Rocket Equation Homework: Explaining Mass Infinity

In summary, the rocket equation shows that as the velocity change (ΔV) over the exhaust velocity (C) increases, the total mass of the spacecraft (M+P) also increases exponentially. At a certain point, usually between ΔV/C = 2 and ΔV/C = 3, the mass of the spacecraft will reach infinity if the materials used are too light and the propellant density is too high. This is due to the mass ratio (M+P)/M being equal to e^ΔV/C, and as the exponential value increases, the total mass increases drastically. This phenomenon is discussed in a USAD Science section study guide.
  • #1
Biosyn
115
0

Homework Statement



The following equation is known as the "Rocket Equation":

[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex] = mass ratio

M = dry mass
P = mass of propellant
C = exhaust velocity
ΔV = velocity changee^1 = 2.72
e^2 = 2.74
e^3 = 20.4

As ΔV/C goes up, the mass of the spacecraft goes up faster than the exponential, so much so that depending on the lightness of the structural materials and the density of the propellants employed, somewhere between ΔV/C = 2 and ΔV/C = 3 the mass of a single spacecraft will go to infinity! Please explain how and why the mass of the spacecraft will reach infinity?

Homework Equations



[itex]\frac{M+P}{M}[/itex]= e[itex]^{ΔV/C}[/itex]

The Attempt at a Solution

Shouldn't the mass ratio be equal to 1 if the mass is a really huge number?
Or, does the propellant mass have something to do with it. I know that the propellant mass needs to increase along with the dry mass of the rocket.
 
Last edited:
Physics news on Phys.org
  • #2
It's unclear whether the question posed refers to M or M+P. If M is fixed, then M+P goes up exponentially with ΔV/C. But I don't get the bit about going to infinity between 2 and 3. I've no idea where that's coming from. Is this the whole question, or is something left out?
Btw, the quoted value for e^2 is wrong. Looks like a typo.
 
  • #3
haruspex said:
It's unclear whether the question posed refers to M or M+P. If M is fixed, then M+P goes up exponentially with ΔV/C. But I don't get the bit about going to infinity between 2 and 3. I've no idea where that's coming from. Is this the whole question, or is something left out?
Btw, the quoted value for e^2 is wrong. Looks like a typo.


I think it's the total mass of the spacecraft (M+P). I'm not entirely sure. This is from a USAD Science section study guide.
 
  • #4
Biosyn said:
I think it's the total mass of the spacecraft (M+P). I'm not entirely sure. This is from a USAD Science section study guide.
Can you provide a link or is it behind a paywall?
 
  • #5
haruspex said:
Can you provide a link or is it behind a paywall?

It's behind a paywall. :/
 

1. What is the rocket equation and why is it important in space travel?

The rocket equation is a mathematical formula that calculates the velocity and distance a rocket can travel based on its mass, the mass of its fuel, and the speed at which it expels that fuel. It is important in space travel because it allows engineers to design rockets that can reach desired destinations and carry necessary payloads.

2. What is "mass infinity" in the context of the rocket equation?

"Mass infinity" is a theoretical concept used in the rocket equation to represent the total mass of the rocket and its fuel. It assumes that the rocket will continue to expel fuel until it reaches an infinite distance, allowing for a more accurate calculation of the rocket's performance.

3. How does the rocket equation take into account the changing mass of a rocket as it expels fuel?

The rocket equation uses the concept of specific impulse, which is a measure of how efficiently a rocket can use its fuel. As the rocket expels fuel, its mass decreases, but the specific impulse also decreases. This change in specific impulse is accounted for in the equation to accurately calculate the rocket's performance.

4. Can the rocket equation be used for all types of rockets?

Yes, the rocket equation can be used for all types of rockets, including liquid-fueled, solid-fueled, and hybrid rockets. However, it may need to be modified for certain types of propulsion systems, such as ion thrusters, which have a continuous rather than instantaneous exhaust.

5. How does the rocket equation impact the design and operation of rockets?

The rocket equation plays a crucial role in the design and operation of rockets. Engineers use it to determine the amount of fuel needed for a rocket to reach a desired destination and carry a specific payload. It also helps in calculating the maximum payload capacity of a rocket and the maximum distance it can travel. Additionally, the rocket equation is used to optimize the efficiency and performance of a rocket's propulsion system.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
180
  • Introductory Physics Homework Help
Replies
10
Views
620
  • Introductory Physics Homework Help
Replies
1
Views
809
  • Introductory Physics Homework Help
Replies
2
Views
980
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
772
  • Introductory Physics Homework Help
Replies
2
Views
637
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
793
Back
Top