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When I was in school learning to derive that fact, it took vector calculus

and some pretty serious geometry to do it.

The answer can't be presented here, for 3 main reasons that I know of:

1). Vector calculus is somewhat beyond the scope of this website.

2). I don't remember how to do it.

3). I don't have any other simpler way to explain it.

More information: Newton's Law of Gravitation is part of it and some calculus is needed, but the most important thing is the fact that "angular momentum" must be conserved. I would say that it is the "law of conservation of angular momentum" that explains this phenomenon (which is "Kepler's second law of planetary motion").

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Q: How does Newtons law of gravitation explain why a planet would sweep out equal amounts of area in equal amounts of time?
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Related questions

What would the mass of an astronaut with the weight of 80 kg be on a planet?

That depends on the planet. Gravitation on different planets varies. On planet Earth, you multiply by 9.8; the result is in Newtons.


Was there any observations of the planet mercury which could not be explained by newtons theory of gravity?

yes there were observations of the planet mercury but were hard to explain by Issac newtons theory of gravity as scienctists didn't have enough information to investigate more on the subject.


What is the planet with the most gravitation?

Jupiter


Withch planet has the most gravitation?

Jupiter


Why does adding a second planet affect the orbit of the first planet?

The law of universal gravitation


How much newtons are in 2 meters?

newtons are how high the gravity of a planet is which relates to measurement of of an object's weight not distance


How many newtons are in 1 kg at planet Venus?

1 kg of mass weighs 9.81 newtons on Earth and 3.7 newtons on Mercury.


On what planet would 1 kg weigh 26 newtons?

uranus


If the planet has less gravitation pull does that effect the speed it orbits around the Sun?

No. A planet's gravitational pull is determined by the planet's mass. A planet's orbital speed is determined by the the mass of the Sun and the planet's distance from the Sun.


Does a planet need to rotate to be considered a planet?

A planet is a celestial body that does not emit substantial amounts of radiation and that circulates around a star (which DOES emit substantial amounts of radiation)


How many newtons for 200 kilogram?

it really depends what planet your on. Fw=Mg Fw=Newtons M=kg g=gravitational force of the planet your on 2000kg in Newtons on earth is: Fw=2000*9.8 Fw=19600N


Could a planet fall out of its orbit?

Not without outside interference. A planet in orbit is effectively already "falling" ... that is, it is behaving in a manner consistent with the law of universal gravitation.