Tutorial: Basic Orbiting (Technical)
Contents
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):
- Launch straight up, and continue to climb up to about 10000 meters.
- Then, gradually start leveling off. You will start gaining horizontal speed.
- 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.
Formulae and Tables
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:
| 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 |
