Isaac Newton The Universal Law of Gravitation

Newton published his famous law of universal gravitation in his Principia Mathematica in 1687 as follows:

F = G x m1 x m2

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2

r

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2

r

where F is the force of gravity, G is the gravitational constant m1 and m2 are the two masses and r is their distance apart.

In this demonstration we have set the Sun's mass to 400 and the Moon's mass at 100

r is point_distance(x,y,object1.x,object1.y)

The direction of the gravity is point_direction(x,y,object1.x,object1.y)

r is point_distance(x,y,object1.x,object1.y)

The direction of the gravity is point_direction(x,y,object1.x,object1.y)

So the force of the Sun's gravity is programmed as mass divided by r squared or:

400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y)) in direction point_direction(x,y,object1.x,object1.y)

400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y)) in direction point_direction(x,y,object1.x,object1.y)

The gravity is broken down into the horizontal components and the Sun's and Moon's components added

COMMENT: Sun's gravity

set variable hspeed relative to cos(pi*point_direction(x,y,object1.x,object1.y)/180)*400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y))

set variable vspeed relative to -sin(pi*point_direction(x,y,object1.x,object1.y)/180)*400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y))

set variable hspeed relative to cos(pi*point_direction(x,y,object1.x,object1.y)/180)*400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y))

set variable vspeed relative to -sin(pi*point_direction(x,y,object1.x,object1.y)/180)*400/(point_distance(x,y,object1.x,object1.y)*point_distance(x,y,object1.x,object1.y))

COMMENT: Moon's gravity

set variable vspeed relative to -sin(pi*point_direction(x,y,object2.x,object2.y)/180)*100/(point_distance(x,y,object2.x,object2.y)*point_distance(x,y,object2.x,object2.y))

set variable hspeed relative to cos(pi*point_direction(x,y,object2.x,object2.y)/180)*100/(point_distance(x,y,object2.x,object2.y)*point_distance(x,y,object2.x,object2.y))

set variable vspeed relative to -sin(pi*point_direction(x,y,object2.x,object2.y)/180)*100/(point_distance(x,y,object2.x,object2.y)*point_distance(x,y,object2.x,object2.y))

set variable hspeed relative to cos(pi*point_direction(x,y,object2.x,object2.y)/180)*100/(point_distance(x,y,object2.x,object2.y)*point_distance(x,y,object2.x,object2.y))

For the moon missions, an initial acceleration was required to leave the earth and then a deceleration to drop into lunar orbit. Later, an acceleration is required to leave moon orbit and a deceleration is required for lower earth orbit.

In this demonstration, an initial speed of 5 is used to escape the Earth's gravity and a further deceleration to speed 1after 40 steps is required to drop into lunar orbit.

Each change of speed uses fuel, energy=1/2mv² so the fuel use is proportional to the square of the speed. What is the minimum amount of fuel which can be used for a complete mission? Why?

In later probes of the outer planets, the gravity of the planets and moons was used to direct the probe to many destinations. Can you re-create this.

How long is a Mars year? How long is a month? Why? Can you re-create this?

Press escape to see the demonstration

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