Speed and Effect on Gravity

[Zipper730]

Flying around the earth at 17500 or 18000 miles an hour 300 miles up or so produces a centrifugal force that completely negates the effect of gravity. I'm curious what effect flying at lower speeds have.

For example, what effect does flying at Mach 5 at 100,000', Mach 10 at 150000' have on centrifugal force relative to earth's gravity?

drgondog GreenKnight121 GregP T ThomasP

 

[mjfur]

For NASA and the U.S. military, for example, space starts at an altitude of 50 miles (around 80 kilometers), according to NOAA. However to the international community, including the Fédération Aéronautique Internationale (FAI), space starts a little higher, at 62 miles (100 km), at the Kármán line. The Kármán Line: Where does space begin?

100,000 ft =18.93 miles 150,000 = 28.40 miles

Gravity Acceleration by Altitude

The Acceleration Due to Gravity at an Altitude calculator estimates the acceleration due to gravity on Earth at a specific altitude above sea level.

www.vcalc.com

 

[pbehn]

Are you mixing things with a geostationary orbit? Which is at an altitude of 22.236 miles and 1.91 miles/ second.

Geostationary orbit - Wikipedia

en.wikipedia.org

 

[Thumpalumpacus]

Flying around the earth at 17500 or 18000 miles an hour 300 miles up or so produces a centrifugal force that completely negates the effect of gravity. I'm curious what effect flying at lower speeds have.

For example, what effect does flying at Mach 5 at 100,000', Mach 10 at 150000' have on centrifugal force relative to earth's gravity?

drgondog GreenKnight121 GregP T ThomasP

Gravity exerts more force when you're lower, per the inverse-square law, so you need more speed or lift to counteract it. On the other hand, at a higher orbit, the object must travel farther in order to stay geostationary, meaning it must run faster, but has less gravity to work against.

I think the balance-point is around 22,300 miles.

 

[Zipper730]

No, what I was talking about had to do with centrifugal force counterbalancing gravity. If you travel at orbital velocity, the two balance each other out. The thing is, what happens if you go 1/5th orbital velocity, 1/2 orbital velocity? That's what I was getting at.

How do you even calculate for that?

 

[pbehn]

No, what I was talking about had to do with centrifugal force counterbalancing gravity. If you travel at orbital velocity, the two balance each other out. The thing is, what happens if you go 1/5th orbital velocity, 1/2 orbital velocity? That's what I was getting at.

How do you even calculate for that?

Anything travelling in a circle is constantly changing direction. A stable orbit is were this change in direction is equal to the acceleration caused by gravity. If you slow down you go into a lower orbit and eventually re enter the atmosphere. Thats what astronauts do to come out of orbit and re enter, they fired the "booster" rocket to slow the whole thing down. The principles are quite simple, the actual calculations are "Clever stuff".

 

[Thumpalumpacus]

The thing is, what happens if you go 1/5th orbital velocity, 1/2 orbital velocity? That's what I was getting at.

You fall out of orbit because you've reduced the amount of centrifugal force.

How do you even calculate for that?

I don't know the equations.

 

[PNW Guy]

No, what I was talking about had to do with centrifugal force counterbalancing gravity. If you travel at orbital velocity, the two balance each other out. The thing is, what happens if you go 1/5th orbital velocity, 1/2 orbital velocity? That's what I was getting at.

How do you even calculate for that?

It's pretty simple.

Mathematics of Satellite Motion

Because most satellites, including planets and moons, travel along paths that can be approximated as circular paths, their motion can be described by circular motion equations. By combining such equations with the mathematics of universal gravitation, a host of mathematical equations can be...

www.physicsclassroom.com

 

[mikewint]

No, what I was talking about had to do with centrifugal force counterbalancing gravity

