I was just thinking??????????????

[Bob in Bristol]

I had some time on my hands, and was wondering if a person stood on a planet the size of our earth (7912 miles in diameter and had the same gravitational force as our earth) , with no atmosphere (a vacuum), or Coriolis Effect (the planet is not rotating on its axis), and fired a projectile horizontal to the position they were standing; What muzzle velocity would be needed to circle this planet? And, how long it would take the projectile to orbit this planet and hit the shooter in the back side?

Answer: Muzzle Velocity = 45,952.91426 feet per second
= 31331.53245 miles per hour
= 0.004% the speed of light

Obit Time = 2855.992185 seconds
= 47 minutes 35.0165364167 seconds

These are the answer I came up with, but I might be wrong. Are there any Physicists out there that see a mistake.

 

[thoricuncle]

For an earth sized planet to exist with no atmosphere would require it to be so hot, the lead bullet would melt.

 

[Warbirds]

Gravity would pull the bullet into the ground before it made it very far.

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[Bighouse Doc]

Orbital velocity should not change based on lack of atmosphere.

The orbital period for the earth is more like 90 minutes. The orbital velocity is closer to 17000mph

-Doc

 

[Bob in Bristol]

For an earth sized planet to exist with no atmosphere would require it to be so hot, the lead bullet would melt.

The planets temperature would be dependant on its distance from a star (heat source), not the lack of an atmosphere. If heat was a problem, we can make the projectile from material similar to the tiles on the Space Shuttle.

Gravity would pull the bullet into the ground before it made it very far

I would agree if the muzzle velocity was slower (under 45,000 feet per second). I was using g=9.81 meter/s(32.18 feet/s). With a muzzle velocity 45952.91426 feet per second I calculated the projectiles drop to parallel the planets circumference.

Orbital velocity should not change based on lack of atmosphere.

The orbital period for the earth is more like 90 minutes. The orbital velocity is closer to 17000mph

I used a no atmosphere condition to remove air drag on the projectile to simpify the calculations. I agree orbital period is 90 minutes, and velocity 17,000 mph for a satellite 100-1240 miles above the planets surface. At that altitude the g-force is reduces, causing the drop of the projectile to also be reduced. At that altitude, any velocity faster than 17,000 mph(aprox) would break the gravitational hold of the planet, and the projectile would go off in space. My example was a person standing on the surface, firing horizontal to the surface (aprox 5' altitude) where the g-force is greater g=9.81m/s (32.18'/s), and more velocity would be needed to counter the increased g-force and projectile drop.

 

[CapGun]

I had some time on my hands, and was wondering if a person stood on a planet the size of our earth (7912 miles in diameter and had the same gravitational force as our earth) , with no atmosphere (a vacuum), or Coriolis Effect (the planet is not rotating on its axis), and fired a projectile horizontal to the position they were standing; What muzzle velocity would be needed to circle this planet? And, how long it would take the projectile to orbit this planet and hit the shooter in the back side?

Answer: Muzzle Velocity = 45,952.91426 feet per second
= 31331.53245 miles per hour
= 0.004% the speed of light

Obit Time = 2855.992185 seconds
= 47 minutes 35.0165364167 seconds

These are the answer I came up with, but I might be wrong. Are there any Physicists out there that see a mistake.

I'm still trying out the answers other important questions. What is the coefficient of friction on a hockey
puck at sea level? and Can you get down off an elephant?

 

[B2Tall]

Gravity would pull the bullet into the ground before it made it very far.

Bingo.

Two other questions -

1. How did you calculate that velocity? That's an awful lot of energy and that leads me to my second question....

2. Newton's 3rd law tells us the shooter will be subject to the same force/energy as the bullet. Could the shooter withstand that much force to properly send the bullet on the way or would the gun come flying back at him/her thereby bleeding off energy (to say nothing of the possibly disasterous consequences)??

 

[B2Tall]

I would agree if the muzzle velocity was slower (under 45,000 feet per second). I was using g=9.81 meter/s(32.18 feet/s). With a muzzle velocity 45952.91426 feet per second I calculated the projectiles drop to parallel the planets circumference.

Your bullet is travelling at approx 9 miles/sec. Assuming your shooter is of average height, gravity would pull the bullet down to the ground in about a second. I don't believe the slug is traveling anywhere near fast enough to bend with the planet's curvature. If I remember correctly from waaaaay back, the horizon (i.e. the edge of the curve, so to speak) for a 6' tall person is about 21 miles. Your bullet traveling 9 miles in the time it takes gravity to pull it down just won't cut it. And remember - your bullet's downward path is accelerating due to gravity (+3 meters/sec).

