Satllite Crashing into the Moon

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In summary, the discussion revolved around finding the speed at which an unmanned spacecraft in circular orbit around the moon would crash into the lunar surface after an on-board thruster malfunction decreased its speed by 20.0m/s. The initial formula used was v=sqrt(GM/R) to find initial velocity, which was then subtracted by 20 m/s. However, this did not yield the correct answer. It was later determined that the gravitational potential energy at the surface of the moon also needed to be accounted for in the equation, leading to the correct answer of 6060 km/hr. The constants used were M=7.35X10^22 kg, R=1.74X10^6 m, and G
  • #1
aldofbg
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< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

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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  • #2
You've almost got it. Find ##\xi = \frac{v^2}{2} - \frac{GM}{r} ## which is the specific mechanical energy of the new orbit. Note that it's the sum of the per-unit-mass KE and PE, where the zero reference for PE is at infinity. For any unperturbed orbit the specific mechanical energy is a constant over the whole orbit.

Then you can find the the speed v at any distance along the orbit using the fact that ##\xi## is a constant.
 
  • #3
aldofbg said:
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

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
Your method is fine but I get the book answer. Please post your working.
 

Related to Satllite Crashing into the Moon

What happens when a satellite crashes into the moon?

When a satellite crashes into the moon, it creates a crater on the surface of the moon. The size of the crater depends on the size and speed of the satellite, as well as the composition of the moon's surface.

Can a satellite crashing into the moon cause damage?

Yes, a satellite crashing into the moon can cause damage to both the satellite and the moon. The impact can create debris and affect the surrounding area, potentially damaging other satellites or structures on the moon's surface.

How often do satellites crash into the moon?

Satellites crashing into the moon is a rare occurrence. Since the moon has a much smaller gravitational pull than Earth, it is less likely for satellites in orbit to experience a malfunction and crash into the moon.

What happens to the debris from a satellite crashing into the moon?

The debris from a satellite crashing into the moon can either stay on the surface of the moon or be ejected into space. Some of the debris may eventually fall back onto the moon's surface, while others may remain in orbit around the moon.

Can a satellite crashing into the moon affect Earth?

In most cases, a satellite crashing into the moon will not have any direct impact on Earth. However, if the debris from the crash falls back to Earth, it could potentially pose a danger to spacecraft or structures on Earth's surface.

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