Does Gravity decrease at a steady rate as we go away from the Earth?

[gary350]

TL;DR Summary

Does Gravity decrease at a steady rate as we go away from earth?

I have several questions related to gravity. I first need to know if gravity decreases at a steady rate for very 1 mile higher up we go?

 

[kuruman]

No, the rate is not steady. The rate per mile higher up decreases the higher you go. That's because the force of gravity is inversely proportional to the distance from the center of the Earth does not decrease linearly with altitude.

 

[gary350]

No, the rate is not steady. The rate per mile higher up decreases the higher you go. That's because the force of gravity is inversely proportional to the distance from the center of the Earth does not decrease linearly with altitude.

At what rate does gravity decrease with altitude?

 

[Drakkith]

The force of gravity scales as 1/r² (r = radius from an idealized point mass, which the Earth is not, but it's close enough to use here in this example), which means that you lose 75% of the force as you move from 1r to 2r. Moving from 2r to 4r, the force only drops another 18.75% to 6.25% of what it was at the surface. Moving from 4r to 8r gets you down to about 1.56% of surface gravity.

 

[gary350]

The force of gravity scales as 1/r² (r = radius from an idealized point mass, which the Earth is not, but it's close enough to use here in this example), which means that you lose 75% of the force as you move from 1r to 2r. Moving from 2r to 4r, the force only drops another 18.75% to 6.25% of what it was at the surface. Moving from 4r to 8r gets you down to about 1.56% of surface gravity.

I don't under stand r ?

Is r radius of Earth about 4000 miles, and 2r about 8000 miles?

 

[phinds]

I don't under stand r ?

Is r radius of Earth about 4000 miles, and 2r about 8000 miles?

What is your level of education?

 

[gary350]

What is your level of education?

I have a degree in Mechanical Engineering with a minor in Electrical Engineering, 2 yr Electronic degree at a technical school. I had 2 physics classes in college.

 

[Delta2]

I don't under stand r ?

Is r radius of Earth about 4000 miles, and 2r about 8000 miles?

Yes, you could take it to be the radius of the earth. In fact it represents the radius of any planet. We could say that at distance 8r from the center of planet the force of gravity is only 1.56% of what is at the surface of that planet(at distance r that is).

 

[Drakkith]

An interesting tidbit of info: the Moon experiences a centripetal acceleration of roughly 0.0026 m/s due to Earth's gravity. That's only 0.000265 g's. Gravity falls off quick.
(assuming my math is correct)

 

[gary350]

Yes, you could take it to be the radius of the earth. In fact it represents the radius of any planet. We could say that at distance 8r from the center of planet the force of gravity is only 1.56% of what is at the surface of that planet(at distance r that is).

OH. r from center of earth. r = about 4000 miles at Earth surface. I should have take more physics classes to under stand this. r at Earth surface has a certain amount of gravity how do we know if Earth surface is r2 or r4 of r8?

 

[phinds]

That's only 0.000265 g's. Gravity falls off quick.
(assuming my math is correct)

Your math may or may not be correct, but your grammar is not. It falls off quickly

 

[kuruman]

Your math may or may not be correct, but your grammar is not. It falls of quickly
View attachment 274100

falls of ?

 

[Drakkith]

r at Earth surface has a certain amount of gravity how do we know if Earth surface is r2 or r4 of r8?

I'm not sure what you're asking. It's the radius, which by definition would be the distance from the center of the Earth to the surface. It would never be anything but r1.

 

[Dale]

It falls of quickly
View attachment 274100

”It falls off quickly.”

Grammar Police
Internal Affairs

 

[gary350]

I am trying to understand several things. Germany started working on the V2 rocket about 1930 but did not launch until until about 1943 & 1944. The rocket had 25 tons of thrust on 75% ethanol 25% water plus liquid oxygen. The engine ran full throttle for 70 seconds that put the rocket 50 miles above earth. The rocket coasted up to a total of 120 miles with no engine thrust before it returned to Earth in 210 seconds.

NASA space program was based on German rocket technology the engine had a fuel pump that makes the engines run at full throttle until fuel is gone.

Space X rockets have no fuel pump. They use 300 psi helium to pressurize the liquid methane & liquid oxygen. SpaceX engines run about 1/4 throttle compared to German technology.

I am trying to understand when fuel runs out how far can a rocket coast with no engine thrust before it reaches maximum distance from earth.

I was thinking if I knew and understood gravity, and know a rocket weights 12 tons, travels at 3400 mph for 70 seconds. I could get a better understanding about how far a rocket could be predicted to travel when fuel runs out.

