# Why is one of the foci of the ellipse of the trajectory of a space rocket in the center of the sun?

According to a book I am currently reading, space rockets and ballistic rockets fly along an elliptic path. However they differ in where the focus of the ellips describing their path lays. For space rockets on of the foci is placed at the center of the sun (for ballistic rockets it is the center of the earth). Could someone explain, why the center of the sun?

I think you have a misleading picture here.

Earth orbit bounds rockets have the earth as the centre of their ellipse.

However; for interplanetary travel, or anything that goes beyond the earth sphere of influence, your rocket will orbit the sun, hence an elliptic sun centred trajectory.

The first part of the trajectory will however, always be earth centred (that is, until you escape the earth system).

• But the trajectory is only elliptic if the rockets engine is off and the influence of the other planets or the sun is neglibile small. If more than one body of the solar system is influencing the trajectory is not pure elliptic.
– Uwe
Mar 31, 2017 at 10:40
• The OP mentioned the ellipse's focus, not the center. The focus in a circular orbit (around the sun or the Earth) does not have either focus inside the body it's orbiting. Mar 31, 2017 at 13:16
• @Steve Actually, a circle can be viewed as an ellipse where both foci are at the same point (which is in the center of the circle) so in a circular orbit both foci are in the body it's orbiting. Mar 31, 2017 at 14:49
• @1337joe Ah, you're right ... But there is no guarantee that the focus is within the body that's being orbited (there are orbits where neither focus is there), at least for non-circular orbits.. Mar 31, 2017 at 15:10
• Yes, all bodies exerce some influence on the rocket making the path non elliptic. However, if you allow some margin and simplification it is close enough to elliptic. Mar 31, 2017 at 15:44