# Change of ellipse while accelerating the rocket

• NODARman
In summary, when a rocket accelerates in space its trajectory changes from an ellipse to a hyperbola.
NODARman
TL;DR Summary
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When the rocket accelerates in space does its trajectory which is an ellipse change in size and not the focal points because the Earth is still in one of two and also the current height doesn't increase, right?

Yes the Earth's centre of mass remains the ellipse's focus that is closest to the rocket's trajectory. The ellipse changes in both shape and size as the speed increases. When the rocket accelerates past escape velocity the trajectory changes from an ellipse to a hyperbola, so it ceases to be an orbit.
I don't know what you mean by "the current height".

NODARman and Lnewqban
When a rocket accelerates (in any direction, not just in the direction of travel), its new path will share the following characteristics:

1) The new ellipse (or hyperbola) will intersect with the old one at the location where the acceleration was applied, so yes, the height at that location in the orbit will remain unchanged

2) The Earth (or body being orbited) will still be a focus, yes.

There's no requirement for the second focus to remain fixed though, and in general the second one will move (aside from a pure inclination change while at either periapse or apoapse)

If you're curious to play around with orbits, the game Kerbal Space Program is a really good way to get a feel for how orbits behave when you thrust in various directions, and how to maneuver in space. It does strictly two body mechanics (using patched conics with spheres of influence to handle travel between different bodies), but it's great for at least getting a feel for the basics, and it does so in a much more intuitive way than just looking at the math in my opinion.

cjl said:
When a rocket accelerates (in any direction, not just in the direction of travel), its new path will share the following characteristics:
I would say that the trajectory is not elliptical whilst the rocket is actually accelerating because there is not just one central attracting force. This could be more and more relevant when propulsion systems start to use low thrust - long acceleration times.

## 1. How does acceleration affect the shape of an ellipse?

Acceleration can cause the shape of an ellipse to change by altering its eccentricity. As the rocket accelerates, it gains speed and moves away from the center of the ellipse, thus increasing its eccentricity.

## 2. Can the direction of acceleration change the shape of an ellipse?

Yes, the direction of acceleration can also affect the shape of an ellipse. If the acceleration is perpendicular to the major axis of the ellipse, it can cause the ellipse to rotate, changing its orientation. This can also change the eccentricity of the ellipse.

## 3. How does the magnitude of acceleration impact the shape of an ellipse?

The magnitude of acceleration can greatly impact the shape of an ellipse. A higher acceleration can cause the ellipse to become more elongated, while a lower acceleration can make it more circular. This is because the speed and distance from the center of the ellipse are directly related to its eccentricity.

## 4. Can the shape of an ellipse change during constant acceleration?

Yes, the shape of an ellipse can change during constant acceleration. This is because the speed and distance from the center of the ellipse are constantly changing, which affects its eccentricity. However, if the acceleration is constant and the direction remains the same, the orientation of the ellipse will not change.

## 5. How does the change in shape of an ellipse affect the trajectory of a rocket?

The change in shape of an ellipse can greatly impact the trajectory of a rocket. As the eccentricity increases or decreases, the orbit of the rocket will become more elliptical or more circular, respectively. This can also affect the altitude and speed of the rocket, ultimately changing its trajectory.

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