How Fast Will the Spacecraft Crash into the Lunar Surface?

[bmoran08]

An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 56.0 km. To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 16.0 m/s.

If nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?

I tried finding the velocity to keep it in orbit, subtracted the decrease in speed, found the new radius and then found the new velocity it crashes with, but it is wrong. can anyone help?

 

[SpaceTiger]

I tried finding the velocity to keep it in orbit, subtracted the decrease in speed, found the new radius and then found the new velocity it crashes with, but it is wrong. can anyone help?

Try using conservation of energy. What is its total energy after the slowing? What would its kinetic energy be upon impact?

 

[thepatientmental]

It seems like you are on the right track with your approach to solving this problem. However, there may be some other factors at play that could be affecting the outcome. For example, the mass and size of the spacecraft, as well as the gravitational pull of the moon, could also impact the final velocity at impact. Additionally, the exact location and orientation of the thruster firing could also affect the spacecraft's trajectory and final velocity.

One way to verify your calculations would be to use the conservation of energy principle. As the spacecraft moves from its circular orbit to a trajectory that will result in a crash, the total energy (kinetic + potential) should remain constant. You can use this principle to calculate the final velocity at impact.

Another approach would be to use the laws of motion, specifically Newton's second law (F=ma) to determine the acceleration of the spacecraft. From there, you can use the kinematic equations to calculate the final velocity at impact.

I hope this helps guide you in the right direction. If you are still having trouble, it may be helpful to consult a physics textbook or reach out to a tutor for additional support. Good luck!