# How fast to shoot a bullet for it to hit the moon?

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1. Nov 28, 2015

### Treva31

Ignoring the fact that the atmospheric friction would probably disintegrate it.

I know that to achieve LEO takes around 10km/s delta v.
But only 2km/s of that is to overcome the drag and gravity.
So you could shoot at 2km/s, get to LEO altitude then it falls back down because it is not at orbital velocity or trajectory right?

And I think that you need around 16km/s (10 to LEO plus 6 from LEO to moon) for a rocket to safely land on the moon from Earth.
But is it less than 16 if you just want to shoot a bullet and hit the moon?
Would it be 2 + 6 = 8km/s ??

Wouldn't it at least be less than the 11.2km/s escape velocity of the Earth since if you shot a bullet to the altitude of the moon (but not near the moon) it would eventually fall back to Earth, so you havent escaped the Earths gravity.

2. Nov 28, 2015

### MarcusAgrippa

Use the conservation of energy to work this out. To reach the moon, the velocity of the bullet must never reverse. To reverse, it must pass through the value zero. Take the potential energy of the Earth and of the Moon into account. In the limiting case, the velocity will be zero at the first Lagrangian point. To push it over the Lagrangian point, its velocity needs to be infinitesimally more than zero there.

3. Nov 28, 2015

### DrStupid

That's not sufficient because the Moon orbits Earth with 1 km/s. It will run away before the bullet gets a chance to reach this speed. In a numerical simulation I did not reach the Moon with a speed minimum of less than 220 m/s (in the inertial system). The corresponding initial speed was 11091 m/s.

4. Nov 28, 2015

### MarcusAgrippa

My apologies. I assumed this was a freshman problem. I guess I should call myself "Dr Stupid", right?

5. Nov 30, 2015

### Treva31

Cool thanks.
How do you do a numerical simulation? Is there some software i can download?

6. Nov 30, 2015

### DrStupid

I just used EXCEL and a velocity verlet algorithm.

7. Dec 1, 2015

### Treva31

So just to clarify, the 11091 m/s doesn't include any velocity needed to overcome the friction of the atmosphere right? Just the gravity.

Any chance I could get a copy of the Excel file?

8. Dec 1, 2015

9. Dec 2, 2015

### tony873004

I just noticed this doesn't display properly unless you have a wide aspect ratio screen.
If you can't see the Moon, press "A" on your keyboard, then press "-" minus under the word Zoom to zoom out.

10. Dec 2, 2015

### Treva31

Wow that is awesome!
Thanks so much guys.

11. Dec 2, 2015

### DrStupid

Yes, it is the initial velocity in the inertial system (not the relative velocity in the rest system of Earth) for a free fall trajectory without any interactions except gravity.

Here it is: http://www.drstupid.de/temp/moonflight.xls

I played a little bit with the starting values and reduced the initial velocity to 11080 m/s.

Here is the same simulation using JavaScript and Runge-Kuta-Nyström: http://tinyurl.com/j5anj3m

12. Dec 2, 2015

### Treva31

Perfect thank you!

13. Dec 3, 2015

### Janus

Staff Emeritus

14. Jan 11, 2016

### Treva31

Is there any way to reduce the impact speed?

Or might it be possible shoot the bullet into lunar orbit?
A decaying/sub-orbit that ends with a softer landing would be good too!

Am I right in saying it is not possible to shoot anything into Earth orbit without a trajectory correction? Even if shot at a very shallow angle (1 degree) at a precise velocity?

The mass of the "bullet" would be 10kg. Would a larger mass (100kg) help the above questions?

Last edited: Jan 12, 2016
15. Jan 11, 2016

### Treva31

Could you use the gravity of the moon to slow the bullet further?

If you shot just "in front" of the moons path, and the bullet moves around to the darkside, it is pulled around the moon and towards the surface by the moons gravity, slowing it down, before it finally lands, at less than 220 m/s?
I'm not sure how far around would be optimal, maybe down almost straight away (we aim closer to the surface), or maybe half an orbit or more.

See my crude illustration attached.

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16. Jan 12, 2016

### Janus

Staff Emeritus
The best you can do is place it at rest with respect to the Moon and then have it fall toward the Moon from there, but it will still impact at over 2300 m/sec.

17. Jan 12, 2016

### Treva31

We already showed that it can hit directly at only 220 m/s without any gravity assist.

18. Jan 12, 2016

### Staff: Mentor

That's not what that post says: that post was referring to the speed at the Legrange point.

There really isn't anything that can be done without power to slow the impact speed: it can't be much below escape velocity otherwise.
Correct.

19. Jan 12, 2016

### tony873004

Janus is right. You can't approach the Moon from beyond its orbit and crash into it with anything less than its escape velocity. It violates the Law of Conservation of Energy. At best you can have 0 Potential Energy at infinity. Subtract that from its PE at the surface (-GMm/r) for a change in Potential Energy. All that lost PE will become Kinetic Energy. So about 2300-2400 m/s is the slowest you can land unpowered.

20. Jan 12, 2016

### Treva31

Ah OK, sorry I misunderstood.