- #1

AwesomeTrains

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## Homework Statement

A satellite is launched one time Earth radius straight above the northpole (two times radius from center), with an angle of 60° to vertical.

Find the launch velocity [itex]v_{0}[/itex] so that the satellite won't orbit further away than six times Earth radius from the center of the earth.

## Homework Equations

F

_{G}=G[itex]\frac{Mm}{r^{2}}[/itex]

F

_{C}=m[itex]\frac{v^{2}}{r}[/itex]

F

_{Net}=[itex]m[/itex][itex]\cdot[/itex][itex]a[/itex]

## The Attempt at a Solution

I tried solving it by finding the satellite's trajectory.

Initial velocity in x and y direction:

[itex]v_{x}=cos 60°[/itex][itex]\cdot[/itex][itex]v_{0}[/itex]

[itex]v_{y}=sin 60°[/itex][itex]\cdot[/itex][itex]v_{0}[/itex]

Velocity from gravitational force in x and y direction:

(Θ the angle the satellite makes with the vertical y-axis through the northpole, when it's in orbit)

[itex]v_{Gx}[/itex]=[itex]\frac{F_{G} \cdot cos Θ \cdot t}{m}[/itex]

[itex]v_{Gy}[/itex]=[itex]\frac{F_{G} \cdot sin Θ \cdot t}{m}[/itex]

Total velocity:

(Vector addition)

[itex]v_{Tot}[/itex]=[itex] (v_{x} - v_{Gx}) + (v_{y} - v_{Gy})[/itex]

I don't know if this approach makes sense/ is correct. If it is, how should I continue?

Feel free to ask if something is unclear. Any help or tips are much appreciated.