1. a) Calculate the reflex motion of the Sun (its radial velocity as it orbits a

Question

1.
a) Calculate the reflex motion of the Sun (its radial velocity as it orbits around the center of mass) due to the presence of Jupiter. Jupiter’s orbital period is 11.86 yr, average distance from the Sun is 5.2 AU, and mass is 0.000955 M. You may assume that Jupiter’s orbit is circular.

b) What is your answer in (a) equivalent to in terms of another common-day speed that you know of (a runner, walker, car, a cheetah, a bird flying, etc.).

c) Repeat the calculation in (a) for Saturn and compare your result to the one you got in (a), commenting on what you think an alien civilization in a nearby star system would conclude about our own solar system if they were making radial velocity measurements of the Sun.

Explanation / Answer

here,

orbital speed Vo^2 = GM/R

G is 6.67 *10^-11 Nm^2/Kg^2

M is mass of juliter = 0.000955* 1.99 e 30

Mj = 1.9 *10^27 kgs

R = 5.2 AU = 5.2* 1.5 e 11 = 7.8e+11m

so

Vo^2 = 6.67 e-11 * 1.9 e 27/(7.8 e 11)

Vo = 403.8 m/s (answer)

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part B :

mass of saturn = 5.68 e 26 kgs

so Vo^2 = 6.67e-11 * 5.68 e 26/(7.8 e11)

Vo = 220.3 m/s (answer)

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