gravitational and tidal force

The effect of the gravitational force is two fold. In the first case Ftot causes the two masses to accelerate towards each other. The second effect of the gravitational force is a stretching of the bodies because not all parts of the man, in this case, are equally distant from m2, and each part is attracted to m2 with a force that depends on the distance from m2 of that part. This second, stretching force is called the tidal force. On earth it gives rise to the familiar ocean tides. The ocean tides are caused by tidal forces due to the moon and sun. The tidal force depends more strongly on distance than the total force. For the case where the distances are nearly equal, that is to say

This means that a small mass m2 could still have a large tidal effect even if its total force is small, provided its distance is small.

Although the total force basically determines the size of orbits, the tidal forces can also have an important effect in the long term because of the physical principle of the "conservation of angular momentum". This principle states that quantity of rotational momentum in a system of particles is constant in time if the system is not disturbed by outside forces ( actually torques).
This principle is what enables us to ride a two wheel bicycle. You can also see this effect in an ice skater's speed of rotation as she draws her arms closer to her body. Her speed of rotation may change, but the total angular momentum remains the same.

For our earth-moon system tidal forces have caused long term pronounced features in our joint motion.

i) The ocean tides, through friction, cause the earth's spin to slow down so that by the end of a year the length of the day has increased by 4.4x10^-8 seconds, or 1.6ms/century. At the same time the moon's distance from the earth changes so as to keep the total angular momentum constant.

ii) Tidal forces of the earth on the moon have caused the moon's rate of rotation on its axis to become equal to its rate of orbital rotation, thus the moon always keeps the same face towards us.

iii) In the early days of the earth-moon system it is believed that the moon was much closer to the earth than at present. The period of the moon's orbital motion was closer to 7days, instead of the present day value of 27.5 days. The solar day was 6 hrs. This would produce tremendous ocean tides.

There are many other effects of tidal forces evident in the solar system. For example, the period of mercury's axial rotation is closely related to its orbital motion( in the ratio of 2/3). The tidal effects of Jupiter, say, on its moons causes enough internal generation of heat ( due to deformations) in the moons' interior to make some of the moons volcanically active (Io).

Exercise
Some Solar system statistics and effects on our 100kg man. Assume Rl-Ru=1m.
G = 6.67x10^-11Nm²/kg²
Ftot = Gm₁m₂/R², Ftidal = Ftot*(Rl-Ru)/R

planet m(kg)x10²⁴ distancex10⁹m from sun for planets Ftot (N) for closest approach Ftidal (N) for closest approach

mercury 0.323 57.9

venus 4.87 108

earth 5.98 150, radius of the earth=6.38x10⁶m

mars 0.645 228

Jupiter 1900. 778

saturn 569. 1426

uranus 86.7 2868

neptune 103. 4494

pluto 0.36? 5900

sun 1.989x10³⁰

moon 0.0735 0.384 from earth

man 100kg 1

How to use powers of ten

Calculate the maximum total force and the tidal force on our 100 kg man, who is standing on the surface of the earth, due to
1) the earth
2) the sun
3) the moon
4) jupiter
5) another 100 kg man standing 1m away.
Physical examples of these forces

Based on your results how signifcant, physically, is the position of the planets on our 100kg man ?

planet	m(kg)x10²⁴	distancex10⁹m from sun for planets	Ftot (N) for closest approach	Ftidal (N) for closest approach
mercury	0.323	57.9
venus	4.87	108
earth	5.98	150, radius of the earth=6.38x10⁶m
mars	0.645	228
Jupiter	1900.	778
saturn	569.	1426
uranus	86.7	2868
neptune	103.	4494
pluto	0.36?	5900
sun	1.989x10³⁰
moon	0.0735	0.384 from earth
man	100kg	1