# physics

How long would our year be if our Sun were two fifths its present mass and the radius of the Earth’s orbit were six times its present value?

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1. period^2= constant*r^3/M

T^2/1year=6^3/1* 1/(2/5)

T^2= 36*6*5/2

period= 6sqrt15 * 1year

check my thinking.
http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html#c6

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2. The gravity force would be less by a factor of (2/5)*(1/6)^2 = 1/90

The centripetal force would have to decrease my the same factor. That means
V^2/R becomes 1/90 of the former value.
Call V1 and R1 the original values and V2 and R2 the new values
V2^2/R2 = (1/90)V1^2/R1
V2^2 = (1/90)(R2/R1)*V1 = 1/15
V2 = 0.258 V1
The period of an orbit is proportional to R/V. It will increase by a factor
6/0.258 = 23.3

That is the new orbital period in years.

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posted by drwls
3. dwls thank you very much

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posted by erin

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