Momentum and Newton's Gravitation force question (2 stars)

physics1311

At t = 0 a star of mass 5.0×1030 kg has velocity < 6.0×10^4, 7.0×10^4, -7.0×10^4 > m/s and is located at < 1.00×10^12, -4.00×10^12, 4.00×10^12 > m relative to the center of a cluster of stars. There is only one nearby star that exerts a significant force on the first star. The mass of the second star is 3.5×10^30 kg, its velocity is < 1.0×10^4, -2.0×10^4, 9.0×10^4 > m/s, and this second star is located at < 1.04×10^12, -3.94×10^12, 3.96×10^12 > m relative to the center of the cluster of stars.
At t = 1.0×105 s, what is the approximate momentum of the first star? (in vector coordinates)
Was told to use Momentum principle, position update formula, and Newton's gravitational force law.
I keep on getting <3E35, 3.5E35, -3.5E35>kg m/s
The force of gravity I keep on calculating is not significant in that time to change the momentum of the particle.

gneill

Hi physics1311, welcome to Physics Forums.

You'll have to show your attempt at a solution (how did you arrive at the momentum vector that you found) before we help.

physics1311

First I used Newtons gravitational force equation. Fg= GM1M2/r^2
M1=5E30 kg is given
M2 = 3.5E30 kg is given
G = 6.66E-11

Calculated R by using pythagorean theory for both coordinates and adding together
I got R =1.14E13

Then using the force calculated I used the momentum principle, delta p = Fnet delta t

gneill

That distance doesn't look right. What's the formula for the distance between two points?

That'll work for the Δp provided that Fnet remains fairly constant over the timestep Δt.

EDIT: Also, you'll need to express Fnet as a vector, since the resulting momentum will also be a vector quantity.

physics1311

Okay, thanks for that tip. I used the distance formula sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) equals distance.
I got r = 8.25E10m

I then plugged it into the equation for gravitational force. F= GM1M2/r^2
I got Fg=1.72E29

Then using this force I did p(final)-p(initial) = Fg delta(t) for each coordinate

My answer was <3.17E35, 3.67E35, -3.33E35>

and I tried making Fg negative which gave me <2.83E35, 3.33E35, -3.67E35>
neiter answers were right, what am I doing wrong?

physics1311

How do you express Fnet as a vector?

gneill

You need to use vector equations to calculate your momentum. You've calculated the MAGNITUDE of the force that occurs between the two stars. Now you need to apply the other part of the vector property: the direction.

The gravitational force acts along a line connecting the centers of the two stars. You need to find a unit vector that lies on that line in the direction which the force is acting on the star in question (star #1 in this scenario). The force vector will then be the magnitude of the force multiplied by that unit vector.



How do you find a unit vector that lies along the line connecting two points?

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