Keplers second law

so, if it takes 1 year to traverse a narrow "wedge" that is 1 million miles
for the sun,
it will take 1 year the traverse a wide wedge that is 1/2 million miles from
the sun.
The "wedges" containing the same area.
This is because the gravity is more intense the closer you gat to the sun?

Thanks,
jojo



"G.P" wrote in message
.rogers.com...

"G.P" wrote in message
.rogers.com...

"jojo" wrote in message
. ..
http://home.cvc.org/science/kepler.htm

keplers second law

ok, I don't get it.

can anyone explain this second law in a "dumbed down" way that I might
better understand?

See those orange "wedges", all of them enclose equal areas, the law
states
that it takes a planet equal amount of time to sweep across the width of
equal area "wedges". That is why in the animation you see that the
closer
a
planet is from the sun the faster it goes (wedges there are shorter that
at
the opposite end of the orbit).

I should have also mentioned that the equal area wedges closer to the sun,
since they are shorter they necessarily have to be wider in order to
enclose
equal area of wedges at the opposite end of the orbit. Therefore, a
planet
has to sweep a wider wedge width in the same amount of time, consequently
the planet has to travel faster.

Guillermo

"jojo" wrote in message
. ..
so, if it takes 1 year to traverse a narrow "wedge" that is 1 million
miles
for the sun,
it will take 1 year the traverse a wide wedge that is 1/2 million miles
from
the sun.
The "wedges" containing the same area.
This is because the gravity is more intense the closer you gat to the
sun?t

Right, I am also a newbie on this, but I can tell you there are several ways
to look at it:

- As per Newton, the gravitational force between 2 objets having masses M
and m, separated a distance R, is proportional to the product of their
masses and inversaly proportional to the square of the distance R:

F = G(Mm/R^2) whre G is the universal constant of gravitation

The closer the 2 orbiting "thing" is from the sun the smaller R is and the
grater the gravitational force between them. This causes the "thing" to
accelerate toward the sun, therefore increasing its speed.

- You can see it from the point of view of Conservation of Angular Momentum.
A "thing" orbiting the sun has an angular momentum equal to its Mass times
its Velocity times the distance from it to the sun (R):

Angular Momentum = M x V x R

The mass doesn't change. In order for the angular momentum to stay constant
when R gets smaller ("thing" getting close to the sun), V has to increase.

- Lastly, there is probably an explanation based on the curvature of
SpaceTime, I'd love to "hear" such explanation it exist.

Guillermo

"jojo" wrote in message
. ..
so, if it takes 1 year to traverse a narrow "wedge" that is 1 million
miles
for the sun,
it will take 1 year the traverse a wide wedge that is 1/2 million miles
from
the sun.
The "wedges" containing the same area.
This is because the gravity is more intense the closer you gat to the
sun?t

Right, I am also a newbie on this, but I can tell you there are several ways
to look at it:

- As per Newton, the gravitational force between 2 objets having masses M
and m, separated a distance R, is proportional to the product of their
masses and inversaly proportional to the square of the distance R:

F = G(Mm/R^2) whre G is the universal constant of gravitation

The closer the 2 orbiting "thing" is from the sun the smaller R is and the
grater the gravitational force between them. This causes the "thing" to
accelerate toward the sun, therefore increasing its speed.

- You can see it from the point of view of Conservation of Angular Momentum.
A "thing" orbiting the sun has an angular momentum equal to its Mass times
its Velocity times the distance from it to the sun (R):

Angular Momentum = M x V x R

The mass doesn't change. In order for the angular momentum to stay constant
when R gets smaller ("thing" getting close to the sun), V has to increase.

- Lastly, there is probably an explanation based on the curvature of
SpaceTime, I'd love to "hear" such explanation it exist.

Guillermo

so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

Thanks,
jojo


"G.P" wrote in message
able.rogers.com...

"jojo" wrote in message
. ..
so, if it takes 1 year to traverse a narrow "wedge" that is 1 million
miles
for the sun,
it will take 1 year the traverse a wide wedge that is 1/2 million miles
from
the sun.
The "wedges" containing the same area.
This is because the gravity is more intense the closer you gat to the
sun?t

Right, I am also a newbie on this, but I can tell you there are several
ways
to look at it:

- As per Newton, the gravitational force between 2 objets having masses M
and m, separated a distance R, is proportional to the product of their
masses and inversaly proportional to the square of the distance R:

F = G(Mm/R^2) whre G is the universal constant of gravitation

The closer the 2 orbiting "thing" is from the sun the smaller R is and the
grater the gravitational force between them. This causes the "thing" to
accelerate toward the sun, therefore increasing its speed.

