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lacgibra t1_ixue9eg wrote

Are you speaking about Newton's law of gravitation? It's used to obtain force of attraction between two planets or it's satellites, which is deduced from f_g = G m_1 m_2/r²

f_g is force of attraction,

G is universal gravitational constant

m_1 mass of the planet

m_2 mass of the other planet

r is distance between them.

The above problem is otherwise called two body problem as well which turns into complicate when you apply classical mechanics

The formula for gravity of the planet obtained from the above equation as folloing as

We know that f = mg and also f = GmM/r²

Here g is gravity due to acceleration G is gravitational constant. m is mass of the object in the earth. M is mass of the earth.

Since the object is bound to the planet the r distance between them would be radius of the planet itself Thus r is radius of the earth

mg = GmM/r²

And you get g = GM/r²

I would suggest you to look into two body problem and barycentre you might find it relevant.

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phrankjones t1_ixvb757 wrote

Their question is more asking the line of: how do you get the mass of the earth?

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lacgibra t1_ixvevls wrote

The comment above still fits, You can obtain mass of the earth by doing the simple pendulum method to obtain g from the equation √g = 2π√L/T

g = earth's gravity L = length of the pendulum T = time period

Note that simple pendulum give adequate answers for small angles only, if you swing the pendulum to wide you won't br arriving at the earth's gravity.

then equate it with g = GM/r²

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Kered13 t1_ixy67ha wrote

It's actually very difficult, because we have to derive it from gravity, and measuring gravity is very difficult. Actually, measuring the acceleration due to gravity is quite easy, that's what /u/lacgibra described. The trouble is measuring the gravitational constant. Of all the fundamental physical constants, the gravitational constant is the one that is known to the least accuracy. The classic experiment for this is Cavendish's experiment, and indeed this was originally conducted in order to estimate the mass of the Earth. This is still basically the technique used, but with much more precise equipment.

Fun fact: We know the mass of the other planets as a ratio to the mass of the Earth much more precisely than we know their absolute mass. This is because the uncertainty in the gravitational constant is greater than the uncertainty in the acceleration due to the planets that we can measure.

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eldude2879 t1_ixvxcai wrote

using newton is not good enuff for precise calculations of planets

we have to use einstein, by that we have to stop thinking of gravety as a force and think of curved space time

Einstein's general relativity states that, in a Schwarzschild spacetime (which approximates our solar system), gravity is slightly different from the inverse square law by an extra fourth power term. It is this extra small term that causes the perihelion motion of Mercury's orbit. If we take this extra term into account and follow the same logic of classical considerations, we find that planets' orbits aren't closed, but are precessing consistently. Mercury's orbit has an apprant precession about 43 arcs per century at its perihelion position which is exactly the amount of precession observed.

https://physicsworld.com/a/correcting-einsteins-calculation-of-the-orbit-of-mercury/

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lacgibra t1_ixw0h05 wrote

Well yeah Newton's doesn't explain Mercury's precession. I were sticking the context of the questioner and I had mentioned defining it classically, you need to think what it is when required. You can't just tell all the concepts that neglected friction, air resistance are wrong, for the classical assumption gravity has to be assumed as force. Relativity got better explanation apsidal precession and all at the end of the day approximately g = 9.81 m/s². Not lower than that or higher than that.

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eldude2879 t1_ixw1mi9 wrote

light behind a galaxy that can be seen because of the mass of the galaxy infront is seen not because of gravity force

as we know photons have no mass so gravity has no effect if you think of it as a force

the space time is bend so the photons get bend with it

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lacgibra t1_ixw20m9 wrote

Okay do me a favour, workout a classical problem considering gravity as curved space time. Simple pendulum, compound pendulum, linear Harmonic oscillator two body problem anything.

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lacgibra t1_ixw2ey4 wrote

I'm simply saying, I apply gravity as space-time curve when I apply the Einstein's relativity in action. If had explained the question in the first scenario using relativity, I would've mentioned gravity as space time curve

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eldude2879 t1_ixw2f7o wrote

well, I am just a simple electrician with some knowledge of Einstein

I admit using Newton is perfectly fine if you dont need super precise

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lacgibra t1_iybna3g wrote

Yeah yeah quantum mechanics is wrong too, because it's foundation was laid by classical mechanics.

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Alfred_The_Sartan t1_ixwbl0l wrote

Is there any reasonable way to use equations to measure the mass of a rogue planet? Like let’s say there’s a brown dwarf that got ejected from its system and is rolling through interstellar space without anything really being able to measurably affect it. Would we have any idea of the mass?

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AstroBryGuy t1_ixxb99l wrote

Sure, via gravitational micro lensing. When the rogue planet or brown dwarf (which is not a planet) passes directly in front of a distant star (as viewed from Earth), the gravity of the rogue planet/brown dwarf will bend the starlight, focusing it towards Earth, causing the distant star to briefly increase in brightness. The amount of brightening depends on the mass of the body.

https://roman.gsfc.nasa.gov/exoplanets_microlensing.html

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