I have an idea that a rocket engine can gradually throttle down at the same rate that gravity degreases and maintain the same speed because at a certain elevation there is no atmosphere and no wind resistance.

In 1930 it is interesting Germany knew with no knowledge of rockets that a rocket would coast 70 more miles up after engine was off. The law of motion probably let then calculate distance assuming they knew the value of gravity at 120 miles up.

I think I answered my own question. I understand something I did not know before. Problem is not much different than a car traveling at a certain speed then running out of gas, how far will it coast before it stops.

 

[Janus]

OH. r from center of earth. r = about 4000 miles at Earth surface. I should have take more physics classes to under stand this. r at Earth surface has a certain amount of gravity how do we know if Earth surface is r2 or r4 of r8?

The equation for gravitational force is
F = GMm/R^2.
M is the mass of one object, m is the mass of the other object, and r is the distance between their centers.
G is a the universal Gravitational constant. It's value depends on the units you are using for R, M&m, and time.
If you use meters for R, Kilograms for M &m, and secs for time, its value is about 6.674 x 10^-11
The answer is in Newtons.
If M is the mass of the Earth(~6 x 10^24 kg), then m is the mass of the other object. This means the answer depends on this. When comparing gravity at different height, it is more convenient to use a equation that doesn't use m.
A = GM/r^2 is such an equation.
Here A is an acceleration. Again, using meters, kilograms and seconds, at the surface of the Earth it is about 9.81 meters/sec^2. This is also called 1g.
Thus, if we measure R in Earth radii, M in Earth masses, and want an answer in gs, we can make G=1
Thus A =1M/(1R)^2 = 1g at the Earth's surface.
Go up to 1R from the surface, and you are 2R from the Earth's center, and
A= 1M/(2R)^2 = 1/4 g.
Gravity is one fourth as much as it is at the surface.
You can also use h for height above the Earth's surface(measured in Earth radii) and then
A = 1/(1+h)^2, .
Again, the answer will be in g

 

[phinds]

”It falls off quickly.”

Grammar Police
Internal Affairs

Damn. Busted.

 

[Drakkith]

I have an idea that a rocket engine can gradually throttle down at the same rate that gravity degreases and maintain the same speed because at a certain elevation there is no atmosphere and no wind resistance.

You are correct, but there isn't any real benefit to this. You are far better off accelerating to a higher velocity and then letting gravity slow you down instead of maintaining a steady velocity for some length of the trip. This is because rockets are more efficient the faster they go, so you end up spending less fuel.

 

[phinds]

In 1930 it is interesting Germany knew with no knowledge of rockets that a rocket would coast 70 more miles up after engine was off.

Why on Earth would you think that Germany had no knowledge of rockets in 1930?
Goddard was launching rockets several years before that and Germans were great Admirers (and students) of his technology.

EDIT: Hm ... just checked some of that and while I was right on both counts, I was wrong on the timing. Goddard did LAUNCH well before 1930 but he was secretive and didn't publish until the mid-30's, AFTER which the Germans were admirers of his technology.

 

[Drakkith]

The fundamentals of rocket propulsion had been worked out by Konstantin Tsiolkovsky by 1903. The fundamentals of gravity and of objects in free fall under gravity had been known for several centuries prior to that.

 

[A.T.]

I think I answered my own question.

Didn't you ask the same question in May already? From your previous thread:

It is very interesting to me German engineers could calculate where the rocket would land, how was it possible to know things like gravity & drag 80 miles up no one had ever been there?

 

[gary350]

Why on Earth would you think that Germany had no knowledge of rockets in 1930?
Goddard was launching rockets several years before that and Germans were great Admirers (and students) of his technology.

EDIT: Hm ... just checked some of that and while I was right on both counts, I was wrong on the timing. Goddard did LAUNCH well before 1930 but he was secretive and didn't publish until the mid-30's, AFTER which the Germans were admirers of his technology.

Actually Germany had rocket technology for many smaller rockets for 20 years or more before 1930 but what I ment to say was, the V2 was the first rocket to go 120 miles up. Germans knew the V2 had 70 seconds of fuel but I wonder now they know the total speed of the rocket. They will need to know speed to predict where the rocket will be in 70 seconds. Newton's law of motion should allow them to calculate how far the rocket coasts to maximum elevation. I know the V2 had a transmitter I think 3 radar stations could probably vector the signal to learn where the rocket is in 70 seconds & know where the rocket goes after that. A lot of things needed to be learned to get the rocket to fly the correct path to hit a target 120 to 200 miles away, it was accurate for a target with a 10 mile radius, they could not miss a town 20 mile diameter if the aim at the center of town even with primitive technology they had. Once they have good data they should be able to hit any target.

