- #1

- 11

- 0

(the direction tangent to an orbit around earth)

from a distance of 40,000km from Earth's center.

How can I calculate its track?

thnks.

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In summary, the object starts at a velocity of 12,000meter/sec, from a distance of 40,000km from Earth's center. It has a resultant vector that keeps it in orbit (at equilibrium), or it signifies an escape, or it signifies a descent towards Earth. You'll need to plot its position as a function of time to plot its path.f

- #1

- 11

- 0

(the direction tangent to an orbit around earth)

from a distance of 40,000km from Earth's center.

How can I calculate its track?

thnks.

- #2

- 286

- 0

The resultant vector will be sufficient to keep the object in orbit (at equilibrium), or it will signify an escape, or it will signify a descent towards earth. You'll need to plot its position as a function of time to plot its path. Make the center of the Earth the origin. Make the mass at (40, 0), and make the x-axis measured in kilometers. Initial vector heads in the +y direction. What's its magnitude? What's the magnitude of the force toward the origin? How does the position of the point change after 1 second, based on its acceleration towards the origin?

- #3

Homework Helper

- 1,248

- 30

(location as function of time, step-by-step)

Or do you want to describe the orbit*

(apogee radius and speed, perigee r & v)?

VPython does a nice job with the momentum vector,

step-by-step changing it according to F(r_vec)

Can you find its KE, total E, and angular momentum?

- #4

Science Advisor

Homework Helper

- 43,008

- 974

One way to do this would be to solve the differential equations for the motion- preferably in polar coordinates but they are non-linear. A good book on oribital motion should have an example of this.

Probably better is to assume the orbit is an ellipse, write down the general equation of an ellipse (again, I would use polar coordinates) and use conservation of energy to determine the coefficients.

- #5

- 11

- 0

HallsofIvy said:One way to do this would be to solve the differential equations for the motion- preferably in polar coordinates but they are non-linear.

ok, tell me if what I am doing here is fine becous I think it isnt:

for the R axis (Polar cordinatsr) it should be:

v^2/r - MG/r^2 = F(r)

now I can integrate this function (dr) from 40,000,000 to wherever I want the final distance from Earth to be. and get the acceleration on this axis.

for the angle Theta I can 360*v*t/2(pai)r

but then I don't what to do with the variable r.

HallsofIvy said:Probably better is to assume the orbit is an ellipse

well, does it? (I thoght it will be some kind of an going-out Spirall)

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