1.Explain why the Earth orbits the Sun, but the moon orbits the Earth.
2.How does size impact gravitational force?
3. How do the Sun’s gravity and the Earth’s inertia keep us orbiting in the solar system?
Force = G m M / d^2
m is small one, M is big one
the attractive force is the same on both
If there is no outside force on the system, they must move around the center of gravity of the 2 body system. When the big one is huge, that point is close to the center of the big one. (so actually the earth does not revolve around the sun, but the center of gravity of the earth sun system is so close to the center of the sun that we do not worry about that.) (same sort of argument for earth and moon, center close to earth center.
NOW if the force F = G m M/d^2 is pulling them togeter, whydon't they crash?
It is because the net force on the little one = its mass m times its acceleration A
F = G m M /d^2 = m A
luckily that A is centripetal acceleration if we are revolving around the sun. If we stipped rotaning in our orbit, we would accelerate straight into the sun
A = v^2/d for tangential orbit speed v
so
G m M /d^2 = m v^2/d if the gravity is balanced by the centripetal acceleration
so
G M = v^2 d
and
v^2 = G M/d
so to stick in orbit at distance d we need tangential speed = sqrt [ G M/d }
1. The Earth orbits the Sun and the Moon orbits the Earth due to the balance between gravitational force and inertia. Here's how it works:
The Earth orbits the Sun because of the force of gravity. Gravity is a natural force that attracts objects with mass towards each other. In this case, the Sun's enormous mass creates a strong gravitational force that pulls the Earth towards it. This gravitational force keeps the Earth in its orbit around the Sun.
Similarly, the Moon orbits the Earth because of the gravitational force between them. The Earth's gravitational force attracts the Moon towards it, causing the Moon to follow a curved path around the Earth.
2. The size of an object does impact the gravitational force it experiences. Here's an explanation of how:
Gravitational force depends on the masses of the interacting objects and the distance between them. The greater the mass, the greater the gravitational force. So, larger objects generally have a stronger gravitational force compared to smaller objects, assuming the distance between them is the same.
For example, if you compare two objects of different sizes but with the same mass, the larger object will have a stronger gravitational force. However, if you compare two objects with the same size but different masses, the object with a greater mass will have a stronger gravitational force.
3. The Sun's gravity and the Earth's inertia together keep us in orbit within the solar system. Here's an explanation:
The Sun's gravity exerts a powerful force that pulls the Earth towards it. Without any other forces, the Earth would simply fall into the Sun. However, the Earth also possesses a property called inertia, which is its tendency to resist changes in motion.
When these two forces, gravity and inertia, work together, they create a balance that keeps the Earth in a stable orbit around the Sun. The Earth's inertia causes it to continue moving in a straight line, while the Sun's gravity constantly pulls the Earth towards it. As a result, the Earth follows a curved path or an orbit around the Sun.
In essence, the Sun's gravitational force keeps the Earth from flying off into space, while the Earth's inertia keeps it from being pulled straight into the Sun. This delicate balance between gravity and inertia allows the Earth to maintain its stable path around the Sun and stay in the solar system.