D&D 5E Levitate is a save-or-die spell

[Oofta]

Hmm. We know a mage hand can produce at least 10 lbs of force. If we assume the Earth is a valid target for mage hand because it is weightless, the spell should be able to deliver at least 10 lbs of force to the Earth. Converting to metric, that's 44.5 N. Pushing the Earth into the sun requires imparting roughly 30 km/s to the Earth. The formula to calculate how long it would take to accelerate the Earth by 30 km/s is:

(time force applied)=(desired velocity change)*(Earth's mass)/(force applied)

Plugging in all the values we get: (time force applied)=(30 km/s)*(5.97*10^24 kg)/(44.5 N)=1.28*10^20 years.

That's about 128 quintillion years. The Earth will collide with the Sun much sooner than that when the Sun starts expanding into a red giant, which suggests that your efforts are futile.

But wait! Colliding with the outer edge of the Sun becomes easier as the Sun starts to expand in about 5.4 billion years. Maybe you can speed up the engulfing processing by pushing the Earth into an orbit that intersects the expanding Sun sooner? Let's find out.

In 5.4 billion years of applying 44.5 N of force to the Earth, you can change it's velocity by:

(44.5 N)/(5.97*10^24 kg)*(5.4 billion years)=1.27*10^-6 m/s

Rats! That's not enough to make an appreciable change in the Earth's orbit. So, tragically, your threat to shove the Earth into the Sun with Mage Hand is toothless. You can't meaningfully speed up the inevitable collision.

You might have better luck if you campaign world is much less massive than Earth (about 7 orders of magnitude), and orbits (at the same distance as Earth) a red dwarf that will last 10 trillion years or so, giving you a longer window to push with mage hand. Sadly, that campaign world would be utterly frozen since it would orbit far outside the red dwarf's habitable zone. If you're serious about pursuing this idea, I recommend the 3.5 sourcebook "Frostburn".

Except that speed is also a relative measurement which you do not take into account. Therefore, the mage tries to move the mage hand 30 ft. Speed is generally measured relative to the planet so therefore as the planet increases velocity, so will the hand.

While the hand itself has no mass and is therefore not limited to the speed of light, the mass of the planet at some point will increase to infinity.

I seriously doubt that it will take that long to hit the sun though. We should be able to effectively accelerate 30 ft every round or 5 ft per second. You are not continuously pushing against a fixed object, you are merely increasing it's velocity slightly every 6 seconds.

This is where, of course I remember that the last time I had physics or a math class was in high school a long, long time ago. So for the sake of The Realms, I hope I am completely mistaken.

EDIT: too much multitasking! Ninja'd by a post over half an hour ago.

 

[Lanefan]

...and if 100 mages decide to all go in together on this silly project, with about 2/3 of them pushing the planet with a Mage Hand at any given time and the other 1/3 sleeping, resting, etc., you might even be able to knock a zero or two off the ridiculous number of years this is gonna take...

But yes, I'd allow a Mage Hand to push someone who is levitating, though how long it'd take for that push to be of much use would depend on the mass of the target - a Gnome would be more affected by the push than would a burly Half-Orc, for example.

 

[Xetheral]

Why stop at 30 km/s? Just keep pushing.

Except that speed is also a relative measurement which you do not take into account. Therefore, the mage tries to move the mage hand 30 ft. Speed is generally measured relative to the planet so therefore as the planet increases velocity, so will the hand.

While the hand itself has no mass and is therefore not limited to the speed of light, the mass of the planet at some point will increase to infinity.

I seriously doubt that it will take that long to hit the sun though. We should be able to effectively accelerate 30 ft every round or 5 ft per second. You are not continuously pushing against a fixed object, you are merely increasing it's velocity slightly every 6 seconds.

This is where, of course I remember that the last time I had physics or a math class was in high school a long, long time ago. So for the sake of The Realms, I hope I am completely mistaken.

EDIT: too much multitasking! Ninja'd by a post over half an hour ago.

My entire post was intended to be satirical, but if we're going to treat it seriously....

@Elfcrusher The problem is that hitting the Sun requires at least 30 km/s, and the caster doesn't have enough time to even reach that high before the expanding Sun engulfs the Earth anyway. Reaching a change in velocity even greater than 30 km/s would take even longer.

@Oofta The 30 km/s change in velocity necessary to hit the sun is measured relative to the sun. I apologize for not being specific.

Even though we're treating the Earth as "weightless" on the grounds that it is in freefall around the Sun, it still has 5.97*10^24 kg of mass, and that inertia will resist the acceleration created by the force from the mage hand. We know that the mage hand can't generate more than about 10 lbs of force, or else it would be able to support objects weighing more than that. (We can't calculate the exact maximum amount of force the mage hand can generate because the spell doesn't contain enough detail about its acceleration profile when it moves objects.) So from a physics standpoint, you definitely can't use mage hand to accelerate the Earth at 30 ft/round per round.

