Why do objects follow different trajectories in freefall and orbit?

In summary, objects do not fall in parabolas, but rather move in an elliptical orbit around the center of mass of the Earth. However, when the major axis of the ellipse is significantly larger than the minor axis, it appears to be a parabola. If the Earth were suddenly reduced in size, the object would follow an elliptical orbit with a perigee of a few dozen yards. While it is not entirely accurate to say that objects fall in parabolas, it is an acceptable approximation. Factors such as air resistance also play a significant role in determining the trajectory of falling objects.
  • #1
Vorde
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Why do objects fall in parabolas, but things orbit in either ellipses or hyperbolas?
 
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  • #2
Vorde said:
Why do objects fall in parabolas
They don't.

They move in an elliptical orbit about the centre of mass of the Earth; it just happens that the orbit intersects the surface of the Earth.

When the minor axis of an ellipse is on the order of few dozen yards, but the major axis is on the order of 4000 miles, an ellipse looks very much like a parabola i.e. the focus (of the ellipse) is so far away it might as well be at infinity (i.e. a parabola) for all the difference it makes.

If you tossed a ball in the air, and and that moment, the Earth suddenly collapsed to the size of a marble while keeping its mass, your ball would fall all the way to the centre, round it (with a perigee of just a few dozen yards) and come back out, following that elliptical orbit.
 
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  • #3
So really whenever anyone tells us that things fall in parabolas, they are lying. Makes sense, but still...

Thank you for the answer.
 
  • #4
Vorde said:
So really whenever anyone tells us that things fall in parabolas, they are lying. Makes sense, but still...

Thank you for the answer.

I don't think that is a fair statement. We do not have instrumentation that can separate the path of a thrown rock from a parabola. In fact, under the assumption that you are close to the Earth's surface, our basic models say that it IS a parabola.
 
  • #5
I don't disagree, but I went through a whole Analytic Geometry class with the term 'things fall in parabolas' etched into my brain. I'm surprised this wasn't at least mentioned.
 
  • #6
Vorde said:
I don't disagree, but I went through a whole Analytic Geometry class with the term 'things fall in parabolas' etched into my brain. I'm surprised this wasn't at least mentioned.

They are parabolas to an acceptable degree of accuracy. Two plumb bobs 10 yards apart, both pointing at the centre of the Earth, will be parallel to within one part in 700,000.

There are many factors affecting ballastic trajectories that are much greater than that.
 

1. What is a trajectory?

A trajectory is the path that an object takes through space, typically due to the influence of forces such as gravity or air resistance.

2. How is a trajectory calculated?

A trajectory is typically calculated using mathematical equations and principles, such as Newton's laws of motion and the laws of gravity.

3. What factors can affect a trajectory?

There are several factors that can affect a trajectory, including initial velocity, air resistance, gravity, and the shape and mass of the object.

4. How can we predict the trajectory of an object?

We can predict the trajectory of an object by using mathematical models and simulations, taking into account the initial conditions and any external factors that may affect the object's motion.

5. Can a trajectory be changed?

Yes, a trajectory can be changed by altering the initial conditions or applying external forces to the object. This is often done in fields such as aerospace engineering and ballistics to achieve a desired trajectory.

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