Weightlessness, or zero gravity, and tidal forces

 Weightlessness, or zero gravity

Gravity exist everywhere in the universe because it is defined as the force that attract two bodies to each other. The sensation of weightlessness or zero gravity happens when the effect of gravity is not felt.

For example, astronauts in the International Space Station (ISS) do not feel the effects. ISS is in perpetual freefall above the Earth. Its forward motion, however, just about equals the speed of its fall toward the Earth. This means that the astronauts inside are not pulled in any particular direction. So they float. 

Height above Earth's surface vs weight force of 10 kg object in Newtons.

How to calculate g at certain altitude. (6371 km is taken as Earth's diameter.)

But anyone who has flown with a small plane can experience weightlessness, for example by sudden push of wind or by a maneuver that you fly as up and turn it down, so you feel weightlessness on top of the rout.

Zero G Flight

Newton's theory of gravitation

Newton described gravitation as a universal force and claimed that "the forces which keep the planets in their orbits must be reciprocally as the squares of their distances from the centers about which they revolve." This statement was later condensed into the following inverse-square law:

F = G (m1 m2) / r^2

where F is the force, m1 and m2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant 6.674×10^−11 m^3⋅kg^−1⋅s^−2.

Gravitational force between the earth and the moon:

Borrowed from Google

G = universal gravitational constant

M = mass of the Earth = 5.96 x 10²⁴ kg 

m = mass of the Moon = 7.33 x 10²² kg

d = center-to-center Earth Moon distance = 3.84 x 10⁸ m

= (6.67 x 10^-11) x [(5.96 x 10²⁴) x (7.33 x 10²²)] / (3.84 x 10⁸)²

= 1.946 x 10²⁰ N

The same way we can calculate the gravitational force between the Sun and the Earth. Mass of the Sun is 1.988 x 10³⁰ kg, and the distance between the Sun and the Earth is 150 million km.  

The Sun exerts a greater force, and it is almost 200 times greater than the force due to the Moon. 

Ocean tides are the result of gravitational tidal forces. These same tidal forces are present in any astronomical body. They are responsible for the internal heat that creates the volcanic activity on Io, one of Jupiter’s moons, and the breakup of stars that get too close to black holes.

Lunar Tides

The rising and falling of the sea level can be observed about twice per day. That is caused by a combination of Earth’s rotation around its axis and the gravitational forces between the Earth and the Moon and between the Earth and the Sun.

The Moon's gravity differential field at the surface of the Earth is known (along with another and weaker differential effect due to the Sun) as the Tide Generating Force. Source Wiki

The tidal force can be viewed as the difference between the force at the center of Earth and that at any other location.

If the Earth wouldn't rotating and the Moon would be fixed, then the bulges would have remained in the same location on Earth. Relative to the Moon, the bulges stay fixed, along the line connecting Earth and the Moon. But the Earth rotates approximately every 24 hours. In 6 hours, the near and far locations of Earth move to where the low tides are occurring, and 6 hours later, those locations are back to the high-tide position. Since the Moon also orbits Earth approximately every 28 days, in the same direction as Earth rotates, the time between high (and low) tides is actually about 12.5 hours. The actual timing of the tides is complicated by numerous factors, the most important of which is another astronomical body: the Sun.

The Effect of the Sun on Tides

In addition to the Moon’s tidal forces on Earth’s oceans, the Sun exerts a tidal force as well. The gravitational force of the Sun on any object on Earth is almost 200 times that of the Moon. However, 

even the Sun causes tides just like the moon does, they are somewhat smaller. 

When the earth, moon, and Sun line up, the lunar and solar tides reinforce each other, leading to more extreme tides, which is called spring tides. When lunar and solar tides act against each other, the result is in unusually small tides, called neap tides. 

The tidal effect of the Sun is less than that of the Moon. Depending upon the positions of the Moon and Sun relative to Earth, the net tidal effect can be amplified or attenuated.

Even the Sun's gravitational force on the Earth is stronger than the Moon's, the tidal bulges it causes are much smaller. That is because tides are not caused by the gravitational forces of the Moon or the Sun lifting up the oceans. Rather, tides are created because the strength and direction of the gravitational force varies depending on where on Earth you are. This variation creates the differential forces or tidal forces that in turn cause tides.

Tidal forces

The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomena, including tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects.

Sun, Earth, and Moon, source Wiki

 Graph showing how gravitational attraction drops off with increasing distance from a bodym source: wiki

Figure above is a graph showing how gravitational force declines with distance. In this graph, the attractive force decreases in proportion to the square of the distance, while the slope relative to value decreases in direct proportion to the distance. This is why the gradient or tidal force at any point is inversely proportional to the cube of the distance.