Newton's Second Law of Gravitation Escape Velocity Keplar's Law of Planetary Motion

Thus, the law states that every particle in the universe exerts a force on every other particle along the line joining their centers. The magnitude of the force is directly proportional to the product of the masses of the two particles, and inversely proportional to the square of the distances between them.

In the figure, the gravitational force and the external force are equal in magnitude and opposite in direction.

m1 exerts a force on m2 .

m2 exerts a force on m1 .

By Newton's third law:

F12 = -F21

The magnitude of the gravitational force is: F12 = G(m1*m2/r2).

G is Newton's constant:

"Change of motion is proportional to the force applied, and take place along the straight line the force acts."

** Newton's Second Law** for the gravity force weight can be expressed as

** F = m g
**
where F = force (weight), m = mass and g = acceleration of gravity.

The force caused by gravity g is called weight.

Note: Mass m is a property.

The acceleration of gravity can be observed by measuring the change of velocity of a free falling object:

where dv = change in velocity and dt = change in time.

A dropped object accelerate to a speed of 9.81 m/s or 32.174 ft/s in one second.

Acceleration of Gravity in SI Units
g = 9.81 m/s2.

Acceleration of Gravity in Imperial Units
g = 32.174 ft/s2.

**
Velocity and Distance travelled of a Free Falling Object**

The velocity of a free falling object can be expressed as: v = g t

where v = velocity

The distance traveled by a free falling object can be expressed as: s = 1/2 g t2

where s = distance traveled by the object

If an object moves fast enough it can escape a massive object's gravity and not be drawn back toward the massive object.
The critical speed needed to do this is the** Escape Velocity**. More specifically, this is the initial speed something needs
to escape the object's gravity and assumes that there is no other force acting on the object besides gravity after the initial boost.
Rockets leaving the Earth do not have the escape velocity at the beginning but the engines provide thrust for an extended period of time,
so the rockets can eventually escape. The concept of escape velocity applies to anything gravitationally attracted to anything else
(gas particles in planet atmospheres, comets orbiting the Sun, light trying to escape from black holes, galaxies orbiting each other, etc.).

Using Newton's laws of motion and law of gravity, you can find that the escape velocity vesc looks very similar to the orbital speed:

**vesc = Sqrt[(2 G M)/r]** .

This is a factor Sqrt[2] larger than the circular orbital speed. Since the mass M is on top of the fraction, the escape velocity increases as the mass increases. More massive bodies exert greater gravity force, so escaping objects have to move faster to overcome the greater gravity. Also, the distance from the center of the object r is in the bottom of the fraction, so the escape velocity DEcreases as the distance increases. Gravity decreases with greater distance, so objects farther from a massive body do not need to move as quickly to escape it than those closer to it.

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Formulae:

Orbital speed = Sqrt[G × Mass / distance].

**Escape velocity = Sqrt[2G × Mass / distance].**
Top

This is a factor Sqrt[2] larger than the circular orbital speed. Since the mass M is on top of the fraction, the escape velocity increases as the mass increases. More massive bodies exert greater gravity force, so escaping objects have to move faster to overcome the greater gravity. Also, the distance from the center of the object r is in the bottom of the fraction, so the escape velocity DEcreases as the distance increases. Gravity decreases with greater distance, so objects farther from a massive body do not need to move as quickly to escape it than those closer to it.

Orbital speed = Sqrt[G × Mass / distance].

Kepler's three laws of planetary motion can be described as follows: