# An object which experiences two gravitational force

1. Apr 21, 2014

1. The problem statement, all variables and given/known data

Let there be a Voyager 5 with two Earth's(I mean they have the same mass and density etc)
At start,Voyager 5 will be stationary.
I want to calculate the path of the Voyager and if possible,draw it on a graph.

2. Relevant equations
$F=\frac{GMm}{r^2}$

3. The attempt at a solution
I know I have to find the resultant force and accelerate the voyager in that direction.
My problem is that if I move it a little bit,the forces will change both direction and magnitude.Then I will again have to find the resultant force and accelerate it.This would be boring.
Is this really that difficult?Is there any other way?

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2. Apr 21, 2014

### voko

This is known as Euler's three-body problem, and its analytical solution requires calculus. If I remember correctly, you are not there yet.

You could try solving this numerically, using a spreadsheet or some programming language, if you know one.

3. Apr 21, 2014

I don't know any programming languages.How can I use a spreadsheet to solve this?

P.S can you recommend a calculus book that will teach it from scratch?

4. Apr 21, 2014

### Staff: Mentor

Even the two-body problem needs calculus to find a solution. The three-body problem has no "nice" solution for the general case.

@adjacent: The idea is to calculate the motion in small steps. For each step, calculate the acceleration, adjust the velocity a bit accordingly, adjust the position a bit accordingly. The quality of the trajectory depends on the step size and the order and formula of those adjustment steps, but to get an idea how it works that does not matter.

5. Apr 21, 2014

### voko

In a spreadsheet, you would arrange rows of cells, where each row has two cells for position, two cells for velocity, two cells for acceleration, all at some instant of time. The acceleration in each row is computed using the force formula for the position in the row. The position in each row is computed from the position in the previous row plus the velocity in the previous row times the time step between rows. The velocity in each row is computed from the velocity in the previous row plus the acceleration in the previous row times the time step between rows. You need to set up just the first two rows in that way, then using the spreadsheet auto-complete feature (select cells and drag them down) to obtain more rows.

As for learning calculus from a book, it can be done, but is much harder than learning it from a teacher. I would not recommend doing that.

6. Apr 21, 2014

### voko

In this particular case, there is a (somewhat) nice solution.

7. Apr 21, 2014

Thanks everyone.I will try to use Microsoft Excel.