I believe it would be impossible to fire a bullet horizontally and have it circle the planet, not without some additional force like wings. You could increase the velocity but I believe at some point the bullet would just break free of the planet's gravity and simply speed out into space.

 

[Warbirds]

Your bullet is travelling at approx 9 miles/sec. Assuming your shooter is of average height, gravity would pull the bullet down to the ground in about a second. I don't believe the slug is traveling anywhere near fast enough to bend with the planet's curvature. If I remember correctly from waaaaay back, the horizon (i.e. the edge of the curve, so to speak) for a 6' tall person is about 21 miles. Your bullet traveling 9 miles in the time it takes gravity to pull it down just won't cut it. And remember - your bullet's downward path is accelerating due to gravity (+3 meters/sec).

I believe it would be impossible to fire a bullet horizontally and have it circle the planet, not without some additional force like wings. You could increase the velocity but I believe at some point the bullet would just break free of the planet's gravity and simply speed out into space.

That explains why I don't hit my target. My bullets are going into space.

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[oldwindways]

with no atmosphere (a vacuum)

This is the part that bugged me. With out an atmosphere, how are you going to achieve the combustion of propellants to initiate the flight of your projectile. That being said, I have doubts that it would be possible to achieve that kind of velocity with simple high explosives anyway.

Its been a while since I have done any legit rocket science, but in that sort of environment you generally have to bring both a propellant and an oxidizer with you, and all of a sudden your projectile is looking pretty substantial. Soon you get to the point you need a multi-stage delivery vehicle, and if you are burning fuel carried on board while traveling, it becomes a differential equation rather than linear algebra and simple physics.

Kinda makes me want to get back into building model rockets.

 

[firelooker]

You forgot to account for bullet drop so you would also need to configure the angle you would need to fire at to compensate. Don't ask me cause physics was too long ago.

 

[firelooker]

Oh that explains everything, I thought it was my fault that I couldn't hit the broadside of a barn. Now I learn physics is against me.LOL

 

[firelooker]

I like the wings idea, better yet why not install the same guidance system the Tomahawk & CRUISE missile use. We'd have to do a bit of miniaturization to fit in the .45 slug but I imagine it can be done.

 

[firelooker]

Well to accomodate Newton we'd have to reinvent the recoilless rifle, thereby isolating the recoil.

 

[firelooker]

That would definetly make for an interesting round, of course we'd have to build a firearm to handle such a projectile assuming we could reduce the round in size to accomodate the average shooter.

 

[firelooker]

Then we'd have to redesign our projectile so as to prevent it from melting, which would make the envornmentalist's happy since we're doing away with lead ammo. Then we'd have to design a suit for the shooter to wear to prevent them from perishing in the extreme heat. Also our firearm would have to be able to resist such extreme heat as well as the propellant, I'm sure there are enough of us armchair scientists out there that it could be acomplished. But of course we'd have to get Obamas permission along with every other gov't body and the enviromentalists would have to get involved to ensure that we weren't disturbing whatever critter's lived in such an atmosphere.

 

[firelooker]

See what happens when you have too much time on your hands! Now get back to something meaningful like shooting tin cans off wooden posts.

 

[wuzfuz]

CapGun, you don't get down off an elephant, you get down off a duck.

 

[tailslide]

I used a no atmosphere condition to remove air drag on the projectile to simpify the calculations. I agree orbital period is 90 minutes, and velocity 17,000 mph for a satellite 100-1240 miles above the planets surface. At that altitude the g-force is reduces, causing the drop of the projectile to also be reduced. At that altitude, any velocity faster than 17,000 mph(aprox) would break the gravitational hold of the planet, and the projectile would go off in space. My example was a person standing on the surface, firing horizontal to the surface (aprox 5' altitude) where the g-force is greater g=9.81m/s (32.18'/s), and more velocity would be needed to counter the increased g-force and projectile drop.

No. The distance from the surface is irrelevant. At altitude the circumference of the orbit is greater, so the lower gravitational pull allows the same velocity to achieve orbit. The only variable is the mass of the planet.

 

[Bob in Bristol]

I guess we can drop this. I left out too many details in this scenario, projectile size, type and amount of propellant, weapon, or that it was possible to achieve a 45,000f/s+ Muzzle Velocity, recoil, etc........
I assumed in my question those thing were overcome, and was just looking at the math part. See what ASSUMING did to me. I am going to e-mail this question (with more detail) to the cast of THE BIG BANG THEORY.

Thanks to everyone who tried to help.
It`s back to the drawing board.