Orbital speed is calculated by Circumference / Period (the unit is AU/year). Circumference is 2πr. If the orbital radius of Mars is 1.52, and its period is 1.88 earth years, calculate the orbital speed of Mars in AU/year
To calculate the orbital speed of Mars in AU/year, we need to find the circumference first and then divide it by the period.
1. Determine the circumference of Mars' orbit:
- The formula for the circumference of a circle is C = 2πr, where r is the radius.
- Given that the orbital radius of Mars is 1.52 AU, substitute this value into the formula:
C = 2π(1.52) AU
2. Calculate the value of C using the given radius:
- Multiply 2π by 1.52:
C ≈ 2(3.14)(1.52) AU
3. Simplify the equation and compute the result:
- Multiply 2 and 3.14: 6.28
C ≈ 6.28(1.52) AU
C ≈ 9.5416 AU
Now that we have found the circumference of Mars' orbit, we can calculate its orbital speed.
4. Divide the circumference by the orbital period:
- Given that the period of Mars is 1.88 Earth years, substitute this into the calculation:
Orbital speed = Circumference / Period
Orbital speed = 9.5416 AU / 1.88 years
5. Perform the division to find the orbital speed:
- Divide 9.5416 by 1.88:
Orbital speed ≈ 5.07 AU/year
Thus, the orbital speed of Mars is approximately 5.07 AU/year.