# How Much Velocity Can a Spacecraft Gain by Shooting Xenon Ions?

• sander2798
In summary, Xenon 1+ ions are shot from the back of the spacecraft with high speeds, and the average speed an ion is accelerated to is 30,000 m/s. This will result in a gain in velocity of the spacecraft according to Newton's 3rd law. Calculate how many velocity a spacecraft with a mass of 1000 kg can gain by shooting away 50kg of Xenon 1+ ions.
sander2798
Hello everyone,

the problem I have to solve is as following.

You're in space and you're moving with a constant speed. Now, you want to accelerate. For this you will be using Newton's third law.

Xenon 1+ iones will be shot from the back of the spacecraft with high speeds, the avarage speed an ion will be accelerated to is 30.000 m/s. This will result in a gain in velocity of the spacecraft , according to Newton's 3rd law. Calculate how many velocity a spacecraft with a mass of 1000 kg can gain by shooting away 50kg of Xenon 1+ iones.

My attempt:

Mass of one Xenon +1 ion:
= 131.30 x 1.660538921 x 10^-27 = 2.18 x 10^-25 kg

Kinetic energy gain of ion:
1/2 mv^2 = 1/2* 2.18*10^-25 *30000^2 = 9.81*10^-17 Joule

According to Newton's third law the gain in kinetic energy of the ion should be equal to the gain in kinetic energy of the spacecraft , right? (not sure about this)

1/2 mv^2 = 1/2 * 1000 * v^2 = 9.81*10^-17
v = 4.43 * 10^-10 m/s for every ion shot

Calculating how many iones we have:
100000 / 131.30u = 761.614 mol.
761.614 * 6,022 * 10^23 = 4.586 * 10^26 iones.

Shooting away all those iones will create a gain in speed of:
4.586 * 10^26 * 4.43 * 10^-10 = 2.03 * 10^17 m/s

But since this is about a few thousand times the speed of light, I assume I did something wrong somewhere. If anyone could help me I'd be very thankful.

Sander.

sander2798 said:
According to Newton's third law the gain in kinetic energy of the ion should be equal to the gain in kinetic energy of the spacecraft , right? (not sure about this)
This is wrong. You should look up the definition on Wikipedia or something.

What you actually did here is apply the principle of conversation of energy. However. conservation of energy doesn't work the way you put it because you neglected the work of the magnetic field that accelerated the ions to begin with.

Can you think of something else that is conserved here instead?

Good for you, though, that you did a reality check at the end and realized you did something wrong.

sander2798
paisiello2 said:
This is wrong. You should look up the definition on Wikipedia or something.

What you actually did here is apply the principle of conversation of energy. However. conservation of energy doesn't work the way you put it because you neglected the work of the magnetic field that accelerated the ions to begin with.

Can you think of something else that is conserved here instead?

Good for you, though, that you did a reality check at the end and realized you did something wrong.
Thanks, now have the correct answer! (I hope :P)

## 1. What is the purpose of calculating shooting ions?

Calculating shooting ions is important for understanding the behavior and trajectory of ions in various scientific experiments. It helps scientists to predict and control the movement of ions, which is crucial for achieving desired results.

## 2. How are shooting ions calculated?

Shooting ions are typically calculated using mathematical equations and computer simulations. These equations take into account factors such as ion mass, velocity, and electric fields to determine the ion's path.

## 3. What types of experiments use shooting ion calculations?

Shooting ion calculations are used in a wide range of experiments, including mass spectrometry, particle accelerators, and ion implantation. They are also used in industrial processes such as semiconductor manufacturing.

## 4. What are the units of measurement used for shooting ion calculations?

The units of measurement used for shooting ion calculations depend on the specific parameters being calculated. Common units include meters for distance, kilograms for mass, and volts for electric fields.

## 5. How accurate are shooting ion calculations?

The accuracy of shooting ion calculations depends on the complexity of the experiment and the precision of the input data. In general, these calculations are highly accurate and are continually being improved with advancements in technology and research.

• Introductory Physics Homework Help
Replies
8
Views
4K
• Special and General Relativity
Replies
40
Views
3K
• Introductory Physics Homework Help
Replies
2
Views
3K
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
4
Views
25K
• Introductory Physics Homework Help
Replies
5
Views
10K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
2K