Question

How would you calculate the distance to Mars in astronomical units, given an orbital period of 1.88 years? (concerned with method)

Answer 1

To calculate the average distance from the Sun to Mars in astronomical units (AU), square the orbital period (1.88 years) to get P², which equals 3.53, then find the cube root of this number, which is 1.52. Therefore, Mars' average distance from the Sun is 1.52 AU.

Step-by-step explanation:

To calculate the distance to Mars or any celestial object in astronomical units (AU) given its orbital period, you would use Kepler's third law, which relates the square of the orbital period (P) to the cube of the semimajor axis (a) of the object's orbit. Given that Mars has an orbital period of 1.88 Earth years, you would perform the following calculation:

1. First, square the orbital period: P² = 1.88² = 3.53.
2. Next, determine the semimajor axis by solving for the cubed root of 3.53, since P² = a³. In this case, a³ = 3.53, so a is approximately 1.52 (since 1.52× 1.52 × 1.52 = 3.53).
3. Therefore, the average distance from the Sun to Mars in astronomical units is 1.52 AU.

One astronomical unit (1 AU) is defined as the average distance between the Earth and the Sun, which is approximately 150 million kilometers (93 million miles). Thus, the average distance of Mars from the Sun is 1.52 times this distance.