Calculate centripetal acceleration of Earth?

Question

Calculate centripetal acceleration of Earth in its orbit around the sun, and net force exerted on Earth. waht exerts this force on Earth? Assume that Earth's orbit is a circle of radius 1.50 X 10 to the 11th power m.

Answer 1

The Sun exerts this force on Earth. It is called gravity. It could be calculated with
F = G * M * m / d^2
G is the constant
M is the mass of the sun
m is the mass of Earth
d is the distance from Sun to Earth.

However, you are apparently asked to calculate it using another technique (just as valid).

You are given the radius of the orbit.
d = 150,000,000,000 metres.

You can find Earth's speed along this orbit

1) find the circumference of the circular orbit (Circumference = 2*pi*d) d is the radius of the orbit.

2) Find the time it takes to go around the orbit (a.k.a. one year) in the units you need
I guess you'll need the year in seconds -- use 365.256363 days times 86,400 seconds per day for the sidereal year, the one we use for such celestial mechanics calculations.

3) Divide the length of the orbit (in metres) by the number of seconds; you'll get the speed.



4) The acceleration "a" is found with
a = (v^2)/d
the (speed squared) divided by d = radius of orbit.

If you use metres and seconds in all your calculations, you will find a in m/s^2 (metres per second squared).

5) Once you have that, you find the mass of Earth (m) in kilograms
(m = 5.9742x10^24 kg)

6) To find the force, you use the gool old formula:

F = m a

where you now have m and a

If you use kg and m/s^2,
F will be in Newtons.

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Just do it one step at a time. Each step is relatively easy by itself.
There are big numbers, that only makes the calculation a bit longer (and you want to watch for the number of zeroes), but that does not make it harder.

Answer 2

The earth travels the circumference of the orbit in one year... the circumference of the orbit is given by doubling the radius and multiplying by pi. Velocity is this distance divided by time. Now that you have the velocity, you can compute the acceleration...