Force Bal: 90%d Earth-Moon Gravitational Forces

In summary, Force Bal: 90%d Earth-Moon Gravitational Forces is a concept that describes the balance between the gravitational forces of the Earth and the Moon. This force is calculated using Newton's law of universal gravitation and is important for understanding tides on Earth and stabilizing the Moon's orbit. It can change slightly depending on the relative positions of the Earth and the Moon and affects all objects in the Earth-Moon system, including satellites and spacecraft.
  • #1
JorgeLuis
3
0
Given that the distance between the Earth and the Moon is d = 3.84 x 10^8 m, show
that a satellite located exactly in-between the Earth and the Moon at a distance of
90% d from the Earth experiences no net force (at least when only the
gravitational force due to the Earth and the Moon at taken into account). Draw a
diagram showing the forces acting on the satellite.
 
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  • #2
1] This belongs in the homework section, Please post there.
2] We do not spoonfeed homework answers. Please show your work, we will help.
 
  • #3


To show that a satellite located at 90% of the distance between the Earth and the Moon experiences no net force, we can use the equation for gravitational force:

F = G * (m1 * m2) / r^2

Where:
F = Gravitational force
G = Gravitational constant (6.67 x 10^-11 Nm^2/kg^2)
m1, m2 = Mass of the two bodies (Earth and Moon)
r = Distance between the two bodies

In this case, the satellite is located at 90% of the distance between the Earth and the Moon, which can be represented as 0.9d. So, the distance between the satellite and the Earth would be 0.9d, and the distance between the satellite and the Moon would be 0.1d.

Now, let's calculate the gravitational force between the satellite and the Earth:

F1 = G * (mE * mS) / (0.9d)^2

Where:
F1 = Gravitational force between the satellite and the Earth
mE = Mass of the Earth
mS = Mass of the satellite
0.9d = Distance between the satellite and the Earth

Similarly, the gravitational force between the satellite and the Moon can be calculated as:

F2 = G * (mM * mS) / (0.1d)^2

Where:
F2 = Gravitational force between the satellite and the Moon
mM = Mass of the Moon
mS = Mass of the satellite
0.1d = Distance between the satellite and the Moon

Since we are assuming that the satellite experiences no net force, F1 and F2 should be equal in magnitude but opposite in direction. This can be represented as:

F1 = -F2

Substituting the values of F1 and F2, we get:

G * (mE * mS) / (0.9d)^2 = -G * (mM * mS) / (0.1d)^2

Simplifying this equation, we get:

mE * (0.9d)^2 = mM * (0.1d)^2

Now, we can cancel out the mass of the satellite (mS) from both sides, as it is common in both terms. This leaves us with:

mE * (0.9d)^
 

1. What is Force Bal: 90%d Earth-Moon Gravitational Forces?

Force Bal: 90%d Earth-Moon Gravitational Forces is a concept that describes the balance between the gravitational forces of the Earth and the Moon. It refers to the fact that the Earth and the Moon exert gravitational forces on each other, with the Earth's force being 90% of the Moon's force.

2. How is this force calculated?

This force is calculated using Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. In this case, the objects are the Earth and the Moon, and the distance between them is the distance between their centers of mass.

3. Why is this force important?

This force is important because it is the main driving force behind the tides on Earth. The gravitational pull of the Moon on the Earth's oceans causes them to bulge, resulting in high and low tides. This force also helps to stabilize the Moon's orbit around the Earth.

4. Does this force ever change?

Yes, this force can change slightly depending on the relative positions of the Earth and the Moon. For example, when the Moon is at its closest point to the Earth (perigee), the force between them is slightly stronger, and when the Moon is at its farthest point from the Earth (apogee), the force is slightly weaker.

5. How does this force affect other objects in the Earth-Moon system?

This force affects all objects in the Earth-Moon system, including satellites and spacecraft. It is an important consideration for spacecraft orbiting the Moon, as they must account for the Moon's gravitational pull in their trajectories. This force can also affect the rotation and shape of the Moon itself.

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