G2. Most people (oddly enough, only about 80% of Americans, according to a recen

Question

G2. Most people (oddly enough, only about 80% of Americans, according to a recent poll)know hat this orbit 10* km), what is the that the Earth orbits the Sun. Most people (sorry, no interesting statistics on this one) knowt roughly 365.25 days. Given that the Earth's orbit is mostly circular (enough that we 'll say that it is, to the math easier), with a radius of 150 million kilometers (that's 1.5 acceleration necessary to keep the Earth moving in this "circular" orbiar? (Hint: How long does it take oe the Earth to complete o Earth's speed? You'll need several conversions t? What is the to get an answer in units you're used to working with.) 5 23.44O 07920 3105 2. ?? need units.. Come frem ! 3o5 23 dys 0c3400x 101) 103 c: 784 303

Explanation / Answer

Please always discuss in the comments if you have any doubt/issue. I will be happy to help.

First, lets convert everything to standard units.

r = 1.5e8 Km = 1.5e11 m

t = 365.25 days = 365.25 days*24 hours*60 minutes*60 seconds = 3.155e7 sec

Now,

velocity = distance / time

distance for circular path = circumference = 2*pi*r = 2*pi*1.5e11 = 9.4247e11 m

Therefore,

v = 9.4247e11 m / 3.155e7 sec

v = 29872.51 m/s

Now,

ac = v2 / r

ac = 29872.512 / 1.5e11

ac = 5.949e-3 m/s2

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