#1 Most importantly!! Centrifugal Force DOES NOT EXIST. IT IS A FICTIONAL FORCE. It is a useful fiction to describe what is observed to be happening in a limited "Frame of Reference".
Newtons First Law states that objects in motion travel in a STRAIGHT LINE unless acted upon by an OUTSIDE FORCE.
Gravitational Force is also a Fictional Force that does not exist BUT as with Centrifugal Force is a convenient fiction to describe what occurs in a limited Frame of Reference.
Finally - The Earth is round. Thus if you travel in a straight line laterally in any direction the surface of the earth will curve AWAY from you (ROUGHFULLY 8 inches per mile squared). The actual drop can be calculated by spherical trigonometry (h = r∗(1−cosθ))
OK Fictional Force Centrifugal, travel around a curve in your car and you experience a force pushing you to the outside of the curve, "AHAH tis Centrifugal Force you say". Well not actually - Leave the car's Frame of Reference and look down upon the car from above (Broader Frame of Reference) and you can now see what is actually happening, i.e. : the ball is moving in a straight line (1st Law) while the car is accelerating toward the CENTER of the curve due to CENTRIPETAL FORCE applied by the tires friction with the road's surface. So the car is curving away from the straight line traveling ball which will roll toward the outside of the curve until striking the door. The door, now in contact with the ball applies a force to push the ball away from its straight path toward the center of the curve.
Now, let's mount a gun so that it fires parallel to the ground's surface (flat for now). As soon as the bullet leaves the barrel it begins to fall towards the earth at an acceleration of 32ft per sec per sec so it (bullet) falls 16ft in one second. In addition to the downward fall it (bullet) is traveling laterally at its muzzle velocity.
So a 6ft tall shooter sees the bullet (ignore air friction) hit the ground 0.6 sec later and assuming a lateral velocity of 1000ft per sec it (bullet) hits the ground at a distance of 600ft. Obviously a faster lateral velocity moves that "hit the ground" distance further away from the shooter - NOW let's consider the Earth's curvature, which is dropping away further and further with distance. IF the bullet falls 16ft in one second and the bullet travels laterally fast enough to cover enough distance so that the Earth's surface has curved away 16ft, the bullet would remain 6ft above the surface and effectively would be IN ORBIT around the Earth.
SO - a Satellite attempts to move in a straight line BUT Gravity applies a force to accelerate it toward the center of the Earth. The CENTRIPETAL FORCE supplied by the Earth's gravitational field (another fiction) produces the curved orbital path as the satellite continually falls toward the earth. The satellite does not hit the ground BECAUSE it (Earth's surface) curves away from it at the same rate as the satellite falls toward it

 

[pbehn]

It's pretty simple.

Mathematics of Satellite Motion

Because most satellites, including planets and moons, travel along paths that can be approximated as circular paths, their motion can be described by circular motion equations. By combining such equations with the mathematics of universal gravitation, a host of mathematical equations can be...

www.physicsclassroom.com

Those are the principles of the basic mathematics. When it comes to an actual satellite how do you determine actual altitude, actual velocity, actual orientation. How do you establish the force applied by the various steering and booster rockets and from that how long they need to burn to get what you want. On a documentary years ago they said that early calculations were "off" by a small amount, because they were taking time as a constant, for bodies moving at orbit velocity, it isnt. Dot ask me how that changes things, I just understand that it does.

 

[PNW Guy]

Those are the principles of the basic mathematics. When it comes to an actual satellite how do you determine actual altitude, actual velocity, actual orientation. How do you establish the force applied by the various steering and booster rockets and from that how long they need to burn to get what you want. On a documentary years ago they said that early calculations were "off" by a small amount, because they were taking time as a constant, for bodies moving at orbit velocity, it isnt. Dot ask me how that changes things, I just understand that it does.

• Check out the example problems "Mathematics of Satellite Motion". Several of the variable have to be known in order to solve the equations.
• Also, check out this link to answer your second question. Go to the "Orbit Manuevers" section to see the maths. Click on the embedded links for example problems.

I guess this is the stuff real Rocket Scientists do.

Basics of Space Flight: Orbital Mechanics

An overview of orbital mechanics including types of orbits, mathematical formulae, and example problems.

www.braeunig.us

 

[special ed]

It makes sense. It makes my brain hurt - must be the reality.