1. The problem statement, all variables and given/known data
R is earth radius.
A satellite is launched 2R from the center of the earth, vertically above the northpole, at an angle of 60° to the vertical.
The satellite crashes on the southpole. Find the launch velocity and the maximum distance to the center of the earth from its trajectory.
2. Relevant equations
Energy conservation.
Angular momentum is also conserved.
3. The attempt at a solution
I tried using those two conservation laws to first get the launch velocity.
Energy conservation:
[itex]\frac{mv^{2}}{2}+\frac{GMm}{2R}=\frac{mu^{2}}{2}+\frac{GMm}{-R}[/itex]
Angular momentum conservation:
[itex]v \cdot 2R \cdot sin(Pi/3) = u \cdot -R [/itex]
Solving first equation for u and plugging into the second gives me [itex]9684.37 m/s [/itex]
Can I find the maximum distance by using the same equations?
R is earth radius.
A satellite is launched 2R from the center of the earth, vertically above the northpole, at an angle of 60° to the vertical.
The satellite crashes on the southpole. Find the launch velocity and the maximum distance to the center of the earth from its trajectory.
2. Relevant equations
Energy conservation.
Angular momentum is also conserved.
3. The attempt at a solution
I tried using those two conservation laws to first get the launch velocity.
Energy conservation:
[itex]\frac{mv^{2}}{2}+\frac{GMm}{2R}=\frac{mu^{2}}{2}+\frac{GMm}{-R}[/itex]
Angular momentum conservation:
[itex]v \cdot 2R \cdot sin(Pi/3) = u \cdot -R [/itex]
Solving first equation for u and plugging into the second gives me [itex]9684.37 m/s [/itex]
Can I find the maximum distance by using the same equations?
0 commentaires:
Enregistrer un commentaire