A star of mass 5 × 10e30 kg is located at ‹ 7 × 10e12, 3 × 10e12, 0 › m. A planet of mass 4 × 10e24 kg is located at ‹ 5 × 10e12, 5 × 10e12, 0 › m and is moving with a velocity of ‹ 0.6 × 10e4, 1.4 × 10e4, 0 › m/s.
A. During a time interval of 1x10e6 seconds, what is the change in the planet's velocity?
B. During this time interval of 1x10e6 seconds, what is the change in the planet's position?
- Newton's Law of Gravity
- Unit Vector = (Vector) / (Magnitude of Vector)
- Momentum Final = Momentum Initial + Force Net * Δt = mass*Velocity initial + Force net Δt
The Attempt at a Solution
I began by listing the variables I was given. I then subtracted the position of the star from the position of the planet.
r = r(planet) - r(star) = ( -2e12, 2e12, 0)
I then found the magnitude of the vector r. |r| = 2.828e12
I then found the force of gravity between the planet and star using Newton's Law of Gravity.
F(grav) = 1.67e20
I then found the unit vector of r with:
Unit Vector = Vector / Magnitude of Vector
r(hat) = (-0.707, 0.707, 0)
I then multiplied my unit vector by F(grav) to obtain the components. I got the values:
(-1.18e20, 1.18e20, 0)
I then listed the formula:
Momentum final = velocity initial * mass of planet + Fnet * Δt
I obtained the value (2.4e48, 5.61e28, 0)
I then used the following formula: v(final) = momentum final / mass
I got the following value: (6e23, 14025, 0)
I then subtracted my initial velocity from my final velocity and obtained:
Δv = (6e29, 1.0009e13)
To approximate my new position I used: Position final = position initial + v(avg)Δt ; where v(avg) = ( 3e29, 2.505e12, 0)
Position final = (3e35, 2.505e18, 0)
I then subtracted my final position from my initial position to obtain:
Δposition = (2.999e35, 2.504e18,0)
I did not receive any points for my answer. I have attempted this problem a few times with no success. I have also attempted sample problems (which have the final solution) but my answer does is not remotely close. I'd really appreciate some advice or someone to review my work.
Last edited by a moderator: