The mass of the Sun is 2 × 1030 kg, the mass of the Earth is 6 × 1024 kg, and their center-to-center distance is 1.5 × 1011 m. Suppose that at some instant the Sun's momentum is zero (it's at rest). Ignoring all effects but that of the Earth, what will the Sun's speed be after 6 days?

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aristocles aristocles · Answer 1 · 2018-10-03T02:54:54+02:00

acceleration due to gravity at the position of sun due to earth is given as

[tex]a = \frac{F}{M_s}[/tex]

[tex]a = \frac{GM_s M_e}{M_s R^2}[/tex]

[tex]a = \frac{GM_e}{R^2}[/tex]

[tex]a = \frac{6.67 * 10^{-11}* 6 * 10^{24}}{(1.5* 10^{11})^2}[/tex]

[tex]a = 1.78 * 10^{-8} m/s^2[/tex]

now we will use kinematics to find the speed of sun after 6 day

[tex]v_i = 0[/tex]

[tex]a = 1.78 * 10^{-8} m/s^2[/tex]

[tex]t = 6 days = 5.184 * 10^5 s[/tex]

[tex]v_f = 0 + 1.78 * 10^{-8} * 5.184 * 10^5[/tex]

[tex]v_f = 9.23 * 10^{-3} m/s[/tex]

so speed of sun after 6 days will be 9.23 mm/s