Understanding Acceleration and its Impact on Time and Velocity - A Question

[Jared Adams]

Hello all,
I am new to the forum and hope to contribute as much help as I ask for. Anyway, wouldn't the acceleration of a first object increase as it gets closer to a second object? If so, is there/ what is the formula for time/velocity if the rate of acceleration varies?
Thanks,
Jared A.

 

[Matterwave]

Are you thinking about gravity increasing between two objects as they get closer to each other? The answer is yes, as two objects get closer together the gravitational force between them increases, and so the acceleration will increase.

The reason we don't talk about this so much in every day life is that 1) the gravitational force is very weak, the only thing that really affects us (as people) gravitationally is the Earth, so we don't really care about the gravitational force between e.g. 2 baseballs, and 2) we tend to stay here on the surface of the Earth. We are ~6700km from the center of the Earth, and when we jump or fall from a height, etc., we are ~1-2m off the ground. This is a change in distance of one part in 6,700,000 so the "increase in acceleration as we are close to the surface vs when we are jumping up off of the surface" is negligible.

 

[Yadama]

Are you thinking about gravity increasing between two objects as they get closer to each other? The answer is yes, as two objects get closer together the gravitational force between them increases, and so the acceleration will increase.

The reason we don't talk about this so much in every day life is that 1) the gravitational force is very weak, the only thing that really affects us (as people) gravitationally is the Earth, so we don't really care about the gravitational force between e.g. 2 baseballs, and 2) we tend to stay here on the surface of the Earth. We are ~6700km from the center of the Earth, and when we jump or fall from a height, etc., we are ~1-2m off the ground. This is a change in distance of one part in 6,700,000 so the "increase in acceleration as we are close to the surface vs when we are jumping up off of the surface" is negligible.

Would it be useful for stuff like landing on a comet? Because as far as I know, it needs to be very precise and even the slightest change in velocity makes a huge difference.

 

[Yadama]

Got this from from the Wikipedia page on gravitational acceleration, this might be what you're looking for. I don't think it shows the acceleration of gravity at specific altitudes but it does give a range."At different points on Earth, objects fall with an acceleration between 9.78 and 9.83 m/s2 depending on altitude, with a conventional standard value of exactly 9.80665 m/s2 (approx. 32.174 ft/s2). Objects with low densities do not accelerate as rapidly due to buoyancy and air resistance."

http://en.m.wikipedia.org/wiki/Gravitational_acceleration

 

[Jared Adams]

Thanks, but I'm working on a simulation that should work for extraterrestrial bodies over much longer distances.

 

[Yadama]

Ah I see, this may be a useful resource then?

https://www.easycalculation.com/physics/classical-physics/learn-gravitational-acceleration.php

Distance would still need to be factored in somewhere though :\

 

[Matterwave]

The force of gravity between two objects is given by Newton's law of universal gravitation:

$$\vec{F}_{12}=-\frac{Gm_1 m_2}{r_{12}^2}\hat{r}_{12}$$

This means the force is directed along the line connecting the two objects (their center of masses) and that the force is attractive (hence the negative sign) and that the force is proportional to the product of the masses and the inverse of the square of the distance between them.

 

[Chronos]

It might be useful to look at the NASA page for calculations used in moon landings - http://www.nasa.gov/audience/foreducators/mathandscience/exploration/Prob_LunarLanding_detail.html

 

[Jared Adams]

Yadama and Matterwave, I could continuously refresh a=GM/(r^2), however it wouldn't work very quickly. I may end up doing that if there is no one equation, however as a last resort. Chronos, thanks for the link, but I couldn't find much that was useful.

 

[dean barry]

Heres something i worked on for someone, you might check it out, don't forget the part about radians.