Earthed - How long will it take an object to reach a planet?

How long will it take an object to reach a planet?

If an object starts at rest and begins accelerating towards a large object such as a planet (assume the planet is also at rest) how can one determine the amount of time it will take for the object to reach the planet considering that the object's acceleration is constantly changing (a=(Gm)/r^2).

Using Earth as a hypothetical example, can anyone solve the amount of time it will take for an object 100,000 km from the earth to reach the planet.

G (gravitational constant)=6.67x10^(-11)

m (earth's mass)=5.9742x10^24

r=distance between center of both objects (radius of earth+distance of object from earth)= 6378100m+100000000m=

106378100m

Can the object's position in relation to the planet be expressed as a function of time?

If not, then is it possible to use a differential equation to find the time required for the object to reach the planet?

Public Comments

I would solve it with an iteration on something easy like an excel spread sheet showing how all changes in accord with the equation of Newtons.
The time that an object will take to fall is given by:

t^2 = h / ((r1/r2)*.5a)

h = the height above the surface (the question assumes there is a surface)

r1 = the radius from the center to the surface

r2 = the radius from the center to the object in question

a = the accelleration at the surface (for earth it's 32.2 feet per second)

t = time of course, in seconds if 32.2 is used as a. h, r1, and r2 must also be of equal units (feet in this case).

This assumes the falling object has no mass, so it's a simplified formula.

I plugged the numbers in for 100,000 kilometers (above the surface) and got 18,443 seconds, or 5 hours 7 minutes and 23 seconds (I know I'm being riduculously exact, but that's what my calculator says).
What is the mass of the object? and the location it is entering our solar system in relationship to our sun, and/or other planets?

or since this is hypothetical, and our planet is presumed to be at rest, are we also assuming that the planet is located in deep space, outside our solar system, and no other forces are acting upon your object?

If you will give more precise details, I will work on your problem.

OK, I have come back here several times to check if you added more information, and after 2 days you have not, so I will explain why there is a big problem with your question as you have ask it.

First. there is no such a thing as an object at rest with in our universe, even though it may appear to us as being at rest.

Second. all other planetary body's, and or the sun will also pull on your Planet, and your object, which will change the equation.

Third. If we are presuming that there are no other relatively close masses acting upon your planet, or your object, then the importance of both masses must be taken into consideration, as your question asks how long will it take an object to reach the planet, and not how long does it take a planet to reach an object.

In other words, If the mass and density of your object is greater than the mass and density of your planet, then your planet will traverse more distance to your object, than your object will traverse toward your planet, and the equation will be totally different.

If both the Planet, and your object are of equal mass and density then they will both traverse the same distance toward each other which changes the outcome of the distance your object traversed, as you have ask your question here on yahoo answers.

Also if your object is presumed to have no mass, then you have no object, and there can be no such a thing as an object with no mass, 'ever'.

Gravitational attraction is what pulls objects together, and it is mass dependent.

I Need more input, and no one here has given you a correct answer, because your question as you have ask it is incomplete.