Planetary Motion Calculator

Kepler's rules of planetary motion are a set of three scientific laws that describe how planets orbit the sun.

• The law of orbits is Kepler's first law.
• The law of equal areas is Kepler's second law
• The law of periods is Kepler's third law.

The first law of Kepler states that each planet orbits the Sun in an ellipse, with the Sun at one of the ellipse's points.

The straight line connecting a planet and the Sun sweeps out equal areas in space in equal intervals of time, according to Kepler's second law.

The square of a planet's orbital period is directly proportional to the cube of its semimajor axis, according to Kepler's third law.

Within the Copernican paradigm, Kepler's three laws provide a precise geometric description of planetary motion. It was feasible to calculate planetary positions with a lot more precision using these methods. Still, Kepler's laws are just descriptive: they don't explain why the planets are forced to follow this path by natural causes.

The cube of the semi-major axis of a planet's orbit is directly proportional to the square of its orbital period.That is what Kepler's third law is all about. Isn't it simple? This statement expresses the link between each planet's distance from the Sun and its orbital period in the Solar System (also known as the sidereal period)

Because physics laws are universal, the previous statement should be true for every planetary system.

The third law of Kepler's equation: We can easily verify Kepler's third law of planetary motion Using Newton's Law of Gravitation. All we have to do now is equalise two forces: centripetal force and gravitational force. We get the following results: m * r * ω²= G * m * M / r²

• m is the mass of the orbiting planet
• r is the orbital radius
• ω is the angular velocity
• ω=v/r for circular motion (v - linear velocity)
• G is the gravitational constant, G = 6.67408 * 10^-11

When we replace with 2 * π/ T (T - orbital period) and rearrange, we get:

R³ / T² = 4 * π² /(G * M) = Constant

We will simply show the final version of this generalised Kepler's third law equation here because the derivation is more complicated:

a³ / T² = 4 * π² /[G * (M + m)] = Constant

As you can see, the more precise version of Kepler's third law of planetary motion also requires mass of the orbiting planet m.

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1. What are the three planetary motion laws?

There are three rules of planetary motion, according to Kepler:

1. Every planet's orbit is an ellipse with the Sun at its centre.
2. A line connecting the Sun and a planet sweeps out equal areas in equal time
3. The square of a planet's orbital period is proportional to the cube of its semi-major axis.

2. Why was it so difficult to describe planetary motion?

Over the course of a year, planets appear to move eastward relative to the stars, but during periods of apparent retrograde motion, they appear to reverse course for weeks or months.

3. What causes the planets to move?

The planets move in roughly circular orbits around the sun due to the force of gravity. They've been circling the sun for billions of years because other factors were too feeble to significantly alter their orbits.

4. What method do you use to calculate the coefficient of friction?

The coefficient of friction can be calculated in two ways: by measuring the angle of movement or by using a force gauge. The friction coefficient is equal to tan(θ). Where, θ is the angle from the horizontal at which an object placed on top of another begins to move.