Orbital mechanics - falling body

In summary, When using Tsiolkovsky's equations to determine the velocity of a body after a certain period of time while the engine of a spacecraft is running, it is a simple process. However, calculating the falling rate of an object that is constantly falling and applying that information to find the change in altitude over time is more complex. This is especially true in the case of a body already in motion with a given velocity and altitude, as the Earth's gravitational acceleration and changes in the velocity vector must also be taken into account.
  • #1
dreamer_asot
3
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Hello, my question id the following: when using Tsiolkovsky's equations to determine the velocity of a body after certain period of time, when the engine of a (space)craft is running, life is simple.

But how do you calculate the falling rate of an object that is constantly falling, and then apply that information to find the change of altitude with respect to some change in time?

Let's say the body is already moving with a velocity ai+bj+ck and is at an altitude h (the object is outside Earth's atmosphere). It stops it's engines at time t1 at that altitude h. How does its velocity and altitude change after time delta t, or in other words at time t2?
 
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  • #2
I think that the problem is not as simple to just account for the Earth's gravitational acceleration, change in h and change in the k component of the velocity vector, that's why I'm asking.
 

FAQ: Orbital mechanics - falling body

1. What is orbital mechanics?

Orbital mechanics is the study of the motion of objects in space, specifically how they move under the influence of gravitational forces.

2. How does a body fall in orbit?

A body falls in orbit due to the balance between its forward motion and the pull of gravity from the object it is orbiting. This results in a curved path around the object.

3. What is the difference between a circular and an elliptical orbit?

A circular orbit is when an object orbits an object at a constant distance and speed, while an elliptical orbit is when the distance and speed of the object vary as it orbits.

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

The mass of an object affects its orbit by determining the strength of its gravitational pull. The greater the mass, the stronger the gravitational pull, resulting in a faster and more elliptical orbit.

5. Can a falling body escape its orbit?

Yes, a falling body can escape its orbit if it reaches a high enough speed, known as the escape velocity. This allows it to overcome the gravitational pull and break free from its orbit.

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