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Chapter 1: 43P (page 1)

Question: Suppose that the radius of the Sun was increased to 5.9010 12m (the average radius of the orbit of Pluto), that the density of this expanded Sun were uniform, and that the planets revolved within this tenuous object. (a) Calculate Earth鈥檚 orbital speed in this new configuration. (b) What is the ratio of the orbital speed calculated in (a) to Earth鈥檚 present orbital speed of 29.8 km/s? Assume that the radius of Earth鈥檚 orbit remains unchanged. (c) What would be Earth鈥檚 new period of revolution? (The Sun鈥檚 mass remains unchanged).

Short Answer

Expert verified

a.121m/s
b.0.00406
c. 248 y

Step by step solution

01

Given Information

The new radius of the sun (R) =5.90脳1012m

02

concept of interstellar space and excitation space

Here, sun is affected by the gravitational force upto the distance from the centre of sun to centre of the earth, say r

So

Mass of the Sun up to radius r

03

calculations

(a)

Total mass of sun in extended radius R.

M=43m3路P

尾=Ms437RS3

M=rR3M8

So, this mass(M/) affect the earth

To find the speed of the earth, set centripetal for to gravitational force

Fc=Fg

(b)

Now the ratio of speeds,

yv0=12129.88脳103

=0.0406

(c)

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