You know what I just realized???

[JoeRoccoCassara]

If the nuclear pulse propelled Super Orion Craft were a thousand times lighter, and had the same amount of propulsion, it would reach a top speed of 374,740.573 m/s according to E=MC2.

 

But with the same weight it has now, it's top speed is 29,979,245.8 m/s.

 

And as far as I know light weight objects move faster than heavier objects when pushed with the same strength. But according to E=MC2 , this just ain't so.

 

Does this have something to do with the Higgs field?

[Qfwfq]

How do you reach such strange conclusions? Can you give them any support at all?

[JoeRoccoCassara]

How do you reach such strange conclusions? Can you give them any support at all?

 

The Super Orion space craft weighs 8,000,000 tons, it takes it 85 years to travel 4 light years, and it's top speed can pan out at around 10% the speed of light according to it's wikipedia article.

 

I could be wrong, but I thought to figure out the number of Joules it would take to propel an object at a theoretical speed, you has to multiply it's weight/mass by c, and then divide that number by what ever speed the object was moving at.

 

Redoing it, it's mass is 7,257,477,920 kg, times c, which is 299,792,458 m/s, divided by it's speed, which we know is 10% of c, 29,979,245.8 m/s, I got 72,574,779,200 Joules.

 

Now say the craft is 1,000 times lighter, but has just as much force pushing it.

 

If I'm, not mistaken you figure out the speed, or v, an object would move if it were being pushed by a theoretical amount of joules, by multiplying it's thrust times c, and then dividing that number by it's mass.

 

So if the Super Oiron Craft was a thousand times lighter it would weigh in at about 7,257,477.92 kg.

 

72,574,779,200 Joules times 299,792,458 m/s, divided by 7,257,477 kg = 2,997,924,960,000 m/s.

 

So my original calculations were way off.

[Janus]

The Super Orion space craft weighs 8,000,000 tons, it takes it 85 years to travel 4 light years, and it's top speed can pan out at around 10% the speed of light according to it's wikipedia article.

 

I could be wrong, but I thought to figure out the number of Joules it would take to propel an object at a theoretical speed, you has to multiply it's weight/mass by c, and then divide that number by what ever speed the object was moving at.

 

 

That's not even close to being right. a Joule is measured in [math]\frac{Kg-m^2}{sec^2}[/math]

 

Your method gives you an answer in kg. And a meaningless value at that.

 

The method for finding out how much energy is needed to get a mass up to a given speed is:

 

[math]E = mc^2 \left ( \frac{1}{\sqrt{1- \frac{v^2}{c^2}}}-1 \right)[/math]

 

Bur even that doesn't pertain to the Orion craft. For action-reaction engines you need to use the rocket equation:

 

[math]V_f = V_e(\ln(MR))[/math]

 

Where Vf is the final velocity

Ve is the velocity of the exhaust

MR is the mass ratio, (mass of fueled ship divided by the mass of the unfueled ship)

 

ln means the natural log.

 

Thus is the exhaust velocity stays the same, and you shrink the size of the ship, as along as maintain the same fuel to ship ratio you will reach the same velocity.

 

For the Orion, with its 0.1c top velocity the above equation will give you a pretty good answer as relativistic effects will be small.

 

But as your top velocity gets closer to the speed of light, you will have to start to use the relativistic rocket equation to get an accurate answer as follows:

 

[math]V_f = c \tanh \left (\frac{V_e}{c} ln(MR) \right ) [/math]

 

Where tanh stands for the hyperbolic tangent.

 

As before, the final velocity only relies on the exhaust velocity and the mass ratio.

[JoeRoccoCassara]

That's not even close to being right. a Joule is measured in [math]\frac{Kg-m^2}{sec^2}[/math]

 

Your method gives you an answer in kg. And a meaningless value at that.

 

The method for finding out how much energy is needed to get a mass up to a given speed is:

 

[math]E = mc^2 \left ( \frac{1}{\sqrt{1- \frac{v^2}{c^2}}}-1 \right)[/math]

 

Bur even that doesn't pertain to the Orion craft. For action-reaction engines you need to use the rocket equation:

 

[math]V_f = V_e(\ln(MR))[/math]

 

Where Vf is the final velocity

Ve is the velocity of the exhaust

MR is the mass ratio, (mass of fueled ship divided by the mass of the unfueled ship)

 

ln means the natural log.

 

Thus is the exhaust velocity stays the same, and you shrink the size of the ship, as along as maintain the same fuel to ship ratio you will reach the same velocity.

 

For the Orion, with its 0.1c top velocity the above equation will give you a pretty good answer as relativistic effects will be small.

 

But as your top velocity gets closer to the speed of light, you will have to start to use the relativistic rocket equation to get an accurate answer as follows:

 

[math]V_f = c \tanh \left (\frac{V_e}{c} ln(MR) \right ) [/math]

 

Where tanh stands for the hyperbolic tangent.

 

As before, the final velocity only relies on the exhaust velocity and the mass ratio.

 

English please.

 

How would I do these formula's on the google calculator, ergo how do I find out the speed a space craft moves???????????????????????

[GAHD]

How would I do these formula's on the google calculator, ergo how do I find out the speed a space craft moves???????????????????????

Take calculus and physics in high school.

[modest]

English please.

 

How would I do these formula's on the google calculator, ergo how do I find out the speed a space craft moves???????????????????????

 

To put the rocket equation,

[math]\Delta V = V_e \ln \frac{M_0}{M_1}[/math]

into google you could type this:

Ve times the natural log of (Mo divided by M1)

 

But you'll have to change where I wrote Ve, Mo, and M1 to numbers. Ve is the velocity of the exhaust, Mo is the starting mass of the ship and M1 is the mass of the fully accelerated ship. For example:

 

Rocket exhaust velocity = 4500 m/s

Starting mass = 1000 kg

Ending mass = 500 kg

 

4500 times the natural log of (100 divided by 50)

 

gives you 3119 m/s.

 

The relativistic equation:

[math]\Delta v = c \cdot \tanh \left(\frac {V_e}{c} \ln \frac{m_0}{m_1} \right)[/math]

is a bit complicated to be typing into google verbally. I put the two equations into an excel file so that if you have microsoft excel, you can input the exhaust value and the two masses and see what the classical and relativistic results are, see the attachment below.

 

~modest

[JoeRoccoCassara]

To put the rocket equation,

[math]\Delta V = V_e \ln \frac{M_0}{M_1}[/math]

into google you could type this:

Ve times the natural log of (Mo divided by M1)

 

But you'll have to change where I wrote Ve, Mo, and M1 to numbers. Ve is the velocity of the exhaust, Mo is the starting mass of the ship and M1 is the mass of the fully accelerated ship. For example:

 

Rocket exhaust velocity = 4500 m/s

Starting mass = 1000 kg

Ending mass = 500 kg

 

4500 times the natural log of (100 divided by 50)

 

gives you 3119 m/s.

 

The relativistic equation:

[math]\Delta v = c \cdot \tanh \left(\frac {V_e}{c} \ln \frac{m_0}{m_1} \right)[/math]

is a bit complicated to be typing into google verbally. I put the two equations into an excel file so that if you have microsoft excel, you can input the exhaust value and the two masses and see what the classical and relativistic results are, see the attachment below.

 

~modest

 

Thanks much Modest.

 

And thanks for the equations themselves CraigD.:)