What are the speeds of two Jupiter sized planets when they collide?

In summary, the two Jupiter-sized planets are released from rest 1.0 X 10^11 m apart. Their speeds as they crash together are 3 x 10^4 m/s.
  • #1
AbigailG
12
1

Homework Statement



Two Jupiter sized planets are released from rest 1.0 X 10^11 m apart. What are their speeds as they crash together?

I think my problem lies in figuring out which radius to use. In an equation like this are the radii of the planets included in the distance between them given? If not, should it be?

Homework Equations


[/B]
Ug = -Gm1m2/r

r (Jupiter) = 6.99 x 10^7 m

m (Jupiter) = 1.9 x 10^27 kg

r (between) = 1.0 X 10^11 m

The Attempt at a Solution


[/B]
Using conservation of energy:

Ei = Ef

Question #1 -- Ei is entirely Ugi...is it 2(Ug) ?

Ef = K + Ugf

Question #2 -- Is there still gravitational potential here? And if so is the radius used equal to twice the radius of Jupiter?

Question #3 -- Is the kinetic energy found for both of the planets or just one?

I need clarification on quite a few points, I apologize...but i feel like once I understand this fully I will be able to work it out myself.
 
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  • #2
For spherical objects, the distance you want to use for gravitational calculations is the distance between their centers.

Make a drawing showing the initial and final configurations. Indicate the separation between the planet centers for each situation.

The system as a whole (the system being both planets) has gravitational potential energy. You are looking for the change in potential energy between the starting configuration and the ending configuration. That change in potential energy will show up as kinetic energy for the whole system. You need to decide how that energy will be split between the components of the system.
 
  • #3
AbigailG said:
In an equation like this are the radii of the planets included in the distance between them given? If not, should it be?
Compare the radii of the planets with their initial distance apart. Does it matter? (The distance is usually between their centers.)

AbigailG said:
Question #1 -- Ei is entirely Ugi...is it 2(Ug) ?
The potential energy is of the two-planet system; the formula quoted is all of it.

AbigailG said:
Question #2 -- Is there still gravitational potential here? And if so is the radius used equal to twice the radius of Jupiter?
The distance between them when they crash will equal twice the radius.

AbigailG said:
Question #3 -- Is the kinetic energy found for both of the planets or just one?
Again, the energy is of the system -- so it is the total KE of both.

(gneill beat me to it!)
 
  • #4
gneill said:
For spherical objects, the distance you want to use for gravitational calculations is the distance between their centers.

Make a drawing showing the initial and final configurations. Indicate the separation between the planet centers for each situation.

The system as a whole (the system being both planets) has gravitational potential energy. You are looking for the change in potential energy between the starting configuration and the ending configuration. That change in potential energy will show up as kinetic energy for the whole system. You need to decide how that energy will be split between the components of the system.

Okay, so I have:

Kf - Ugf = Ugi Where: Ugi = -Gm1m2/r(between) and Ugf = -Gm1m2/2r(Jupiter)

1/2(m1+m2)-Ugf = Ugi

v = sqrt((2(ugi+ugf)/(m1+m2))
= 3 x 10^4 m/s

This is the correct answer. But why did I not have to divide the velocity amongst the two masses? Is it because I divided by the sum of the masses?
 
  • #5
AbigailG said:
Kf - Ugf = Ugi
That should be a + sign.

AbigailG said:
1/2(m1+m2)-Ugf = Ugi
You left out the v^2 in your KE term. Note that your first term is the total KE of both planets!

AbigailG said:
This is the correct answer. But why did I not have to divide the velocity amongst the two masses? Is it because I divided by the sum of the masses?
You already included that "sharing" when you wrote the total KE earlier.
 
  • #6
Doc Al said:
That should be a + sign.You left out the v^2 in your KE term. Note that your first term is the total KE of both planets!You already included that "sharing" when you wrote the total KE earlier.

Oops, just a typo. Sorry.

Thank you so much! I appreciate your help.
 

Related to What are the speeds of two Jupiter sized planets when they collide?

1. What is gravity?

Gravity is a force that attracts objects with mass towards each other. It is responsible for keeping our feet on the ground and for the motion of celestial bodies in space.

2. How does gravity work?

Gravity works by the principle of mass attraction. The larger the mass of an object, the greater its gravitational pull. This means that the more massive an object is, the more it will attract other objects towards it.

3. What is the formula for calculating gravity?

The formula for calculating gravity is F = G(m1m2)/r^2, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

4. Does gravity affect all objects equally?

Yes, gravity affects all objects with mass equally. However, the perceived effect of gravity may vary depending on an object's mass and distance from other massive objects.

5. Can gravity be manipulated or controlled?

No, gravity cannot be manipulated or controlled. It is a fundamental force of nature and cannot be altered by human intervention.

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