43P - Fundamentals Of Physics

Question

Question: Suppose that the radius of the Sun was increased to 5.9010 ¹² m (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’s orbital speed in this new configuration. (b) What is the ratio of the orbital speed calculated in (a) to Earth’s present orbital speed of 29.8 km/s? Assume that the radius of Earth’s orbit remains unchanged. (c) What would be Earth’s new period of revolution? (The Sun’s mass remains unchanged).

Step-by-Step Solution

Answer

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

Given Information

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

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 

calculations

(a)

Total mass of sun in extended radius R.

$M=\frac{4}{3}{\mathrm{m}}^3·P$

$\beta =\frac{M^s}{\frac{4}{3}7R_S}3$

$M={\left(\frac{r}{R}\right)}^3{M}_8$

So, this mass(M^/) affect the earth 

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

        F_c=F_g

(b)

 Now the ratio of speeds,

$\frac{y}{v_0}=\frac{121}{29.88\times {10}^3}$

        =0.0406

(c)