Space station-nature of orbit?

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Homework Help Overview

The discussion revolves around a space station transitioning from a circular orbit to a new bound orbit after firing its engine radially outward. Participants are exploring the nature of the resulting orbit, considering options such as a larger circle, a smaller circle, an ellipse, or a parabola.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are examining the effects of thrust on the free-body diagram of an object in circular orbit, questioning how the thrust alters the velocity components. There are inquiries about the nature of the velocity required for different types of orbits and how to modify existing equations for elliptical orbits.

Discussion Status

The discussion is active, with participants providing hints and exploring various interpretations of the problem. Some guidance has been offered regarding the representation of velocity as radial and tangential components, as well as the implications of thrust on the orbit's characteristics.

Contextual Notes

Participants are considering the implications of thrust duration and its effect on the velocity vector, as well as the assumptions inherent in the problem setup. There is an emphasis on the need for clarity regarding the nature of the orbit post-thrust application.

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Homework Statement



A space station moving in a circular orbit around the Earth goes into a new bound orbit by firing its engine radially outaward.This orbit is...

Choices are;
(a) A larger circle
(b)A smaller circle
(c)An ellipse
(d)a parabola

Homework Equations




The Attempt at a Solution



I think it'll be a larger circle or parabola.
But donno how to work it out.
 
Last edited:
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What is the free-body diagram of an object in a circular orbit?
The engine applies thrust radially outward - what does that do to the free body diagram?
Do the engines fire continuously or for a short while?

The change in velocity is important to this.
What can you say about the kind of velocity needed for a circular orbit?
(velocity is a vector - talk in terms of tangential and radial components)
What can you say about the kind of velocity needed for a parabolic orbit?
... an elliptical one?
 
mv2/r = GMm/r2

v = Sqrt[GM/r] for circular orbit.

How can i modify these equations for elliptical orbit.
 
Hint:
1. velocity is a vector - represent as radial and tangential.
2. free body diagram

the v in your equation is purely tangential.
when the thrust is applied for a short time it changes the velocity vector ...
what happens to the radial component
what happens to the tangential component

is it possible for an object in a circular orbit to have a radial component to it's velocity?
 
btw: you equation gets modified as follows...

[tex]\underbrace{ma = F_g+F_{thrust}}_{\text{from FBD}} \Rightarrow \frac{mv_\perp^2}{R} = mg_R -\frac{m}{T}\Delta v_r[/tex]... the thrust is applied for a fixed time T, so creates a change in speed Δv. You'll have heard of thrust being referred to as a "delta-vee"? R is the radius of the orbit so gR is the local acceleration of gravity at R. The minus sign is because the thrust is radially outwards, making the positive direction to be radially inwards. The instantanious velocity after the thrust has been applied is given by
[itex]\vec{v}=v_r\hat{r}+v_\perp\hat{\small \perp}[/itex]
...which has magnitude [itex]v =\sqrt{v_r^2 + v_\perp^2}[/itex]
...and the angle this makes to the radius is [itex]\tan^{-1}(v_\perp / v_r)[/itex].

Lesson: start with the Free Body Diagram, then resolve the vectors.
 

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