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An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0km . To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0m/s

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

What I've done is used the formula for circular orbit to find initial velocity. v=sqrt(GM/R). I got the velocity and subtracted 20 m/s to account for lost speed. I then used potential and kinetic energy to set up an equation such

KEfinal=KEinitial+Uinitial using the formula U=GM/R. I got the wrong answer. I thought about it and decided that I had to account for Gravitational Potential energy at the surface of the moon. Thus KEfinal+Usurface=KEinitial+Uinital -> KEfinal=KEinitial+Uinitial-Usurface. My answer is 5785 km/h but the correct answer is 6060 km/hr. (if anyone wants to know I've disregarded mass of the satellite b/c it cancels out in the equation). I would appreciate any help. I've never posted here so please excuse my formatting.

Constants are M=7.35X10^22 kg

R=1.74X10^6 m

G=6.673x10^-11

An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0km . To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 20.0m/s

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

What I've done is used the formula for circular orbit to find initial velocity. v=sqrt(GM/R). I got the velocity and subtracted 20 m/s to account for lost speed. I then used potential and kinetic energy to set up an equation such

KEfinal=KEinitial+Uinitial using the formula U=GM/R. I got the wrong answer. I thought about it and decided that I had to account for Gravitational Potential energy at the surface of the moon. Thus KEfinal+Usurface=KEinitial+Uinital -> KEfinal=KEinitial+Uinitial-Usurface. My answer is 5785 km/h but the correct answer is 6060 km/hr. (if anyone wants to know I've disregarded mass of the satellite b/c it cancels out in the equation). I would appreciate any help. I've never posted here so please excuse my formatting.

Constants are M=7.35X10^22 kg

R=1.74X10^6 m

G=6.673x10^-11

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