 

[gary350]

The fundamentals of rocket propulsion had been worked out by Konstantin Tsiolkovsky by 1903. The fundamentals of gravity and of objects in free fall under gravity had been known for several centuries prior to that.

Yes, technology is always way in advance of the actually machines that man builds. I have a machine shop in my garage I can build almost anything. I built a rocket engine the size of a D flash light battery powered by alcohol & oxygen, it produces 120 lbs of thrust. With no cooling system I can only fire the engine for about 6 seconds. I have also built several pulse jet engines several different sizes.

Actually thrust is calculated by the pushing power of the engine x cross sectional area of the exhaust pipe. It is interesting most pulse jet engines all measure about 3 lbs of pushing power on scales. If cross section area is 1" x 3 lbs = 3 lbs of thrust. A larger engine with cross sectional area of 20" x 3 lbs = 60 lbs of trust. I tested several different size engines on a bicycle it needs about 40 lbs of thrust minimum to push the bike and 100 lbs thrust is very noticeable faster take off speed. Pulse jets are speed engines they do 300 lbs but I won't go faster than 40 mph on my bike.

I have no liquid fuel rocket engines that I can put on a bicycle the whole fuel system is too big I heavy it will need to be on a trailer to pull behind the bike.

I am retired now I spend more time thinking about projects than building projects.

 

[hutchphd]

Just to clean up a few facts (these days why bother?) but

Space X rockets have no fuel pump. They use 300 psi helium to pressurize the liquid methane & liquid oxygen. SpaceX engines run about 1/4 throttle compared to German technology.

Both the Merlin and the Raptor engines have centrifugal pumps for propellants. They additionally pressurize the tanks not always with helium. I have no idea what you are talking about 1/4 throttle.

 

[jbriggs444]

At the sorts of altitudes that you are discussing (up to 120 miles above sea level), the acceleration of gravity will have dropped off by about six percent.

##\frac{4000^2}{(4000+120)^2}## = 94% of surface gravity.

 

[gary350]

Just to clean up a few facts (these days why bother?) but

Both the Merlin and the Raptor engines have centrifugal pumps for propellants. They additionally pressurize the tanks not always with helium. I have no idea what you are talking about 1/4 throttle.

Information online says, engines are throttled up starting at about 1/4 throttle. Once every thing is go engine throttle up more than rocket takes off but still not full throttle for several seconds. I only found information that side tanks are pressurized with helium. I believe they were talking about the new 8 meter diameter rocket bodies. The older rocket bodies were 5 meters diameter. So maybe some are different or maybe the new ones are different. I might need to check that information out again.

 

[jbriggs444]

Normally this is done to avoid excessive speed where the atmosphere is most dense. Excessive speed is bad because 1. it wastes energy and 2. it batters the craft.

Once the craft is into regions where the air is less dense, the engines are throttled up. Ignoring the atmosphere, launch efficiency is greatest for a given delta-v when you burn your fuel fast -- giving gravity less time to reduce your velocity. [In the limit you get zero efficiency if you sit there hovering on your engines].

 

[gary350]

Normally this is done to avoid excessive speed where the atmosphere is most dense. Excessive speed is bad because 1. it wastes energy and 2. it batters the craft.

Once the craft is into regions where the air is less dense, the engines are throttled up. Ignoring the atmosphere, launch efficiency is greatest for a given delta-v when you burn your fuel fast -- giving gravity less time to reduce your velocity. [In the limit you get zero efficiency if you sit there hovering on your engines].

That makes good sense. Getting smarter every day.

 

[jbriggs444]

I played lunar lander in high school in the 70's. A perfect landing is the mirror image of an ideal take-off. You wait until the last moment, go full thrust and hope you got it right.

 

[anorlunda]

I played lunar lander in high school in the 70's. A perfect landing is the mirror image of an ideal take-off. You wait until the last moment, go full thrust and hope you got it right.

Oh that was a fun game. Any timidity waiting for the right moment led to crashes; lots and lots of crashes.

 

[Dale]

launch efficiency is greatest for a given delta-v when you burn your fuel fast -- giving gravity less time to reduce your velocity. [In the limit you get zero efficiency if you sit there hovering on your engines].

This is also why they tip over as soon as they can get out of the atmosphere. The important thing is to get to the right speed, and that works better the more you go sideways and the less you go up.

