Suppose that scientists discover an asteroid that is 2.0 AU from the sun. If 1 AU - 150 million km, how long would the asteroid's orbital period be in Earth years?
Social Studies · Middle School · Tue Nov 03 2020
Answered on
The orbital period (P) of an object in space is related to its semi-major axis (a) by Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis. The formula is given by:
P2=a3
P2
=a3
In this formula:
- P
- P is the orbital period in years.
- a
- a is the semi-major axis in astronomical units (AU).
Given that the asteroid is 2.0 AU from the sun, we can substitute this value into the formula:
P2=(2.0 AU)3
P2
=(2.0AU)3
P2=8.0 AU3
P2
=8.0AU3
Now, to find P
P, take the square root of both sides:
P=8.0 AU3
P=8.0AU3
P≈2.83 AU3/2
P≈2.83AU3/2
So, the orbital period (P)
P) is approximately 2.83 Earth years.