target="_blank" rel="nofollow" href="#fb3_img_img_fa7c2697-38e5-5c94-9d1a-c1778d284edb.png" alt="images"/> km, its altitude decays very rapidly, and it re‐enters the atmosphere after only 3.5 orbits (Fig. 1.2). Hence, the life of the spacecraft is only about 3.5 revolutions in a circular orbit of altitude 180 km above Earth. As Figs. 1.1 and 1.2 indicate, a stable orbit around Earth for this spacecraft should have Table 1.1 Variation of density with altitude in Earth's atmosphere
|
Altitude, |
Density, |
| 0 | 1.2252 |
| 1 | 1.1119 |
| 5 | 0.7366 |
| 10 | 0.4136 |
| 20 | 0.0891 |
| 30 | 0.0185 |
| 40 | 0.0041 |
| 50 | 0.0011 |
| 60 |
|
| 70 |
|
| 80 |
|
| 90 |
|
| 100 |
|
| 110 |
|
| 120 |
|
| 150 |
|
| 200 |
|
| 250 |
|
Apart from the atmospheric effects, there are other environmental perturbations to a spacecraft's flight around a central body, which is assumed to be spherical as required by Eq. (1.2). These are the gravity of the actual (non‐spherical) shape of the central body, as well as the gravity of other remote large bodies, and the solar radiation pressure. However, such effects are typically small enough to be considered small perturbations when compared to the spherical gravity field of the central body given by Eq. (1.2). Such effects can be regarded as small perturbations applied to the orbit governed by Eq. (1.2), and should be carefully modelled in order to predict the actual motion of the spacecraft.
Figure 1.1 Decay in the orbit due to atmospheric drag for a spacecraft initially placed in a circular orbit of
Figure 1.2 Decay in the orbit due to atmospheric drag for a spacecraft initially placed in a circular orbit of
1.1.2 Gravity as the Governing Force
Space flight is primarily governed by gravity. “Governing” implies dictating the path a given body describes in a three‐dimensional space. Aircraft and rocket flights are not primarily governed by gravity, because there are other forces acting on the body, such as the lift and the thrust, which are of comparable magnitudes to that of gravity and therefore determine the flight path. Discovered and properly analyzed for the first time by Newton in the late
1.1.3 Topics in Space Dynamics
Space dynamics consists of two parts: (a) orbital mechanics, which describes the translation in space of the centre of mass of a rigid body primarily under the influence of gravity, and (b) attitude dynamics, which is the description of the rotation of the rigid body about its own centre of mass. While these two topics are largely studied separately, in some cases orbital mechanics and attitude
