UNIVERSAL GRAVITATION

Newton's Law of Universal Gravitation

G:  universal gravitation constant (G = 6.67 x 10^-11 N.m²/kg²)

Calculation of gravitational field intensity of the Earth:

g:  gravitational field intensity of the Earth
mo:  Mass of the any object on the surface of the Earth
m_E:  Mass of the Earth (m_E = 5.98 x 10²⁴ kg)
r_E:  Radius of the Earth (r_E = 6,38 x 10⁶ m)

When you substitute the above given values, you will get gravitational field intensity of the Earth:  9,8 N/kg.

Newton's Law of Universal Gravitation formula can be applied anywhere in universe.  Universal gravitation constant (G = 6.67 x 10^-11 N.m²/kg²) is same everywhere in the universe, but gravitational field intensity may be different in different places.  It depends on the mass, the radius of the celestial bodies and also distance from the centre of the body.

Mass of the Earth:  m_E = 5.98 x 10²⁴ kg
Radius of the Earth:  r_E = 6,38 x 10⁶ m
Gravitational field intensity = 9.80 N/kg

Mass of sun:  m_E = 1.98 x 10³⁰ kg
Radius sun:  r_E = 6.95 x 10⁸ m
Gravitational field intensity = 270.00 N/kg

Mass of the moon:  m_E = 7.34 x 10²² kg
Radius of the moon:  r_E = 1.74 x 10⁶ m
Gravitational field intensity = 1.62 N/kg

APPARENT WEIGHT AND ARTIFICIAL GRAVITY

You are inside an elevator.
m:  Your mass
F_G:  Your weight = 70 kg
t: the tension in the line that pulls the elevator.
Up direction: Positive
Down:  Negative

1 - If the elevator does not move or move with a constant speed in any direction:
F_G = m.g = 70 x (- 9,80) = - 686 N = 686 N [down]
Tension in the line: t = -F_G = 686 [up]

2- If the elevator accelerate upward, example:  a = 5 m/s² [up]
w = m.(g - a) = 70 [(- 9.80) - (5)] = -1036 N = 1036 N [down]
t = 1036 N [up]

3-  If the elevator accelerates downward, example:  a = 5 m/s² [down]
w = m.(g - a) = 70 [(- 9.80) - (-5)] = -336 N = 336 N [down]
t = 336 N [up]

4 - If the line of the elevator is broken, it means in a free fall (a = g = - 9.80 m/s²), you will be weightless.
w = m.(g - a) = 70 [(- 9.80) - (-9,8)] = 0
t = 0