if mars orbits the sun at an angular velocity of 1.06x10-7 rad/s, how long is a year on mars in earth days assuming it travels in a circular orbit?pls explain

How long to do 2 pi radians ? (a full circle)

1.06*10^-7 t = 2 pi

t = 5.93 * 10^7 seconds

how many seconds/day
1 day = 24*3600 s
= 86400 s = 8.64*10^4 s
5.93 *10^7 / 8.64*10^4

= 6.86 * 10^2 days

= 686 days

To find out how long is a year on Mars in Earth days, we need to understand the relationship between angular velocity and the duration of a year.

The angular velocity of a celestial body is the rate at which it rotates or orbits around a central point, in this case, the Sun. The formula to calculate the duration of a year is:

Year = (2 * π) / ω

Where:
Year is the duration of a year in Earth days
π (pi) is a mathematical constant approximately equal to 3.14159
ω (omega) is the angular velocity of Mars, given as 1.06 x 10^(-7) rad/s

Now, let's substitute the values into the formula:

Year = (2 * π) / (1.06 x 10^(-7))
= 2π / 1.06 x 10^(-7)
≈ 6.28 / (1.06 x 10^(-7))
≈ 5.92 x 10^6

Therefore, a year on Mars, assuming it travels in a circular orbit, is approximately 5.92 x 10^6 Earth days.