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maddie93 · Nov 13, 2012, 06:08 PM

The next three questions pertain to the following situation. Planet X of mass m1 orbits a Sun in uniform circular motion at a distance r1 and speed v1. The mass of the Sun is MS1 and its radius is RS1 as shown in the figure below.

http://https://smart2.physics.illino...bitPlanetX.gif

If the planet's mass were doubled, how would its speed v1 change?

v1 would remain the same
v1 would increase by a factor of the square root of 2
v1 would increase by a factor of 2

Consider another solar system in which Planet Y of mass m2 = 2 m1 orbits a Sun of mass MS2 = 4 MS1 and radius RS2 = 2RS1 at a distance r2 = 2r1. Further, suppose R2, the radius of Planet Y is twice R1, the radius of Planet X.

w2 < w1
w2 = w1
w2 > w1

How does v2, the speed of Planet Y in its orbit, compare to v1, the speed of planet X in its orbit?

v2 = (1/sqrt(2))v1
v2 = (1/2)v1
v2 = v1
v2 = sqrt(2)v1
v2 = 2v1

ebaines · Nov 13, 2012, 06:55 PM

All of these can be answered by considering that the force of gravity between sun and planet must equal the centripedal force on the planet:

$<br /> \frac {GM_1m_2} {R^2} = m_2 \omega ^2 R<br />$

which after a bit of rearranging gives:

$<br /> G m_1 = \omega^2 R^3<br />$

Note that the mass of the planet, m_2, has no bearing on the equation of motion. So use this, plus the fact that the velocity of the planet is $v_2 = \omega R$ , to answer the questions.