Suppose a new planet X is discovered in our solar system at a distance of 4 AU (astronomical units) from the S

Question

Which one is the correct answer?

Suppose a new planet X is discovered in our solar system at a distance of 4 AU (astronomical units) from the Sun. How long does it take planet X to go around the Sun (period)?


1-16 years


2-4 years


3-8 years


4-2 years


5-2.5 years

Answer 1

http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

the answer is eight years.

Answer 2

well.. one astronomical unit is the average distance between the earth and the sun.

We have a planet in our solar system that is roughly two AUs from the Sun, Mars, which takes roughly two years to orbit the sun, so option 4 is out.

We have a bunch of debris in orbit around the sun at roughly four AUs, called the asteroid belt, so, all we really have to do is find out how long their orbits are.

We also hava a planet, Jupiter, which is 5.2 AU out, whose orbit is about 12 years, so, sixteen is out.

So, I would go with option number 3, which is 8 years.

Answer 3

You use Kepler's Third Law, which says the square of the period is proportional to the cube of the orbital radius. So a year on Planet X is sqrt(4^3) = 8 years.

Draco's math is correct, except 4 times the radius implies 4x the circumference, not 8 as he stated.

Answer 4

3 - 8 years.

Answer 5

1-16

Answer 6

4 AU so it has 4 times the radius.
Circular acceleration (it's actually inwards but...) is v²/r
Acceleration from the sun is GM/r². 4* earth's orbit radius so acceleration is 1/16*Earth's.
Thus "v²/r" is 1/16 Earth's = v²/4r so v² is 1/4 of the period.
Therefore v(X) = 1/2 v(earth)
4r => 8*circumference => 16 * period so period is 16 Earth years

Answer 7

Mars is at 1.5 a.u. and orbits in 1.88 years

Jupiter is at 5.2 a.u. and orbits in 11 earth years so your answer should be 8 years.

http://en.wikipedia.org/wiki/Planet