How Fast Does Mars Travel Around the Sun?

[lanvin]

Mars travels around the sun in 1.88 {Earth} yrs,in an approximately circular orbit with a radius of 2.28 * 10^8km.Determine
{a}The orbital speed of Mars {relative to the sun}Answer {a}:
period {T} = 1.88 * 365 *24 * 3600 sec , R = 2.28 * 10^8 * 10^2 = 2.28 * 10^11
d = 2 pie R ------> 2 * 3.14 * 2.28 * 10^11
V=d / T -------> { 2 * 3.14 * 2.28 * 10^11 } / { 1.88 * 365 *24 * 3600 }
=2.4 * 10^4m/sIs that correct?or do I use

acceleration of centripetal motion = (4)(pi^2)(r)(f^2)

then use the acceleration and find velocity in

V = √(acceleration x radius)

which method is correct? if any...

 

[Chi Meson]

You did this correctly, though longishly.

And the second way is the same thing just with with extra steps. Notice that your initial solution was to find v=d/t, where d is the circumference, 2 pi r , and t is the period, T.

so v=(2 pi r)/T (all done right there)

and since f= 1/T , v=2 pi r f

Your second solution takes the square of this, divides by radius, then multiplies by radius, then square roots it.

 

[thomate1]

Both methods are correct, but they may give slightly different results due to rounding errors. The first method uses the formula V=d/T, which calculates the average orbital speed over the entire orbit. The second method uses the formula V=√(a*r), which calculates the instantaneous orbital speed at a specific point in the orbit. It is up to you to decide which method is more appropriate for your question.