/sci/ - Science & Math

>>6206808
The moon orbits both, technically, but for whatever reason fell into Earth's gravity well instead of the sun's gravity well.

The moon does orbit the sun. It's just revolving around the earth when doing so.

The reason that the earth has so much stronger and effect on the moon, then it's because it's closer (despite being less massive). The force of gravity increases exponentially as objects move closer according to the formula.

>>6206833
>exponentially
lol

>moon
>revolving around the earth
>implying the earth and moon aren't both rotating around a common center of mass

>>6206836
My bad I should have said quadratically. You know what I meant

>>6206841
Right

>>6206844
you mean linear

>>6206849
No. Look at the equation. F is proportional to the inverse of the distance squared. So there is 100 times as much force if you go from 10 km to 1 km. Do you even

>>6206849

No, under Newtonian gravity, the strength of the force is inversely proportional to the square of the distance between two masses.

Do you understand what you're reading?

>>6206859
no, if you have planet A and B, and you half the distance from A to B, then you get a factor of 2 (because its linear), but then the distance from B to A is also halved so you get another 2 and the total is 4. So you see both are linear.

>>6206863

Your reasoning doesn't make any sense.

Are you not looking at the denominator in >>6206844? Do you not appreciate what this term does to the value as distance increases or decreases?

>>6206863
>implying r2 = 2r

>>6206863
>implying r squared = 2r

>>6206863
>also implying you should cut the distance in half when using this formula. you don't. the force is just as it says.

>>6206863

What do you mean "you get a factor of 2"? If you halve the distance between two masses A and B, the gravitational force between them increases as such:

G(MaMb / D^2)
G(MaMb / (D/2)^2)

For an initial value of D = 10, we have G(MaMb / 100). For half that value, we have G(MaMb / 25). For a fifth of that value, we have G(MaMb / 4). The denominator does not decrease linearly and neither does the force increase linearly. It increases quadratically.

>>6206871
2*2 = 4

>>6206879

>>6206879

2*2 = 4
3*3 = 9
4*4 = 16
5*5 = 25

This is not linear growth. This is quadratic growth.

>>6206888
ive been wanting to know who this is for so long. thanks!

>>6206894
it seems like that because BOTH are linear, As distance to B AND Bs distance to A, if you increase the distance by 10, the force of A on B is 10 times weaker, and B on A is 10 times weaker. so you see its 100 times weaker.

hi OP here. the previous question was to show that the sun has approx. 2.2x the gravitational pull on the moon. I have mathematically solved it, which sorta confused me. thanks guys /sci/ saves the day :)

>>6206901
>if you increase the distance by 10, the force of A on B is 10 times weaker

No! The force is 100 times weaker on B, and B's force on A is 100 times weaker.

>>6206911
>sun/moon : 4.35157803 × 10^37 kg^2
>earth/moon : 2.08129156 × 10^37 kg^2

Pretty interesting. What is the extended explanation for the moon remaining close to Earth, given these figures?

>>6206913
then it would be 10000 times weaker in total. (remember newtons 3rd law)

>>6206924
I give you a 10 kg cake, and you give me a 10 kg cake, therefore we have 100kg of caek!!!111one

>>6206928
going between us that is

>>6206924

I don't see why you're multiplying the forces of each on the other to obtain the common force between the two masses. That's very obviously not how the formula works.

Newton's Third Law states that Fa = - Fb. Not that the combined force between them is Fa * Fb.