Using Gravitational Force Equilibrium to Calculate M2/M1 Ratio

• erykah722
In summary, the objective of this experiment is to find the equilibrium position for a test mass between two point masses by adjusting its starting position. The mass ratio M2/M1 can be calculated using the latest value of x/L without knowing the values of L or the test mass. The equations used are F= M*m*G/r2 and m1/0.163 = m2/0.355. The ratio of y/x can be found using basic algebra.
erykah722

Homework Statement

Here is the objective: To experiment with the resultant of two gravitational forces. In particular, you will find the equilibrium position for a test mass located on a line between two point masses.

Here are the instructions:
(1) Drag the test mass (red disk) to an arbitrary point on the line and release. Note the value given for x/L, where x is the distance measured from the center of M1 to the center of the test mass.
(2) Repeat (1), but start the test mass farther away from the mass to which it was attracted.
(3) Continue adjusting the starting position of the test mass until you see the message close enough! Think about how to do that in the most efficient way.
(4) From your latest value of x/L, you can compute the mass ratio M2/M1, without needing to know either L or the value of the test mass. You will have to perform a short derivation to get the simple equation you need. (Hint: start by setting the two gravitational forces acting on the test mass equal to one another.)

I got .404L for the equilibrium value.

F= M*m*G/r2

The Attempt at a Solution

I set the equations up as:

M*m1*G/0.4042 = M*m2*G/0.5962

I then canceled out the M and G on each equation because they are equal and am left with

m1/0.163 = m2/0.355

I'm stuck here. Am I even doing this right?

This is just basic algebra, if you have an equation that reads x/a = y/b and you want the ratio of y/x, how would you do that one?

...Wow. I'm sorry, I've been really stressed out. Now I'm embarrassed. Thank you though!

1. How can gravitational force equilibrium be used to calculate the M2/M1 ratio?

Gravitational force equilibrium refers to the state in which the gravitational forces acting on two objects are equal and opposite, resulting in a stable and balanced system. In order to calculate the M2/M1 ratio, we can use the equation F1/F2 = M1/M2, where F1 and F2 are the gravitational forces acting on the two objects and M1 and M2 are their respective masses. By rearranging this equation, we can solve for the M2/M1 ratio.

2. What are the applications of using gravitational force equilibrium to calculate the M2/M1 ratio?

Calculating the M2/M1 ratio using gravitational force equilibrium can be useful in various fields such as astronomy, physics, and engineering. It can help determine the mass of celestial bodies, the strength of gravitational forces between objects, and the stability of structures.

3. Can the M2/M1 ratio be calculated for objects with irregular shapes?

Yes, the M2/M1 ratio can still be calculated for objects with irregular shapes. The key is to determine the center of mass for each object and use that as the point where the gravitational force acts. From there, the M2/M1 ratio can be calculated using the same equation (F1/F2 = M1/M2).

4. How does the distance between the two objects affect the M2/M1 ratio?

The distance between two objects affects the M2/M1 ratio in the sense that the closer the objects are to each other, the stronger the gravitational force between them. This means that as the distance decreases, the M2/M1 ratio will also decrease.

5. Can the M2/M1 ratio be used to determine the type of orbit for a celestial body?

Yes, the M2/M1 ratio can be used to determine the type of orbit for a celestial body. For example, if the M2/M1 ratio is 1, the orbit will be a circular orbit. If the ratio is greater than 1, the orbit will be an elliptical orbit, and if it is less than 1, the orbit will be a hyperbolic orbit. This is based on Kepler's Third Law, which states that the square of the orbital period is proportional to the cube of the semi-major axis, and the ratio of the two objects' masses is equal to the inverse ratio of their semi-major axes.

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