
460 km 1824.88 m/s
465 km 1820.60 m/s
470 km 1816.34 m/s
475 km 1812.11 m/s
480 km 1807.91 m/s
485 km 1803.74 m/s
490 km 1799.60 m/s
495 km 1795.48 m/s
500 km 1791.40 m/s
505 km 1787.34 m/s
510 km 1783.31 m/s
515 km 1779.31 m/s
520 km 1775.33 m/s
525 km 1771.38 m/s
530 km 1767.46 m/s
535 km 1763.56 m/s
540 km 1759.69 m/s
545 km 1755.84 m/s
550 km 1752.02 m/s
555 km 1748.23 m/s
560 km 1744.45 m/s
565 km 1740.71 m/s
570 km 1736.98 m/s
575 km 1733.28 m/s
580 km 1729.61 m/s
585 km 1725.95 m/s
590 km 1722.32 m/s
595 km 1718.72 m/s
600 km 1715.13 m/s
605 km 1711.57 m/s
610 km 1708.03 m/s
615 km 1704.51 m/s
620 km 1701.02 m/s
625 km 1697.54 m/s
630 km 1694.09 m/s
635 km 1690.65 m/s
640 km 1687.24 m/s
645 km 1683.85 m/s
650 km 1680.48 m/s
655 km 1677.13 m/s
660 km 1673.80 m/s
665 km 1670.49 m/s
670 km 1667.20 m/s
675 km 1663.92 m/s
680 km 1660.67 m/s
685 km 1657.44 m/s
690 km 1654.22 m/s
695 km 1651.02 m/s
700 km 1647.85 m/s
705 km 1644.69 m/s
710 km 1641.54 m/s
715 km 1638.42 m/s
720 km 1635.32 m/s
725 km 1632.23 m/s
730 km 1629.16 m/s
735 km 1626.10 m/s
740 km 1623.07 m/s
745 km 1620.05 m/s
750 km 1617.04 m/s
755 km 1614.06 m/s
760 km 1611.09 m/s
765 km 1608.13 m/s
770 km 1605.20 m/s
775 km 1602.27 m/s
780 km 1599.37 m/s
785 km 1596.48 m/s
790 km 1593.61 m/s
795 km 1590.75 m/s
800 km 1587.90 m/s
805 km 1585.08 m/s
810 km 1582.26 m/s
815 km 1579.47 m/s
820 km 1576.68 m/s
825 km 1573.91 m/s
830 km 1571.16 m/s
835 km 1568.42 m/s
840 km 1565.69 m/s
845 km 1562.98 m/s
850 km 1560.29 m/s
855 km 1557.60 m/s
860 km 1554.93 m/s
865 km 1552.28 m/s
870 km 1549.64 m/s
875 km 1547.01 m/s
880 km 1544.39 m/s
885 km 1541.79 m/s
890 km 1539.20 m/s
895 km 1536.62 m/s
900 km 1534.06 m/s
905 km 1531.51 m/s
910 km 1528.97 m/s
915 km 1526.45 m/s
920 km 1523.94 m/s
925 km 1521.44 m/s
930 km 1518.95 m/s
935 km 1516.47 m/s
940 km 1514.01 m/s
945 km 1511.56 m/s
950 km 1509.12 m/s
955 km 1506.69 m/s
960 km 1504.27 m/s
965 km 1501.87 m/s
970 km 1499.47 m/s
975 km 1497.09 m/s
980 km 1494.72 m/s
985 km 1492.36 m/s
990 km 1490.01 m/s
995 km 1487.67 m/s