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Warframe Differentiation (And Gravitational Field Strength)

Renegade343

By Renegade343,
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Renegade343

Renegade343

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I had another question to myself when walking down a street: 

 

What is the acceleration due to gravity of Warframe?

 

So, I went back, took out my Codex Scanner, stood on top of a scannable flat surface (an Explosive Barrel), then jumped. From multiple tests, I found out that all Warframes but Zephyr will jump 1.8m into the air before falling, and the time taken to jump up and return back to its original position is around 1.4s (three trials are taken). Knowing that the distance is so small that terminal velocity will not affect the descent acceleration/speed, I assumed 0.7s as the time where the Warframe is at maximum jump height (i.e. a parabola). I found out the parabola by the following: 

 

(ax^2) + bx + c = y

Let x = 0, y = 0,

c = 0

(ax^2) + bx = y

Let x = 1.4 when y = 0, and x = 0.7 when y = 1.8,

 

1.96a + 1.4b = 0   (1)

0.49a + 0.7b = 1.8   (2)

(2) * 2 - (1),

 

-0.98a = 3.6

a = -3.67

b = 7.19/1.4 = 5.14

 

Parabola formula: (-3.67 * x^2) + 5.14x = y

Now, to find the acceleration, we will have to differentiate the formula twice with respect to time (known as x), meaning it is: 

 

dy/dx (=v) = -7.34x + 5.14

v/dx (=a) = -7.34

 

That means the acceleration due to gravity is 7.34 m/s^2.

 

Now, since I have done this test on Earth, that means there may be one of the two things that happened: 

 

Mass has decreased from now. 

Radius has increased from now. 

 

Since decreasing mass seems slightly more plausible (intensive mining), the mass of Earth in Warframe is: 

 

g = (G*kg)/r^2 (where G = gravitational field constant)

7.34 = ((6.7E-11) * kg) / 4.096E7

kg = 4.48726E18

 

Compared to the current mass of the Earth (5.97219E24), the mass of the Earth in Warframe is: 

 

((4.48726E18)/(5.97219E24)) * 100% = 0.000075% of the current Earth's mass. 

 

So yes. Grineer mining operations are very efficient and invasive. 

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Guest Tehnoobshow

Guest Tehnoobshow

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Good question. 

 

The answer is maybe, but not sure. But definitely not hollow, or I think the gravity would be even lower and the crust would just break apart from the gravitational pull of other planets. 

Swiss-cheesed?

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Llyssa

Llyssa

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You botched somewhere.

 

If the acceleration due to gravity is 7.34, and the radius is 1 earth, then the mass of earth would need to be ~4.465*10^24, or roughly 75% of the current mass. So, nowhere near as efficiently mined as you calculated. 

 

EDIT: Also, theoretically, as planets aren't solid, the rotational speed should rather directly affect the radius. As warframe takes place at some unknown time in the future (possibly billions of years), it's quite possible that the earth's size has altered, perhaps dramatically, from any number of events.

Edited by Llyssa
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Renegade343

Renegade343

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You botched somewhere.

 

If the acceleration due to gravity is 7.34, and the radius is 1 earth, then the mass of earth would need to be ~4.465*10^24, or roughly 75% of the current mass. So, nowhere near as efficiently mined as you calculated. 

No, not really. 

 

Using the formula for gravitational field strength: 

 

g = F/m, where m = 'test' mass

 

And the formula for the force of gravity attracting two masses is: 

 

F = [G*m*m(1)]/r^2 (where m(1) is the mass of the planet)

 

Combining the two together will give: 

 

g*m = [G*m*m(1)]/r^2

g = [G*m(1)]/r^2

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Renegade343

Renegade343

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EDIT: Also, theoretically, as planets aren't solid, the rotational speed should rather directly affect the radius. As warframe takes place at some unknown time in the future (possibly billions of years), it's quite possible that the earth's size has altered, perhaps dramatically, from any number of events.

Earth is a solid planet. The phenomenon of rotational speed affecting the radius does not apply to it, only to gas planets. 

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Llyssa

Llyssa

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You can compare and contrast with other planets. Or even use utilities: http://www.ajdesigner.com/phpgravity/gravity_acceleration_equation.php#ajscroll

 

Or just do simple math: If the equation is all multiplication(which it is) and all other values are equal(which they are), the equation simply becomes  comparison of the two values. 7.34 is 75% of 9.8.

 

You have far too many steps, and you lost track in there. Sorry.

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Llyssa

Llyssa

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Earth is a solid planet. The phenomenon of rotational speed affecting the radius does not apply to it, only to gas planets. 

LOL. No. The earth isn't solid.

The core of the earth involves layers of magma and molten iron. That's why we have volcanoes, plate tectonics, and magnetic poles.

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Wyzilla

Wyzilla

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You botched somewhere.

