# Relationship between the distance from sun and orbital period

### Kepler's 3rd Law: Orbital Period vs. Distance | Science project | senshido.info

There are 8 planets (and one dwarf planet) in orbit around the sun, hurtling around at tens of thousands or even hundreds of thousands of miles an hour. Kepler's third law - shows the relationship between the period of an objects orbit and the average distance that it is from the thing it orbits. This can be used (in its . Infernoraptor's interactive graph and data of "Relationship Between Distance from the Sun and Period of Revolution" is a scatter chart, showing Col2; with.

If an object has an orbital period of 85 years and is at an average distance of 24 AU from the object it orbits, what is the value of "k"?

### Is it true that the further a planet is from the Sun, the faster it rotates around itself?

If an object is orbiting the Sun with an orbital period of 15 years, what is its average distance from the Sun? If an object is orbiting the Sun at an average distance of 71 AU, what is its orbital period? Since this is a physics class I am not going to have you use actual values in this law, but just relational values, so that you can determine how the parts of the formula change one one or more parts are changed. It is the measure of how much material is in an object.

And acceleration doesn't just mean "go faster", but denotes an change in motion, including deceleration and change in direction. So if you want to change the way something is moving, you have to exert a force on it. You have two cars stuck in the snow. One car the blue one has a mass that is 3 times greater than the other the red one.

You push them both with the same force, since you have only so much strength. How do their accelerations compare? Think of it like a balancing act - but in this case the value of "ma" has to balance for both cars. So you have ma for the red car and ma for the blue car.

And they have to be equal one another since you are exerting the same force on both of them. Two asteroids with the same mass are moving through space. Asteroid Beatles is accelerating 6 times more than asteroid Stones. Both will hit the Moon.

Which will have a greater force of impact and how much greater will it be? It is 6 times greater for the Beatles, so the force that exerted by it is 6 times greater than the force exerted by asteroid Stones. That's all there is to it.

## Is it true that the further a planet is from the Sun, the faster it rotates around itself?

This one you really have to know and know how it is changed by different circumstances. And like the previous law, we won't be plugging in actual values in general, only when it is vital to a problem, which isn't very often.

If the planet changes its distance from the Sun as it orbits, then the force of gravity between them must change. If the force that the Sun exerts on the planet increases as the planet moves closerthen the acceleration of the planet must increase, resulting in a higher orbital speed, and vice versa. You don't need a single equation! For any force on any mass: The force of gravity between 2 bodies and Newton's 2nd Law of Motion: That is, the acceleration of a planet in its orbit around the Sun depends upon the mass of the Sun and the inverse square of the planet's distance from the Sun.

As the planet moves further away in its orbit around the Sun, the gravitational force exerted by the Sun on the planet decreases.

We won't worry about how orbital acceleration is converted into orbital speed in this class. Just think of accelerating a bowling ball down the bowling alley - a ball undergoing a greater acceleration from rest in your hands attains a higher speed moving down the lane.

That's all you need to understand, and you already knew that. The two very important conservation laws in nature: In the first case, as the planet's distance from the Sun here called 'r' decreases, it's orbital speed must increase in order that its orbital angular momentum r x m x v remains constant.

Just the opposite occurs as the planet's distance increases from the Sun. In the second case, as the planet's distance from the Sun decreases, so does its gravitational potential energy.

- As distance to the sun decreases, what happens to the orbital velocity?
- Kepler's 3rd Law: Orbital Period vs. Distance

And of course, just the opposite applies as the planet's distance increases from the Sun - its potential energy increases, thus its kinetic energy and so orbital speed must decrease. After deriving gravitational orbital motion from the laws of motion, law of gravity and quite a bit of calculus, Newton found that Kepler's 3rd Law should actually be this: How can we understand this relation between the period of the orbit, mean distance, and sum of masses?

Just as we did above. Recalling the underlined statement above, the acceleration of a more distant planet due to the force of gravity between it and the Sun must be smaller than the acceleration of a planet near to the Sun. Slower orbital speed and a larger orbit mean that its orbital period must be longer!

The force of gravity between the Sun and a planet can be larger than that between the Sun and Earth, yet that planet's acceleration can be either larger if closer to the Sun or smaller if further from the Sun than Earth's accleration in its orbit around the Sun. This is because the force depends upon the product of both masses and the square of the distance between them, whereas the planet's acceleration depends on just the mass of the Sun and the square of the distance between the Sun and planet.

For example, the force between Jupiter and the Sun is Review the discussion of Kepler's 2nd Law, above.

Back to the 3rd law. Note that the relationship between the orbital period and the average separation between the masses actually depends upon the sum of the two masses orbiting the common center of mass. That this relationship should involve mass should make some sense given what you know about the relationship between force, mass, and acceleration, and that the force of gravity itself depends upon masses of the bodies involved.

Surely, you can imagine that if the star that Earth orbited were more massive than our Sun, Earth's acceleration would be greater, it's orbital speed faster, and so its orbital period shorter. Thus Kepler had it nearly right in his description of the orbits of the objects around our Sun. On the other hand, this mass correction term is important, i.