# Math Help - Average orbital velocity of planets

1. ## Average orbital velocity of planets

Hi,

I'm having a bit of trouble with this problem.

The distance D is the distance in millions of miles from the sun, and P is the period in years it takes to revolve one time around the sun.

Earth:
D = 92.9
P = 1.0

I know that the formula for angular velocity is: omega = theta/t, with t being the time
and also that the linear speed is: v = radius*omega
also that 1 revolution is 360 degrees or 2pi

I think the problem I'm having though is with unit conversion. There are problems for other planets too, but if I can get help with just one, I can figure the rest of them out.

2. Hello, qleeq!

The distance $D$ is the distance in millions of miles from the sun,
and $P$ is the period in years it takes to revolve once around the sun.

Earth: . $D = 92.9,\;P = 1.0$

Find the average orbital velocity of Earth.

Assuming that Earth's orbit is a circle, its radius is 92,900,000 miles.

The length of this orbit is: . $2\pi(92,\!900,\!000) \:=\:583,\!707,\!915$ miles.

The Earth travels that far in one year (365 days = 8760 hours).

Therefore, its average velocity is: . $\dfrac{583,\!707,\!915}{8,\!760} \;\approx \;66,\!633$ mph.

3. Originally Posted by Soroban
Hello, qleeq!

Assuming that Earth's orbit is a circle, its radius is 92,900,000 miles.

The length of this orbit is: . $2\pi(92,\!900,\!000) \:=\:583,\!707,\!915$ miles.

The Earth travels that far in one year (365 days = 8760 hours).

Therefore, its average velocity is: . $\dfrac{583,\!707,\!915}{8,\!760} \;\approx \;66,\!633$ mph.
Ah! I knew it. Thanks a lot. I looked in the solution manual, and it ran me through the unit conversion steps which made it a little more confusing than helpful.