 

If the acceleration due to gravity is 7.34, and the radius is 1 earth, then the mass of earth would need to be ~4.465*10^24, or roughly 75% of the current mass. So, nowhere near as efficiently mined as you calculated. 

 

EDIT: Also, theoretically, as planets aren't solid, the rotational speed should rather directly affect the radius. As warframe takes place at some unknown time in the future (possibly billions of years), it's quite possible that the earth's size has altered, perhaps dramatically, from any number of events.

Warframe doesn't take place billions of years in the future, or millions. North America looks the exact same as it does in the modern day, as does China/Asia.

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Renegade343

Renegade343

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Or just do simple math: If the equation is all multiplication(which it is) and all other values are equal(which they are), the equation simply becomes  comparison of the two values. 7.34 is 75% of 9.8.

That value was about comparing the Warframe Earth's mass to the current Earth's mass, not about comparing gravity. 

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Renegade343

Renegade343

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LOL. No. The earth isn't solid.

The core of the earth involves layers of magma and molten iron. That's why we have volcanoes, plate tectonics, and magnetic poles.

More solid than gas planets and thus rotational speed manipulation will not affect it as much, until we get to high values of manipulation and centrifugal force starts overcoming the force of gravity and start to rip the Earth apart. 

Edited by Renegade343
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Llyssa

Llyssa

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Warframe doesn't take place billions of years in the future, or millions. North America looks the exact same as it does in the modern day, as does China/Asia.

Except phobos is no longer anywhere near mars, and earth shows deserts and oceans, which according to the intro dialogue, shouldn't exist. The artistic interpretations are curious, but even a few thousand years should have some massive changes to geography. I take that more as a mistake or convenience--players recognize it as "earth", despite it being wrong.

 

That value was about comparing the Warframe Earth's mass to the current Earth's mass, not about comparing gravity. 

Yeah, so if the gravity of WF earth is 75% of real earth, and they have the same size, and the same universal constants, but different masses, then WF earth has to have 75% of real earth's mass.

 

More solid than gas planets and thus rotational speed manipulation will not affect it as much, until we get to high values of manipulation and centrifugal force starts overcoming the force of gravity and start to rip the Earth apart. 

As much, but it still could affect it quite dramatically. Imagine the core was going thousands of times faster or had stopped completely. What then?

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Renegade343

Renegade343

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Yeah, so if the gravity of WF earth is 75% of real earth, and they have the same size, and the same universal constants, but different masses, then WF earth has to have 75% of real earth's mass.

No. Try calculating it again. I think you may have misunderstood something, or left out a few magnitudes of 10. 

 

And using the website you gave me, the values are all consistent to my calculations, to within 0.02 of each other. 

 

EDIT: Actually, I think I messed up radius magnitudes of 10. 

Edited by Renegade343
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Renegade343

Renegade343

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As much, but it still could affect it quite dramatically. Imagine the core was going thousands of times faster or had stopped completely. What then?

Well, if it goes thousands of times faster than what it is now, then it would make the Earth have a slightly increased radius, but it would be somewhat insignificant compared to the current Earth's radius. If it starts to go at relativistic speeds, then it would simply rip the Earth apart. 

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Llyssa

Llyssa

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Well, if it goes thousands of times faster than what it is now, then it would make the Earth have a slightly increased radius, but it would be somewhat insignificant compared to the current Earth's radius. If it starts to go at relativistic speeds, then it would simply rip the Earth apart. 

If it was going faster, it would be hotter(more friction, and more total energy), if it was hotter, the pressure would increase, increased pressure would want to expand, and the plates that are floating on top of it would be pushed further out. If it were going even a single digit multiple of the current speed, it would be a big difference. Thousands of times the speed would be quite dramatic.

 

EDIT: Actually, I think I messed up radius magnitudes of 10. 

Yeah. If you just plug in the numbers for the current earth(the notation they use would be 5.972E+24 for mass; radius can just be 6371 km), and then just try hitting the calculate button, you'll get the right gravity for current earth. If you then just try adjusting the numbers(change the 5 to a 4, for example), you can see the difference changes make. If you keep your E+24 on the end, it's pretty easy to get to 7.34.

 

I wasn't trying to track all of your equations(php blows for math legibility), but your final conclusion was several magnitudes off(venus, for example, has gravitational acceleration of 8.8m/s^2, which is roughly a half step between the WF earth and real earth, and it's just ever-so-slightly smaller than real earth). Very tired(and it's in php), so I'm not sure exactly where you picked up all the extra zeroes, but you definitely have too many.(If I had to guess, I'm thinking you forgot to convert something from like meters to kilometers).

 

Like I said, though, you really have too many unnecessary steps, since it's a rather straight conversion with so many constants being the same.

Edited by Llyssa
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