At what distance from the Earth and the moon have zero net force?

In summary, the zero net force point, also known as the Lagrange point, is a stable equilibrium where the gravitational pull from the Earth and the moon cancel out. It is important for space missions and satellite placements. The distance between the Earth and the moon for this point can be calculated using their masses and distance between them. There are five Lagrange points in total, with the zero net force point being the third one, known as L3. These points provide a stable equilibrium for objects in space, reducing the need for constant propulsion and correction. While the zero net force point can change over time, these changes are small and can be accounted for in calculations.
  • #1
Gardalay
20
0

Homework Statement



At what distance from the Earth will a spacecraft traveling directly from the Earth to the Moon experience zero net force because the Earth and Moon pull with equal and opposite forces?

Homework Equations



GM(earth)/(R-d)^2=GM(moon)/d^2

The Attempt at a Solution


Me/Mm=81.3
root 81.3=(R-d)/d

I have no idea how to figure out the rest of the question. Please help.
 
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  • #2
(a-b)/c = a/c - b/c

use this and solve
 
  • #3
(a-b)/c = a/c - b/c

use this and solve
 

1. What is the significance of finding a distance from the Earth and the moon where there is zero net force?

The zero net force point, also known as the Lagrange point, is a place where the gravitational pull from the Earth and the moon cancel each other out, creating a stable equilibrium. It is important to understand these points for space missions and satellite placements.

2. How is the distance from the Earth and the moon determined for the zero net force point?

The distance can be calculated using the masses of the Earth and the moon, and the distance between them. This is done using the formula for gravitational force, which is F = (G*m1*m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the Earth and the moon respectively, and r is the distance between them.

3. Are there multiple zero net force points between the Earth and the moon?

Yes, there are multiple Lagrange points between the Earth and the moon. There are five points in total, with the zero net force point being the third one, also known as the L3 point. The other four points are L1, L2, L4, and L5.

4. Why is it important to consider zero net force points in space missions?

The zero net force points provide a stable equilibrium, where objects can remain in constant position without the need for propulsion or constant correction. This is useful for placing satellites or conducting space missions, as it reduces the amount of fuel and energy needed for maintaining a specific position.

5. Can the zero net force point change over time?

The zero net force point can change over time due to various factors, such as the changing positions of the Earth and the moon, or the influence of other celestial bodies. However, these changes are relatively small and can be accounted for in calculations for space missions or satellite placements.

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