Game Development Reference
In-Depth Information
Figure 11-8.
Velocity profile for vertical ascent simulation
The profiles shown in Figure 11-8 are for a rocket traveling vertically throughout its ascent.
To achieve orbit, a rocket has to gradually pitch itself over so at the end of its ascent its velocity
vector is horizontal or nearly horizontal relative to the earth. In the next section, we'll discuss a
little bit about orbits and some other related topics.
Orbits
An object that is traveling in a curved path around a planet is said to be in
orbit
about the
planet. An object, whether natural or man-made, that is in orbit around a planet is known as a
satellite
. One of the main functions of large-scale rockets is to put satellites into orbit around
the earth. The subject of orbital mechanics can become fairly complicated, so this section will
only provide a brief introduction.
In order to achieve orbit, a satellite must counteract the gravitational pull of the earth. In
Chapter 3, you learned that the gravitational force,
F
G
, on an object due to the earth is propor-
tional to the mass of the earth,
m
e
, the mass of the object,
m
1
, and the square of the distance,
r
,
between the center of the two bodies.
mm
m
F
=
6.67
e
−
11
e
1
=
3.985
e
+
14
1
(11.15)
G
r
2
r
2
Gravitational force pulls the satellite towards the center of the earth. Balancing this force
is the centripetal force caused by the motion of the satellite as it travels in orbit around the
planet. The centripetal force is equal to the mass of the satellite multiplied by the square of the
velocity divided by the instantaneous radius of curvature of the flight path of the satellite.
