What is Earth's orbital velocity around the sun?

Question

Given the Earth's mass as 5.9742E24 kg and the Sun's mass as 1.98892E30 kg, and the Earth's distance to the sun as 1.5E11 m, what is the earth's orbital velocity around the sun in meters per second? How would you go about to solve this problem? I know this involves Newton's law of universal gravitation and the centripetal acceleration equation, but I'm stuck.

I'd appreciate any help! Thanks.

Answer 1

The circimference of circle is 2 Pi r.

Time is one year = 365.25 days = 8766 hours =525960 minutes=31557600 seconds.

The speed of earth is 2 Pi r / 31557600 m/s = 29786m/s

29.786 km/s.

Or

G =6.673x10^-11

Mass of sun M=1.99x 10^30kg

Mass of earth m= 5.977 x 10^24 kg.

Distance of earth from sun r = 1.496 x10^11 m.

Since v^2 = G M/r

using the above value v = 29.79 km/s.

Answer 2

not exactly clear what your asking but it looks like angular velocity. which is revolutions/time. if you know the mean distance to the sun (ie r) then the distance traveled in 1 revolution is 2 x pi x r and the time taken is 365 and 1/3 days. the rest of the math is yours.

a more accurate way is to assume the orbit is elliptical with the sun at one foci. you would need to know where in the orbit your distance measurement was made.

in either case, mass, Newton, and acceleration has little to do with it.

are you sure there isn't a bit more to this question?

Answer 3

The speed of the Earth in reality changes continuously as it travels in an ellipse around the sun.
The average velocity is easy to calculate.
The length of the orbit is close to the circumference of a circle which is Pi * R * 2.
Pi * 1.5E11 * 2 = 9.42E11
the number of seconds in a year is
60*60*24*365.25= 31557600
The average velocity is the distance traveled divided by the time taken to travel the distance
29865.32

Answer 4

actually newton isnt required, you can use keplers third law of planitery motion

The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits. divide by that by(365*24*60*60) and you have your answer in m/s

at least thats how i would do it. of course if your current section of study is newtons graitational laws then you probably should use that approach instead :/

Answer 5

its all relative:

The Galaxy Song



Prelude/Intro:

Whenever life gets you down, Mrs. Brown,
And things seem hard or tough,
And people are stupid, obnoxious or daft,
And you feel that you've had quite eno-o-o-o-o-ough...

Just remember that you're standing on a planet that's evolving
and revolving at 900 miles an hour,
It's orbiting at 19 miles a second, so it's reckoned,
the sun that is the source of all our power.
The Sun and you and me, and all the stars that we can see,
are moving at a million miles a day,
In the outer spiral arm, at 40,000 miles an hour,
of the Galaxy we call the Milky Way.

Our Galaxy itself contains 100 billion stars,
it's 100,000 light-years side-to-side,
It bulges in the middle, 16 000 light-years thick,
but out by us it's just 3 000 light-years wide.
We're 30,000 light-years from galactic central point,
we go round every 200 million years,
And our galaxy is only one of millions of billions
in this amazing and expanding universe.

The universe itself keeps on expanding and expanding,
in all of the directions it can whizz,
As fast as it can go, at the speed of light you know,
twelve million miles a minute, and that's the fastest speed there is.
So remember, when you're feeling very small and insecure,
how amazingly unlikely is your birth,
Pray that there's intelligent life somewhere up in space,
because there's bugger all down here on Earth.

Composers: Eric Idle & John Du Prez
Author: Eric Idle
Singer: Eric Idle
From the 'Meaning of Life' album, MCA Records MCA 6121

:)