Time it take for small objects to come together under gravity

[hover]

Hey everyone!

I've done http://www.fourmilab.ch/gravitation/foobar/" and i find it interesting how objects of any mass just randomly attract each other. Anyway, i always wanted to find out how long it should take for a mass in this experiment to gravitate towards the other. The problem is it isn't like doing it on Earth where at the surface everything accelerates at 9.8m/s. The only relevant equation for acceleration in this case would be
G*M/r^2
G=6.67*10^-8cm³/g-sec²
m=mass in grams
r=distance in cm
I just learned a LITTLE calculus but so far i can only calculate how long it will take for an dropped object to hit the ground. I was hoping i could use this but since the acceleration is always changing i don't know how to do this out. Can someone help??

Thanks

 

[ranger]

Hi hover,

I've done this experiment and i find it interesting how objects of any mass just randomly attract each other.

Really? Where you expecting them to repel each other

So you want to complicate things more with non constant acceleration I see. I don't know the extent of your calculus knowledge, but this involves integrating the acceleration function.

http://www.sunybroome.edu/~biegen_j/phys1/modules/varacc/Mod4_3.htm
http://hyperphysics.phy-astr.gsu.edu/hbase/avari.html

I recommend for situations like this, you should use constant acceleration and find the time like you would normally.

 

[sir-pinski]

Hi there! It's great that you're exploring the concept of gravity and its effects on objects. The time it takes for small objects to come together under gravity can vary depending on several factors such as the masses of the objects and their distance from each other. As you mentioned, the equation G*M/r^2 can be used to calculate the acceleration due to gravity, but it does not take into account the changing acceleration as the objects get closer to each other.

To calculate the time it takes for objects to come together, you would need to use the concept of Newton's law of gravitation and the equations of motion. This would involve setting up a differential equation and solving it using calculus. If you're just starting to learn calculus, it may be a bit challenging to do this calculation. However, there are online calculators and resources available that can help you with this calculation.

Additionally, the time it takes for objects to come together under gravity can also be affected by other factors such as the presence of other objects, the shape of the objects, and their initial velocities. So, it may not always be a straightforward calculation.

I hope this helps and good luck with your exploration of gravity! Keep learning and asking questions.