If I have two objects with an initial setting of object 1: mass is 2000, x1 (pos

Question

If I have two objects with an initial setting of

object 1: mass is 2000, x1 (position) is 0, y1 (position) is 0, x1 (velocity) is 0, y1 (velocity) is 0

object 2: mass is 10, x2 (position) is 160, y2 (position) is 0, x2 (velocity) is 0, y2 (velocity) is 354

Now if I decrease object 2 mass to 1 and decrease object 1 mass to 500 and leaving all the other values the same and then re-adjusted the velocity in the y direction for object 2 (y2) until object 2 maintains a circular orbit. What will be my new velocity in the y direction for object 2 y2(velocity)?

In reviewing the content discussed in lecture related to Newton’s Law of Universal Gravitation and circular orbits, is this the type of the change in velocity you would expect by decreasing the mass of object 1 by 4 fold? Please explain. Below is a sample image to give an idea, please help. The image is just a sample. Use the values I have written above

atti Word Sign in File Home Insert DesignLayout ReferencesMailingsReview View Tell me what you want to do Share- My Solar System 2.04- Mozilla Firefox - https://phet.colorado.edu/sms/my-solar-system/my-solar-system en html oct Preset Stop system centered Show Traces Show Grid Tape Measure Initial Settings: of bodies PhET Page 1 of 1 0words English (United States) + 100% 2:18 PM Type here to search ENG 10/11/2017

Explanation / Answer

given two masses
m1 = 2000, x1 = 0, y1 = 0, Vx1 = 0, Vy1 = 0
m2 = 10, x2 = 160, y2 = 0, Vx2 = 0, Vy2 = 354
for m2 rotating about m1 in circukar orbit
km1*m2/x2^2 = m2*Vy2^2/x2
km1/x2 = Vy2^2
k*2000/160 = 354^2
k = 10025.28
now, if m1 becomes 500, m2 = 1
then ,
km1/x2 = V'^2
10025.28*500/160 = V'^2
so new velocity for object 2 iun y direction V' = 177

so decreasing the mass of object by 4 fold, the decrease in speed should be 2 fold ( as m is proportional to square of v)
hence this change in speed is the change coresponding to 4 fold decrease in mass of object 1

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