How can gravity hold galaxy groups togehter?

[Tryggvas]

Thought experiment: Assume two galaxies in a galaxy group, initially at rest (with respect to one another). The distance between the centers of the galaxies is r = 1 Mpc.

The total mass of each galaxy is m_g = 6 ∙ 10⁴² kg (including dark matter). This is ≈ 3 ∙ 10¹² solar masses.

The gravitational pull between the galaxies will be F= G ∙ m_g² /r² = 2.67 ∙ 10³⁰ N, and the corresponding acceleration will be a = F/m_g = 4.45 ∙ 10^-13 m/s only. (Using G= 6.67 ∙ 10^-11 m³kg^-1s^-2).

How can this tiny force withstand the expansion of space (which at this distance is ≈ 70 km/s)?

 

[mfb]

The timescale is millions to billions of years, over such a timescale even small acceleration values matter. The gravitational potential is 8*10⁵² J, giving the galaxies an escape velocity of 160 km/s. If they are slower than that, they are gravitationally bound.

 

[Chronos]

Put your example in perspective, make predictions and explain how they differ from mainstream predictions - along with the math that supports your predictions.

 

[Drakkith]

How can this tiny force withstand the expansion of space (which at this distance is ≈ 70 km/s)?

Notice that the latter is a speed, not an acceleration or a force. You cannot directly compare them in this manner.

 

[Bandersnatch]

Thought experiment: Assume two galaxies in a galaxy group, initially at rest (with respect to one another). The distance between the centers of the galaxies is r = 1 Mpc.

The total mass of each galaxy is m_g = 6 ∙ 10⁴² kg (including dark matter). This is ≈ 3 ∙ 10¹² solar masses.

The gravitational pull between the galaxies will be F= G ∙ m_g² /r² = 2.67 ∙ 10³⁰ N, and the corresponding acceleration will be a = F/m_g = 4.45 ∙ 10^-13 m/s only. (Using G= 6.67 ∙ 10^-11 m³kg^-1s^-2).

How can this tiny force withstand the expansion of space (which at this distance is ≈ 70 km/s)?

Assuming both galaxies are initially at rest with respect to the Hubble flow, the analogous situation here is that of the standard projectile motion problem in one dimension. Construct the equation with acceleration given by the gravitational attraction, initial distance equal to 1 Mpc, and initial velocity equal to 70 km/s (because that's essentially the meaning of the Hubble constant in the absence of dark energy, which we can assume here for simplicity).
Since acceleration is changing, this will require a bit more calculus than it would for a constant case (but then again, this is an 'I' thread).

Alternatively, write kinetic and potential energy equations using these values, and see if the system is gravitationally bound (Ek<Ep).*This looks like the often made mistake of thinking of the standard (no dark energy) expansion as 'pushing' galaxies apart, whereas it should be thought of as simple inertial motion, with some initially imparted velocity and varying gravitational acceleration.

*I can see mfb already calculated the required escape velocity, corresponding to the case Ek=Ep. You can see that it is higher than 70km/s.

 

[Tryggvas]

Thank you very much for your explanations and clarifications. I fully understand that you cannot compare an acceleration or force with a velocity. I just thought it was strange that the tiny gravitational pull could have such a strong effect as to keep galaxy groups together, and suspected that I had made some mistake in my calculations. I had not thought of calculating the escape velocity, when you do that it is easier to understand.

Cosmology and gravity is very exciting! I hope that we will get an explanation of the “dark” components of our universe during my lifetime.