# One question about Parabolic and Hyperbolic trajectory.

• IPhO' 2008
In summary, the focus point of a parabolic and hyperbolic trajectory is at the center of mass (CM) of the two objects. If the body on the trajectory has a comparable mass to the sun, the CM may be outside the surface of the sun. For example, the CM of the Sun-Jupiter system is about 83,500 km outside the sun's surface.
IPhO' 2008
In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?

Hi IPhO' 2008!
IPhO' 2008 said:
In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?

Yup!

To be more precise, the focus is at the center of mass (CM) of the two objects. If the body on a parabolic/hyperbolic trajectory had a mass comparable to that of the sun, the CM might be outside the surface of the sun.

It might interest you that the CM of the Sun-Jupiter system is outside the surface of the sun by about .12 solar radii = 83,500 km.

Thank you.

## 1. What is the difference between a parabolic and hyperbolic trajectory?

A parabolic trajectory is a path that follows a parabola, which is a symmetrical curve. It is often seen in objects that are thrown or launched at a specific angle and velocity. A hyperbolic trajectory, on the other hand, is a path that follows a hyperbola, which is a curve that has two separate branches. It is commonly observed in objects that are affected by gravity and/or the gravitational pull of other objects.

## 2. What factors affect the trajectory of an object?

The trajectory of an object is affected by several factors, including the initial velocity, the angle at which it is launched, the air resistance, and the presence of external forces such as gravity or other objects.

## 3. Can an object have both a parabolic and hyperbolic trajectory?

Yes, an object can have both a parabolic and hyperbolic trajectory. This can occur when an object is launched at a specific angle and velocity, causing it to follow a parabolic path initially. However, if the object is affected by other forces such as the gravity of another object, it can then switch to a hyperbolic trajectory.

## 4. How does the mass of an object affect its trajectory?

The mass of an object does not directly affect its trajectory. However, the mass can indirectly impact the trajectory if it affects the initial velocity or the strength of external forces acting on the object.

## 5. What real-life applications involve understanding parabolic and hyperbolic trajectories?

Understanding parabolic and hyperbolic trajectories is crucial in various fields, including physics, engineering, and astronomy. It is used to predict the paths of projectiles, spacecraft, and other objects affected by gravity. It also plays a significant role in the study of orbital mechanics and the motion of celestial bodies in space.

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