- You can see it from the point of view of Conservation of Angular
Momentum.
A "thing" orbiting the sun has an angular momentum equal to its Mass times
its Velocity times the distance from it to the sun (R):

Angular Momentum = M x V x R

The mass doesn't change. In order for the angular momentum to stay
constant
when R gets smaller ("thing" getting close to the sun), V has to increase.

- Lastly, there is probably an explanation based on the curvature of
SpaceTime, I'd love to "hear" such explanation it exist.

Guillermo

so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

Thanks,
jojo


"G.P" wrote in message
able.rogers.com...

"jojo" wrote in message
. ..
so, if it takes 1 year to traverse a narrow "wedge" that is 1 million
miles
for the sun,
it will take 1 year the traverse a wide wedge that is 1/2 million miles
from
the sun.
The "wedges" containing the same area.
This is because the gravity is more intense the closer you gat to the
sun?t

Right, I am also a newbie on this, but I can tell you there are several
ways
to look at it:

- As per Newton, the gravitational force between 2 objets having masses M
and m, separated a distance R, is proportional to the product of their
masses and inversaly proportional to the square of the distance R:

F = G(Mm/R^2) whre G is the universal constant of gravitation

The closer the 2 orbiting "thing" is from the sun the smaller R is and the
grater the gravitational force between them. This causes the "thing" to
accelerate toward the sun, therefore increasing its speed.

- You can see it from the point of view of Conservation of Angular
Momentum.
A "thing" orbiting the sun has an angular momentum equal to its Mass times
its Velocity times the distance from it to the sun (R):

Angular Momentum = M x V x R

The mass doesn't change. In order for the angular momentum to stay
constant
when R gets smaller ("thing" getting close to the sun), V has to increase.

- Lastly, there is probably an explanation based on the curvature of
SpaceTime, I'd love to "hear" such explanation it exist.

Guillermo

"jojo" wrote in message
. ..
so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay
close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

Thanks,
jojo

Don't top post.

Energy. Gravity is not an inflexible, inextensible
rope.

Consider a marble rolling down the inside of a bowl.
Why, when the marble gets to the bottom, doesn't it
just stop there?

"jojo" wrote in message
. ..
so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay
close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

Thanks,
jojo

Don't top post.

Energy. Gravity is not an inflexible, inextensible
rope.

Consider a marble rolling down the inside of a bowl.
Why, when the marble gets to the bottom, doesn't it
just stop there?

"jojo" wrote in message
. ..
so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay
close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

The answer is inertia/conservation of momentum (Newton's 1st law). Any
planet orbiting the sun is continuously falling toward the center of the
sun, but the angular momentum causes a motion that is perpendicular to the
fall, as a result it moves forward as it moves down, allowing the planet to
keep falling toward the sun but also continually missing it. If a planet
had a velocity smaller than:

V = SQRT((GM)/R) (a)

where G is the universal gravitational constant, M is the mass of the sun
and R is the radius of the orbit

That planet would in fact fall into the sun. If its velocity is exactly as
given by formula (a) its orbit would be circular, if its velocity is
greater than (a) but smaller than (a) times square root of 2, it would
have an elliptical orbit, if its velocity is (a) times square root of 2,
or greater, it would have a parabolic orbit (hyperbolic if the velocity is
way bigger than (a) times square root of 2), it'd go around the sun just
once to never return.

BTW, (a) times square root of 2 is known as the escape velocity

Corrections welcomed

Guillermo

"jojo" wrote in message
. ..
so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay
close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

The answer is inertia/conservation of momentum (Newton's 1st law). Any
planet orbiting the sun is continuously falling toward the center of the
sun, but the angular momentum causes a motion that is perpendicular to the
fall, as a result it moves forward as it moves down, allowing the planet to
keep falling toward the sun but also continually missing it. If a planet
had a velocity smaller than:

V = SQRT((GM)/R) (a)

where G is the universal gravitational constant, M is the mass of the sun
and R is the radius of the orbit

That planet would in fact fall into the sun. If its velocity is exactly as
given by formula (a) its orbit would be circular, if its velocity is
greater than (a) but smaller than (a) times square root of 2, it would
have an elliptical orbit, if its velocity is (a) times square root of 2,
or greater, it would have a parabolic orbit (hyperbolic if the velocity is
way bigger than (a) times square root of 2), it'd go around the sun just
once to never return.

BTW, (a) times square root of 2 is known as the escape velocity

Corrections welcomed

Guillermo

"jojo" wrote in message ...
so...why isn't the orbit circular instead of elliptic?
Once the planet is close pulled close tot he sun, why doesn't it stay close?
what force (or lack of force) allows it to move away for the sun in an
ellipse?

Momentum. When it's closest to the sun, it's moving too fast for a
circular orbit -- that extra velocity (beyond what's needed for a
circular orbit at that distance) throws it further out.