Problem-solving worksheet challenging students to calculate and compare the distances of our nearest stars.

Let’s solve each part of the problem step by step.

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1) Write down the distance of each star from our planet to the nearest light year in the table.

We need to round each distance (in light years) to the nearest whole number.

- Alpha Centauri A: 4.37 → 4
- Barnard’s Star: 5.96 → 6 (since 0.96 ≥ 0.5)
- Lalande 21185: 8.29 → 8
- Procyon: 11.4 → 11
- Proxima Centauri: 4.24 → 4
- Ross 154: 9.68 → 10
- Sirius A: 8.58 → 9 (since 0.58 ≥ 0.5)
- Wolf 359: 7.78 → 8

✔ So, the completed “DISTANCE (nearest light year)” column is:

| STAR | DISTANCE (light years) | DISTANCE (nearest light year) |
|-------------------|------------------------|-------------------------------|
| Alpha Centauri A | 4.37 | 4 |
| Barnard’s Star | 5.96 | 6 |
| Lalande 21185 | 8.29 | 8 |
| Procyon | 11.4 | 11 |
| Proxima Centauri | 4.24 | 4 |
| Ross 154 | 9.68 | 10 |
| Sirius A | 8.58 | 9 |
| Wolf 359 | 7.78 | 8 |

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2) Write down the order of stars from our planet, from 1 to 8, with 1 being the closest and 8 the furthest away.

We need to rank the stars by their actual distances (not rounded), from smallest to largest.

List of stars with exact distances:

- Proxima Centauri: 4.24 → closest
- Alpha Centauri A: 4.37
- Barnard’s Star: 5.96
- Wolf 359: 7.78
- Lalande 21185: 8.29
- Sirius A: 8.58
- Ross 154: 9.68
- Procyon: 11.4 → furthest

✔ So, the “ORDER OF STARS” column is:

| STAR | ORDER OF STARS |
|-------------------|----------------|
| Alpha Centauri A | 2 |
| Barnard’s Star | 3 |
| Lalande 21185 | 5 |
| Procyon | 8 |
| Proxima Centauri | 1 |
| Ross 154 | 7 |
| Sirius A | 6 |
| Wolf 359 | 4 |

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3) How much further is Ross 154 away from us than Barnard’s Star?

Subtract Barnard’s Star’s distance from Ross 154’s distance:

> 9.68 - 5.96 = 3.72 light years

✔ Answer: 3.72 light years

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4) How much closer is Proxima Centauri to us than Wolf 359?

Subtract Proxima Centauri’s distance from Wolf 359’s distance:

> 7.78 - 4.24 = 3.54 light years

✔ Answer: 3.54 light years

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5) How much further is Procyon away from us than Sirius A?

Subtract Sirius A’s distance from Procyon’s distance:

> 11.4 - 8.58 = 2.82 light years

✔ Answer: 2.82 light years

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6) Tyger says “The distance to Proxima Centauri and back is less than the distance to Sirius A.” Is this true?

- Distance to Proxima Centauri and back = 2 × 4.24 = 8.48 light years
- Distance to Sirius A = 8.58 light years

Compare: 8.48 < 8.58 → True

✔ Answer: Yes, it is true.

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7) Tyger says “In the time it takes light to travel from Earth to Procyon, it could get to Barnard’s Star and back again.” Is he correct?

Let’s check:

- Time for light to go to Procyon = 11.4 years (one way)
- Distance to Barnard’s Star and back = 2 × 5.96 = 11.92 light years

So, light would take 11.92 years to go to Barnard’s Star and back.

But light only has 11.4 years (the time to reach Procyon).

Since 11.4 < 11.92, light cannot make the round trip to Barnard’s Star in that time.

✔ Answer: No, he is not correct.

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## ✔ Final Answers Summary:

1. Rounded distances:
Alpha Centauri A: 4
Barnard’s Star: 6
Lalande 21185: 8
Procyon: 11
Proxima Centauri: 4
Ross 154: 10
Sirius A: 9
Wolf 359: 8

2. Order of stars (closest=1 to furthest=8):
Proxima Centauri: 1
Alpha Centauri A: 2
Barnard’s Star: 3
Wolf 359: 4
Lalande 21185: 5
Sirius A: 6
Ross 154: 7
Procyon: 8

3. Ross 154 is 3.72 light years further than Barnard’s Star.
4. Proxima Centauri is 3.54 light years closer than Wolf 359.
5. Procyon is 2.82 light years further than Sirius A.
6. Tyger’s statement about Proxima Centauri and back vs. Sirius A: True
7. Tyger’s statement about light to Procyon vs. Barnard’s Star and back: False

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You can now fill in the table and answer all questions confidently! 🌟