m and 2m respectively, orbiting the same star in circular orbits, the more massive planet is 9.3 times as far from the star as the less massive one.
What is the ratio v1:v2 of the speeds of the 2 planets?
What is the ratio T1:T2 of the orbital speeds of the 2 planets?
Please & Thank You!!
2 Answers
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f/F = 2m/(9.3r)^2//m/r^2 = 2(r/9.3r)^2 = 2/9.3^2 = 0.023 = g/G where f = force from 2m at R = 9.3r and F = force from m at R = r. ANS.
We get this by noting the gravitational fields G ~ m/r^2 and g ~ 2m/(9.3r)^2 are proportional to the forces exerted by the planets. A fact we use next.
g/G = .023 = V^2/9.3r//U^2/r = a/A where A and a are the radial accelerations A = U^2/r and a = V^2/(9.3r) So we can write V/U = sqrt(.023*9.3) = 0.462 where V is for 2m at R = 9.3r and U is for m at R = r. ANS
Finally V/U = .462 = w 9.3r/W r = (2pi/T) 9.3r//(2pi/t) r = (t/T) 9.3; so that t/T = .462/9.3 = 0.0497 where w is the angular velocity and T is the period for 2m at 9.3r and W is the angular velocity and t is the period for m at r. ANS.
Note, as you failed to specify which variables went with which planet, I explicitly specified my ratio variables so you can identify them with the planets m and 2m. My ratios might be upside down from what you were looking for; in which case just invert my answers.
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probable truly one of three issues might want to happen. difficulty One: The planet, assuming it is not transferring, is pulled via both stars both. This pressure stretches the planet so as that interestingly like an ellipsoid. If the pull of each star is solid adequate, the planet might want to be ripped aside. difficulty 2: that’s more advantageous probable. in this difficulty, the planet is in action. The planet will be attracted in route of the large call that it is transferring closest to, and could connect that huge call’s orbit, till it comes into the gravity container of the different star lower back, at which factor it would want to move to orbit the different star. This cycle might want to easily repeat see you later because the planet persevered to exist, in idea. difficulty 3: This one has easily been shown via scientists. because both stars are transferring (they must be, via the guidelines of Astrophysics), they could easily be pulled into one yet another’s gravity fields, with the planet both being beaten between them or orbiting both stars as besides the indisputable fact that they were one. truly one of two issues can happen with the celebrities from this factor: they could both a) orbit one yet another, so as that the gadget has a center with 2 suns, or b) the celebrities might want to collide, at which factor they could both fuse or explode, the latter being more advantageous probable.
