Question

Johannes Kepler analyzed a large collection of data about the motion of objects in the Solar System. He discovered that objects orbiting the Sun follow a number of laws. One of these laws is that the size of an object's orbit times the square of its velocity is equal to a constant. If r is the size of the orbit (how far the object is from the Sun) and v is the velocity, then

Earth's average orbital velocity is about 6.7 times faster than that of the planetoid Makemake. Rounded to the nearest whole number, Makemake's orbit is about times larger than Earth's orbit.

Answer 1

Its 45

Step-by-step explanation:

STUDY ISLAND

Answer 2

45

Step-by-step explanation:

Let us rewrite this equation. Let r1 be size of Earth's orbit and v1 its velocity and r2 size of Makemake's orbit and v2 its velocity. Then we have:

r2/r1 = (v1/v2)^2

We know that the Earth's velocity is 6.7 times faster then Makemake's. That means:

v1 = 6.7•v2

Now we can write:

r2/r1 = (6.7v2/v2)^2

That means that:

r2/r1 = 6.7^2

So:

r2/r1 = 44.89

That means that r2 is 44.89 times bigger then r1 and if we round this to the nearest whole number we see that the size of Makemake's orbit is 45 times bigger then the size of the Earth's orbit.