Even ignoring force and inertial mass, the spell description suggests that 30 ft/round is the mage hand's maximum velocity (relative to the Earth), not its maximum acceleration. So going only by the spell text, mage hand is capable of changing the Earth's velocity by no more than 30 ft/round total. If so, the mage hand will never be able to push the Earth into the Sun, no matter how long you push, because you'll never get the net change in velocity higher than 30 ft/round. At 5 ft/s, that's a far cry from the required 30 km/s.

 

[Maxperson]

Even ignoring force and inertial mass, the spell description suggests that 30 ft/round is the mage hand's maximum velocity (relative to the Earth), not its maximum acceleration. So going only by the spell text, mage hand is capable of changing the Earth's velocity by no more than 30 ft/round total. If so, the mage hand will never be able to push the Earth into the Sun, no matter how long you push, because you'll never get the net change in velocity higher than 30 ft/round. At 5 ft/s, that's a far cry from the required 30 km/s.

But once moving, the planet will keep moving right? So additional castings of mage hand should be able to increase the speed.

 

[Oofta]

My entire post was intended to be satirical, but if we're going to treat it seriously....

@Elfcrusher The problem is that hitting the Sun requires at least 30 km/s, and the caster doesn't have enough time to even reach that high before the expanding Sun engulfs the Earth anyway. Reaching a change in velocity even greater than 30 km/s would take even longer.

@Oofta The 30 km/s change in velocity necessary to hit the sun is measured relative to the sun. I apologize for not being specific.

Even though we're treating the Earth as "weightless" on the grounds that it is in freefall around the Sun, it still has 5.97*10^24 kg of mass, and that inertia will resist the acceleration created by the force from the mage hand. We know that the mage hand can't generate more than about 10 lbs of force, or else it would be able to support objects weighing more than that. (We can't calculate the exact maximum amount of force the mage hand can generate because the spell doesn't contain enough detail about its acceleration profile when it moves objects.) So from a physics standpoint, you definitely can't use mage hand to accelerate the Earth at 30 ft/round per round.

Even ignoring force and inertial mass, the spell description suggests that 30 ft/round is the mage hand's maximum velocity (relative to the Earth), not its maximum acceleration. So going only by the spell text, mage hand is capable of changing the Earth's velocity by no more than 30 ft/round total. If so, the mage hand will never be able to push the Earth into the Sun, no matter how long you push, because you'll never get the net change in velocity higher than 30 ft/round. At 5 ft/s, that's a far cry from the required 30 km/s.

But you're thinking physics. We've established that the planet has no weight so therefore it qualifies to be pushed by the spell. If it can be pushed then it will be pushed 30 ft. Magic overrides physics and is ignorant of this "mass" of which you s

So I stand by my hypothesis.

 

[Guest 6801328]

Once it’s moving 30 ft/round you drop concentration and re-cast from the new frame of reference.

 

[jaelis]

Once it’s moving 30 ft/round you drop concentration and re-cast from the new frame of reference.

By this logic you could use mage hand to push yourself while levitated.

 

[Greenstone.Walker]

But can you cast levitate on a stone that is being thrown at you with a readied action? If you do, what happens?

Yes, you can. The stone immediately rises 20 feet up and continues on its way, almost certainly missing you. Since its altitude doesn't change, it flies a long way, probably out of sight. When your turn comes around you can change its altitude, though you'll be doing it by guesswork since you can't see it any more.

 

[FrogReaver]

Actually Astronauts do weigh something in space while orbiting the earth.

We can determine the force of the gravitational force acting upon them at that altitude. We can determine their mass. After that it's just force times mass equals weight. Keep in mind weight is specifically derived from the gravitational force acting upon a mass

There's some terribly shoddy physics in here.

On Weightlessness:
What weightlessness means is not that astronauts are no longer affected by any gravity - as that would be impossible. It means there is another force acting upon them in an equal and opposite direction - centripetal force. Because gravity still effects them they still have weight in that situation.

Instead what we typically mean by weightless is that you are in state such that you are behaving as if you were weightless. Another force counteracting gravity may cause this - in the case of orbiting the earth. Or being far away from any massive object could also cause this as the magnitude of the gravitational force becomes very small.

To be actually weightless you need to be infinitely far away from all other matter - or at least in a position such that the gravitational forces of all matter in the universe netted out to 0 on you.

 

[jaelis]

Ugh, FrogReaver. My eyes are bleeding...