If a force stopped earth from orbiting around the sun, how long

>>8714878

So you're asking how long it would take to fall straight down towards the Sun from the orbital height of the Earth.

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you know the masses of both and distance. figure it our yourself.

>>8714886
Yes, pardon me if I didn't express myself clearly, english is my third language

You would accelerate at 0.005931m/s^2, so it would take 7.10259*10^6 seconds to reach the sun, or about 82 days.

>>8714925
the acceleration varies with time
OP read this link
https://www.physicsforums.com/threads/remarkably-difficult-newtonian-problem.360987/#post-2497264

>>8714972
adding on to this if you want a numerical answer it would be about 5602228 seconds or roughly 64.8 days.

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>>8714925
I arrived to the same conclusion with pic related, but I didn't understand >>8714972 how would it vary with time?

>>8715058
recall the formula for universal gravitation is
[eqn]F=G\frac{m_1m_2}{r^2}[/eqn]
note that r changes, the closer you get to the sun, the more acceleration you'll have. you need to solve a differential equation to obtain a relationship between position and time for this (its helpful to use energy when doing this). see the link i provided in my first post.

>>8715068
Ah you are correct, I shall try to wrap my mind around the differential equation. Thanks for the link

>>8714925
REEEEEEEEEE WHAT THE FUCK
Ill give you a hint: you need an integral

>>8715078
no worries mate, gravitation of free bodies can start to get pretty hairy. If you're curious and want more, you can look at the two-body problem and the unsolved three-body problem

>>8714878
mr''=-GMm/r^2
r''=-GM/r^2
dr'/dt=-GM/r^2
dr'/dr*r'=-GM/r^2
r'dr=-GMdr/r^2
.5r'^2=GM/r
r'=sqrt(2GM/r)
dr/dt=sqrt(2GM/r)
sqrt(r)dr=sqrt(2GM)dt
.66r^(3/2)=sqrt(2GM)t
t=sqrt(2r^3/GM)/3

>>8715089
this

>>8715157
this

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>>8714925
>/sci/ doesn't know what an integral is
Brilliant. Why do I even come here?

>>8715401
>why do I come here
To act superior when others make mistakes or ask questions. They are trying to learn, fuck off.

Not a physics or astronomy pro, but I think that if the sun simply stopped the Earths orbit right now, we would be thrown away from the solar system in a tangent line. Like when you're spinning a ball attached by a line and accidentally let it go from your hand.

>>8715522
The sun is still assumed to be here dumbass.

>>8715530
I know that, but isn't like that simulations that two massive celestial bodys (like two stars) pass really close by and then are thrown away from each other? I mean, isn't the same logic?

>>8715539
He's saying what would happen if velocity was 0

What about an N body problem? The outer planets would be pulling away at a negligable force that should be accounted for. Depending on the orbits, time to impact could be reduced or increased by a matter of days.

>>8714925
Acceleration due to gravity isn't constant in general.

You can treat it like it's constant in your high school physics classes because moving from 6371km above the surface of the earth to, say 6372 (when you're 1km up in the air) doesn't make much of a difference

>>8715577
>Assuming no other forces apply except the gravitational pull of the sun.


not the OP, but

>Assuming no other forces apply except the gravitational pull of the sun.

>>8716023
What the fuck are you trying to say you fucking retard? Gravitational force is inversely proportional to distance between the two masses. As you get closer to the sun the acceleration it induces will be higher. You can't treat it as constant for the hole journey.

>>8716037
I think >>8716023 was replying to >>8715575

>>8715522
>Not a physics pro
no fucking shit, you sound like a retard.

>>8716023
Literally just neck yourself you fucking retard, if this isn't bait you should really consider killing yourself.