 

[hutchphd]

It turns out that the human capsule requires a much less pronounced "tip" on the way up because of possibility of an abort. Too much altitude with no forward speed apparently produces an unfortunate reentry profile involving high g loads for a ballistic reentry. So the crewed rockets don't go straight but ascend at an increasing angle.
I grew up watching project Mercury et seq and I am a true space geek.

 

[mfb]

Space X rockets have no fuel pump. They use 300 psi helium to pressurize the liquid methane & liquid oxygen. SpaceX engines run about 1/4 throttle compared to German technology.

I believe they were talking about the new 8 meter diameter rocket bodies. The older rocket bodies were 5 meters diameter.

This is a strange combination of different rocket engines and rockets.
SpaceX developed three rocket engines, two of them are still in operation:

• Kestrel: Retired, was used in the upper stage of Falcon 1. Pressure-fed with liquid oxygen and RP-1 (basically kerosene) at 9 bar (135 psi). Thrust was 30 kN.
• Merlin: Active, used in both stages of Falcon 9. It uses fuel pumps. Burning liquid oxygen and RP-1 at 97 bar (1410 psi). Thrust increased from 350 kN to 850 kN over its multiple iterations.
• Raptor: Active, used on Starship prototypes. It uses fuel pumps. Burning liquid oxygen and methane at up to ~300 bar (4400 psi). Thrust is about 2000 kN.

Falcon 1 had a diameter of 1.7 m, Falcon 9 has a diameter of 3.7 m, Starship has a diameter of 9 m.

I am trying to understand when fuel runs out how far can a rocket coast with no engine thrust before it reaches maximum distance from earth.

Rocket engines are irrelevant for that. You only need the velocity and the height when the thrust stops. How the rocket got there doesn't matter.

Typically suborbital flights don't go higher than 600 km or 1/10 the radius of Earth. At that altitude you still have 80% the gravitational acceleration you have on the ground. For a rough estimate you can neglect that change and simply use the constant acceleration equations you learn in high school.

In 1930 it is interesting Germany knew with no knowledge of rockets that a rocket would coast 70 more miles up after engine was off. The law of motion probably let then calculate distance assuming they knew the value of gravity at 120 miles up.

Of course they knew. They even had experimental data from 400,000 km up - from the Moon.

This is also why they tip over as soon as they can get out of the atmosphere. The important thing is to get to the right speed, and that works better the more you go sideways and the less you go up.

It's not very notable, but typically rockets start that as soon as they clear the launch pad. Thrust goes in the (now slightly tilted) direction of the rocket, gravity goes downwards, so over time the trajectory gets flatter on its own while the rocket always flies and fires along its length to minimize aerodynamic forces.

 

[mpresic3]

I have an idea that a rocket engine can gradually throttle down at the same rate that gravity degreases and maintain the same speed because at a certain elevation there is no atmosphere and no wind resistance.

This is an interesting idea, but what would this buy you. Why would you want to throttle down to maintain constant speed. In your diagram of the V-2 flight (very informative, by the way), there is an event called "jet switched off at correct range velocity combination.

Historically (and presently), The rocket scientist / military targeteer calculates at all times on the trajectory path, (in practice this would be a calculation done onboard the rocket, with input from the inertial guidance system which would give the control system, the current rocket location):

1. Given the target location, the rocket current position, and time of flight to target
2. What velocity is needed for the rocket to free-fall to the target? (This is called correlated velocity)

After this velocity is calculated, the rocket control system directs the thrust, (by controlling the nozzles), to "speed" towards this " correlated" velocity.

The reason this procedure is used is because, scientist/mathematicians/engineers, have known for 100 years or so, how to calculate the correlated velocity from the current position, and time of flight. Control system engineers know how to direct the nozzles to continuously approach the correlated velocity. So thrust is terminated and free-fall begins at the correlated velocity.

Probably the most important aspect to all this is the problem in control theory. In my personal view, (this might not be shared by more informed engineers and historians), the Wright Bros success was due to their advances in control (ideas in wing warping, and others), more so than (for example) propulsion.

Thrust to maintain constant speed rather than thrust cut-off (called switch off), would involve harder calculations that calculating the correlated velocity, and what would be the advantage?

With the poster's background in Mechanical and Electrical Engineering, I would recommend books in Aero-engineering like Siouris, or Vallado, or Bate, Mueller, White (fundamental of Astrodynamics). I will be glad to add titles to these authors if requested. I do not have them at my fingertips, right now