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1-What are the Kepler's Laws of planetary motion?
2-What is Surface tension?


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Answer 1

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1 -

Kepler’s Law states that the planets move around the sun in elliptical orbits with the sun at one focus. There are three different Kepler’s Laws. Law of Orbits, Areas, and Periods. Let us know about them one by one.

kepler's laws of planetary motion

Kepler’s Three Law:

Kepler’s Law of Orbits – The Planets move around the sun in elliptical orbits with the sun at one of the focii.

Kepler’s Law of Areas – The line joining a planet to the Sun sweeps out equal areas in equal interval of time.

Kepler’s Law of Periods – The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit.

Kepler’s 1st Law of Orbits:

This law is popularly known as the law of orbits. The orbit of any planet is an ellipse around the Sun with Sun at one of the two foci of an ellipse. We know that planets revolve around the Sun in a circular orbit. But according to Kepler, he said that it is true that planets revolve around the Sun, but not in a circular orbit but it revolves around an ellipse. In an ellipse, we have two focus. Sun is located at one of the foci of the ellipse.

Kepler’s 2nd Law of Areas:

This law is known as the law of areas. The line joining a planet to the Sun sweeps out equal areas in equal interval of time. The rate of change of area with time will be constant. We can see in the above figure, the Sun is located at the focus and the planets revolve around the Sun.

Assume that the planet starts revolving from point P1 and travels to P2 in a clockwise direction. So it revolves from point P1 to P2, as it moves the area swept from P1 to P2 is Δt. Now the planet moves future from P3 to P4 and the area covered is Δt.

As the area traveled by the planet from P1 to P2 and P3 to P4 is equal, therefore this law is known as the Law of Area. That is the aerial velocity of the planets remains constant. When a planet is nearer to the Sun it moves fastest as compared to the planet far away from the Sun.

Kepler’s 3rd Law of Periods:

This law is known as the law of Periods. The square of the time period of the planet is directly proportional to the cube of the semimajor axis of its orbit.

T² ∝ a³

That means the time ‘ T ‘ is directly proportional to the cube of the semi major axis i.e. ‘a’. Let us derive the equation of Kepler’s 3rd law. Let us suppose,

m = mass of the planet

M = mass of the Sun

v = velocity in the orbit

So, there has to be a force of gravitation between the Sun and the planet.

F = GmMr²

Since it is moving in an elliptical orbit, there has to be a centripetal force.

Fc = mv²r²

Now, F = Fc

⇒ GMr = v²

Also, v = circumferencetime = 2πrt

Combining the above equations, we get

⇒ GMr = 4π²r²T²

T² = 4π2r3)GM

⇒ T² ∝ r³

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2-

What is Surface tension ________

The attractive force exerted upon the surface molecules of a liquid by the molecules beneath that tends to draw the surface molecules into the bulk of the liquid and makes the liquid assume the shape having the least surface area.

Examples of surface tension in a Sentence

Recent Examples on the Web

The imbalance between the surface tension of the wine in the glass and the water-rich liquid on the walls of the glass pulls even more wine up the glass.

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Answer 2

Explanation:

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