Getting About in Earth Orbit
To change from one circular orbit to another in the same plane, the most
economical path is known as the Hohmann transfer orbit. This is an
elliptical orbit whose perigee (closest approach to earth) is the same
as the radius of the lower orbit, and whose apogee (highest point above
the Earth) is the same as the radius of the higher orbit.
To change the altitude of an orbit therefore requires two engine burns:
the insertion burn to change the circular starting orbit to the
elliptical transfer orbit; and the arrival burn to change the elliptical
transfer orbit to the circular destination orbit.
The magnitude of the required burns for selected orbits is given in the
Earth Orbit Burn Table below.
Figures above the diagonal are for perigee burns; figures below the
diagonal are apogee burns; diagonal figures are the orbital velocities
for circular orbits at that altitude.
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Earth Orbit Burn Table
Altitude | 100 | 250 | 500 | 1000 | 2500 | 5000 | 10,000 | 22,240 | 50,000 | 100,000 | 235,000 | escape |
100 | 4.8 | 0.04 | 0.1 | 0.2 | 0.5 | 0.8 | 1.2 | 1.5 | 1.8 | 1.9 | 2.0 | 2.0 |
250 | 0.04 | 4.8 | 0.1 | 0.2 | 0.5 | 0.8 | 1.1 | 1.5 | 1.7 | 1.8 | 1.9 | 2.0 |
500 | 0.1 | 0.1 | 4.7 | 0.1 | 0.4 | 0.7 | 1.1 | 1.4 | 1.7 | 1.8 | 1.9 | 1.9 |
1000 | 0.2 | 0.2 | 0.1 | 4.4 | 0.3 | 0.6 | 0.9 | 1.3 | 1.6 | 1.7 | 1.8 | 1.8 |
2500 | 0.5 | 0.4 | 0.4 | 0.3 | 3.9 | 0.3 | 0.7 | 1.0 | 1.3 | 1.4 | 1.5 | 1.6 |
5000 | 0.7 | 0.7 | 0.6 | 0.5 | 0.3 | 3.3 | 0.3 | 0.7 | 1.0 | 1.2 | 1.3 | 1.4 |
10000 | 0.9 | 0.8 | 0.8 | 0.7 | 0.5 | 0.3 | 2.6 | 0.4 | 0.7 | 0.9 | 1.0 | 1.1 |
22240 | 0.9 | 0.9 | 0.9 | 0.8 | 0.7 | 0.5 | 0.3 | 1.9 | 0.3 | 0.5 | 0.7 | 0.8 |
50000 | 0.8 | 0.8 | 0.8 | 0.8 | 0.7 | 0.6 | 0.5 | 0.3 | 1.3 | 0.2 | 0.4 | 0.6 |
100000 | 0.7 | 0.7 | 0.7 | 0.7 | 0.6 | 0.6 | 0.5 | 0.4 | 0.2 | 0.9 | 0.2 | 0.4 |
235000 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.5 | 0.4 | 0.4 | 0.2 | 0.1 | 0.6 | 0.3 |
Altitude in miles above the Earth's surface; delta-V in miles per second. 22,240 miles altitude is geostationery orbit; 235,000 miles is the altitude of L4, L5 and the Moon; The "Escape" column gives the minimum burn required to leave Earth orbit and enter solar orbit.
For example: The Sanford class Junker "Harold" is orbitting at 250 miles
and needs to move to geostationary orbit (22240 miles). The insertion
burn is a perigee burn, so cross-referencing above the diagonal we find
a 1.5 mile/s burn is required. The arrival burn is therefore 0.9
miles/s.
Later, "Harold" moves down to 1000 mile altitude orbit. In this case,
the insertion burn is an apogee burn, so cross-referencing below the
diagonal gives a burn of 0.8 miles/s. The arrival burn is then 1.3 miles/s.
The time required for a transfer orbit can be found from the table
below. Values below the diagonal are the transfer times (a complete
orbit will take twice this time); values on the diagonal are the period
of a circular orbit at that altitude.
Transfer Orbit Times
| Perigee |
| 100 | 250 | 500 | 1000 | 2500 | 5000 | 10,000 | 22,200 | 50,000 | 100,000 | 235,000 |
Apogee |
100 | 87m |
250 | 45m | 92m |
500 | 47m | 48m | 101m |
1000 | 51m | 52m | 55m | 2.0h |
2500 | 64m | 66m | 68m | 73m | 2.9h |
5000 | 1.5h | 1.5h | 1.5h | 1.6h | 1.9h | 4.8h |
10,000 | 2.4h | 2.4h | 2.5h | 2.6h | 2.9h | 3.5h | 9.3h |
22,241 | 5.2h | 5.3h | 5.4h | 5.5h | 5.9h | 6.6h | 8.0h | 1.0d |
50,000 | 13.9h | 14.0h | 14.1h | 14.3h | 14.8h | 15.7h | 17.6h | 22.6h | 2.9d |
100,000 | 1.5d | 1.5d | 1.5d | 1.5d | 1.5d | 1.6d | 1.7d | 2.0d | 2.6d | 7.9d |
235,000 | 5.0d | 5.0d | 5.0d | 5.0d | 5.0d | 5.1d | 5.3d | 5.7d | 6.6d | 8.3d | 27.4d |
m = minutes; h = hours; d = days
Changing Planes
Not all Earth satellites are stationed tidily in equatorial orbits.
Where the exact inclination is not critical to a satellite's function,
they usually share the inclination of their launching space-ports'
latitude. For example, launching from Cape Canaveral to an orbit
inclined at 28 degrees from equatorial is the most economical option.
Other specialised satellites (especially space defence platforms) may
be highly inclined, even into polar orbits. It is therefore necessary
from time to time for those who work in orbit to change their orbital plane.
To change the orbital plane of a satellite or spacecraft, look up the
orbital velocity on the diagonal of the Earth Orbit Burn Table above,
check the difference in inclination on the table below and apply the multiplier for
the required burn. For example, to move from an orbit inclined at 40
degrees and an altitude of 1000 miles to a polar orbit (90 degrees) at
the same altitude requires a burn of 4.4 x 0.8 = 3.5 miles/s.
Note that it's easier to change the orbital plane the higher the orbit is.
Orbital Plane Change Table
Angle | Multiplier |
10° | 0.2 |
20° | 0.3 |
30° | 0.5 |
40° | 0.7 |
50° | 0.8 |
60° | 1.0 |
70° | 1.1 |
80° | 1.3 |
90° | 1.4 |
Spaceport Latitudes
Quito (Ecuador) | 0° |
Kiritimati (Christmas Island) | 0° |
Alcantara (Brazil) | 2° |
Kourou (Guiana) | 5° |
Siriharikota (India) | 14° |
Sanya (China) | 20° |
Gando (Canary Islands) | 28° |
Cape Canaveral (USA) | 28° |
Xichang (China) | 28° |
Hammaguira (Algeria) | 31° |
Kagoshima (Japan) | 31° |
Woomera (Australia) | 31° |
Vandenburg (USA) | 35° |
Overberg (South Africa) | 37° |
Taiyuan (China) | 37° |
Jiuquan (China) | 41° |
Baikonor (Khazakstan) | 46° |
Plesetsk (Russia) | 63° |
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This page updated Tues, Nov 1st, 2005 around about 01:00 ish (GMT)