Trying to prove a student in my physics class wrong

[Izack]

So here it is how it played out. He said that a cannon that is fired laterally will hit the same point on earth that the cannon was fired from. Like I stated before, the start point would be from orbit. My question is how is it able to hit the same point without landing on the other side of earth due to the atmosphere.

EDIT: Can someone simulate this in orbiter?

Hate to nitpick, but you've stated an antithesis. You ask if the projectile will land at the location on Earth's surface that the cannon is fired from, and yet the cannon is in orbit. Which do you mean?

With a purely Keplerian orbit, as others and I stated earlier the maximum downrange is 180 degrees of orbital longitude along the axis given by the cannon (the direction it was fired in.) Now, including the atmosphere and using either a propelled or lift-generating projectile, this could be extended, possibly to the point of landing directly below the hypothetical statite cannon after a 360 degree orbit. If this is what your student is thinking, give him a hearty clap on the back and a .

However, if the projectile is 'dumb' (ie no notable lift, propulsion) like, say, a coconut, the problem still rules to be false.

 

[statickid]

ok update:

I just tried again. i guess i just have more finesse these days. I was easily able to do the flybylol of Brighton Tower. It was awesome. However, I did have to maintain the orbit with RCS because it tried to decay several times during the flight.

On second thought, my experiment probably has little to do with this discussion, but buzzing the tower at 35 meters and orbital velocity is priceless.

---------- Post added at 05:22 PM ---------- Previous post was at 05:19 PM ----------

p.s. I then tried to wheel down. I made contact at <.1 m/s va. the wheels instantly disappeared, then the hover doors came off so I decided to do a barrel roll and the poor DGIV came apart

 

[palebluevoice]

I think you might have the problem wrong; either way, there's just so many variables I can change to make the conjecture false. If I fire the cannon prograde, it will increase the cannon's orbit, if I fire it retrograde, it will make it fall, but if I fire it retrograde at near the speed of light, it won't hit. The diagram you've drawn requires a very accurate, specific set of variables to work; a particular gravity, circumference, velocity and starting orbit. There's just no reason other than logic to assume it would hit.

 

[statickid]

sorry i just have to ask this:

are you trying to solve a word problem?

 

[C3PO]

Note that the original question isn't about hitting the same spot--it's about hitting the ground *under* the same spot (it was originally fired from altitude)>

I did notice that.

My diagram shows the situation if you disregard all forces except for gravity. There are only 3 possible results:
V-initial > escape vel. = Well, it will escape :lol:
Pe < Earth radius = Projectile will hit the suface within a ½ orbit.
Anywhere in between = Projectile will hit the back of the cannon.

To get any other result you will have to add or remove energy after the shot, or include relative movement such as rotation.

That means that it is impossible to hit a spot directly under the cannon if the only force on the projectile is gravity.

 

[Sword7]

Yeah. I think that student is right. If you are on earth without atmosphere at sea level, fire cannon and ball travels at 18,000 mph, it is in circular orbit. A hour and half later, a ball return to hit back of the cannon. If a ball travels above 250 miles at 17,500 mph, it is in circular orbit.

With atmosphere, a ball will be burned at friction and slowed down due to drag and fell down to hit ground before it reach to the back of the cannon.

Sword7

 

[Hielor]

Yeah. I think that student is right. If you are on earth without atmosphere at sea level, fire cannon and ball travels at 18,000 mph, it is in circular orbit. A hour and half later, a ball return to hit back of the cannon. If a ball travels above 250 miles at 17,500 mph, it is in circular orbit.

With atmosphere, a ball will be burned at friction and slowed down due to drag and fell down to hit ground before it reach to the back of the cannon.

Sword7

...Which means the student is wrong, because the student said it would hit the ground directly beneath the cannon.

I feel like I'm the only one who actually read the OP...

 

[PhantomCruiser]

No, I caught that too.

I'd like to hear the students argument and hear his thought process on this. 'Cause I'm not "seeing" it.