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- Thread starter TheSerpent
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The formula for escape velocity is v=√(2GM/r) where v= velocity, G=universal gravitational constant (G=6.67*10

v=√(2GM/r)

E

m (rocket)=1000 kg

r (orbit)=13620 km

E

m (earth)=5.98*10

r (earth)=6380 km

First, find the velocity that the rocket has...

E

9.97165*10

v=√((2*(9.97165*10

v=1.412*10

Then, find the velocity that the rocket would need to escape...

v=√(2GM/r)

v=√(2GM/r

v=√((2*(6.67*10

v=1.997*10

Compare the two -- the rocket will not have sufficient velocity to escape.

Good luck! I hope this helps.

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gneill

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From that velocity determine what the escape velocity would be; escape velocity has a particular relationship to the circular orbit velocity. Then determine what the new velocity would be given the rail gun boost of energy. Compare to the escape velocity.

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gneill

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The rocket begins in a circular orbit at the given altitude. Therefore it will have an initial velocity and kinetic energy appropriate for a circular orbit at that location. Next additional energy is supplied via a rail gun boost. The probe will gain that energy as KE and thus have a new velocity. Compare to the escape velocity for that orbital radius.Hi TheSerpent,

The formula for escape velocity is v=√(2GM/r) where v= velocity, G=universal gravitational constant (G=6.67*10^{-11}Nm^{2}kg^{-2}), M is the mass of the body, and r is the separation distance.

v=√(2GM/r)

E_{kinetic}=0.5mv^{2}

m (rocket)=1000 kg

r (orbit)=13620 km <--- That's its altitude, not its orbital radius

E_{kinetic}=9.97165*10^{10}J <--- That's the energy added, not the total

m (earth)=5.98*10^{24}kg

r (earth)=6380 km

First, find the velocity that the rocket has...

E_{kinetic}=0.5mv^{2}

9.97165*10^{10}J = 0.5(1000 kg)v^{2}

v=√((2*(9.97165*10^{10}J))/1000 kg)

v=1.412*10^{4}m/s

Then, find the velocity that the rocket would need to escape...

v=√(2GM/r)

v=√(2GM/r_{orbit}+r_{earth})

v=√((2*(6.67*10^{-11}Nm^{2}kg^{-2})*(5.98*10^{24}kg))/(13620 km + 6380 km))

v=1.997*10^{5}m/s

Compare the two -- the rocket will not have sufficient velocity to escape.

Good luck! I hope this helps.

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Thanks for the correction!The rocket begins in a circular orbit at the given altitude. Therefore it will have an initial velocity and kinetic energy appropriate for a circular orbit at that location. Next additional energy is supplied via a rail gun boost. The probe will gain that energy as KE and thus have a new velocity. Compare to the escape velocity for that orbital radius.

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So what's going to be changed in the calculation process (how do you find the new velocity?)Thanks for the correction!

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gneill

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The rail gun adds kinetic energy. Velocity depends upon kinetic energy.So what's going to be changed in the calculation process (how do you find the new velocity?)

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Find orbital velocity:The rocket begins in a circular orbit at the given altitude. Therefore it will have an initial velocity and kinetic energy appropriate for a circular orbit at that location. Next additional energy is supplied via a rail gun boost. The probe will gain that energy as KE and thus have a new velocity. Compare to the escape velocity for that orbital radius.

v = √(GM/r)

v = √((6.67*10^-11)(5.98*10^24)/(13620000 + 6380000)

v = 4.466 * 10^3 m/s

Find orbital kinetic energy:

K = mv^2/2

k = (1000)(4.466*10^3)^2/2

K = 9972578000 = 9.973 * 10^9 J

Find escape velocity:

v esc = √2 v

v esc = √2 (4.466 * 10^3)

v esc = 6.316 * 10^3 m/s

How would you include the energy boost from the rail gun into the answer, that is what I am not sure of.

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gneill

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Okay! Good to here!Find orbital velocity:

v = √(GM/r)

v = √((6.67*10^-11)(5.98*10^24)/(13620000 + 6380000)

v = 4.466 * 10^3 m/s

Find orbital kinetic energy:

K = mv^2/2

k = (1000)(4.466*10^3)^2/2

K = 9972578000 = 9.973 * 10^9 J

Find escape velocity:

v esc = √2 v

v esc = √2 (4.466 * 10^3)

v esc = 6.316 * 10^3 m/s

Kinetic energy adds. Add the boost energy to the energy k that you found above. Find the new velocity from that.How would you include the energy boost from the rail gun into the answer, that is what I am not sure of.

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Find new velocity:Okay! Good to here!

Kinetic energy adds. Add the boost energy to the energy k that you found above. Find the new velocity from that.

K = mv^2 / 2

(9.973 * 10^9)+(9.97165 * 10^10) = (1000)v^2 / 2

v = √(2)(1.096895*10^11)/1000

v = 14811.44827 = 1.481 * 10^4 m/s

This is the actual velocity so therefore the rocket will have sufficient velocity to escape.

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gneill

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Yup. That looks good.Find new velocity:

K = mv^2 / 2

(9.973 * 10^9)+(9.97165 * 10^10) = (1000)v^2 / 2

v = √(2)(1.096895*10^11)/1000

v = 14811.44827 = 1.481 * 10^4 m/s

This is the actual velocity so therefore the rocket will have sufficient velocity to escape.

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Thank you for your help!!!! Can you also help us in our other post you commented on? We posted an idea but unsure!Yup. That looks good.

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gneill

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You're welcome.Thank you for your help!!!! Can you also help us in our other post you commented on? We posted an idea but unsure!

I see that you have two threads, this one and one other. I've made a suggestion for you to work on in that other thread.

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