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.
Ok, draw a diagram. The force from Earth minus the Force from the Moon adds to zero if it is no net force.
ForceEarth-ForceMoon=?
GMeMs/(.9)^2 - GMmMs/(.1d)^2=?
Me/.81 - Mm/.01=?
can you do that?
how do i do a diagram?
To 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, we will analyze the gravitational forces acting on the satellite.
The gravitational force between two objects can be calculated using the equation:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 x 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of the two objects
r is the distance between the centers of the two objects
Let's consider the satellite at a distance of 0.90d from the Earth. The gravitational force exerted by the Earth on the satellite can be calculated as:
F_Earth = (G * m_s * m_Earth) / (0.90d)^2
= (G * m_s * m_Earth) / (0.81 * d^2)
Similarly, the gravitational force exerted by the Moon on the satellite can be calculated as:
F_Moon = (G * m_s * m_Moon) / (0.10d)^2
= (G * m_s * m_Moon) / (0.01 * d^2)
Since the distance between the Earth and the Moon is much larger than the distance between the satellite and the Earth, we can neglect the effect of the Moon's gravity on the satellite compared to the Earth's gravity. Therefore, we will only consider F_Earth.
To demonstrate that there is no net force on the satellite, we need to show that F_Earth is canceled out by the opposite direction of the force. As the satellite is exactly in-between the Earth and the Moon, the gravitational force exerted by the Earth and the Moon are in opposite directions.
Now, let's draw a diagram to illustrate the forces acting on the satellite:
```
F_Earth
|
<-- Satellite -->
|
F_Moon (negligible)
```
In the diagram, F_Earth and F_Moon represent the gravitational forces exerted by the Earth and the Moon, respectively. Since the Moon's gravitational force is negligibly small, we can consider F_Earth as the only significant force acting on the satellite.
Due to the equal magnitudes of F_Earth and F_Moon, but opposite directions, the net force on the satellite is zero. Thus, the satellite located exactly in-between the Earth and the Moon at a distance of 90% d from the Earth experiences no net force.
Please note that in real-life space scenarios, other factors such as the gravitational forces from other celestial bodies, the Sun's gravity, and the satellite's own velocity need to be considered. This explanation assumes an ideal scenario with only the gravitational forces between the Earth, the Moon, and the satellite.