Question

1. using the second scale

(1 m = 3,000,000 km)
you used for distance in your
model of the solar system:
a) how far away would proxima
centauri be from earth?
b) how far away would the
andromeda galaxy be on your
scale, given that andromeda is
767 kiloparsecs or 2.5 million
light-years away?

1. the moon is 384,000 km from

earth and has a diameter of
3476 km. calculate the diameter
of the moon and its distance from
the earth using the scale of the
model you developed in the
investigate section.

Explanation:

Step1: Define scale conversion

Scale: $1\ \text{m} = 3,000,000\ \text{km} \implies 1\ \text{km} = \frac{1}{3,000,000}\ \text{m}$

Step2: Get Proxima Centauri distance

Proxima Centauri is ~4.24 light-years = $4.01×10^{13}\ \text{km}$

Step3: Calculate scaled distance (a)

$\text{Scaled distance} = 4.01×10^{13} \times \frac{1}{3×10^6} \approx 4.24\ \text{m}$

Step4: Convert Andromeda distance to km

2.5 million light-years = $2.37×10^{19}\ \text{km}$

Step5: Calculate scaled distance (b)

$\text{Scaled distance} = 2.37×10^{19} \times \frac{1}{3×10^6} \approx 2.68×10^8\ \text{m}$

Step6: Calculate scaled Moon diameter

$\text{Scaled diameter} = 3476 \times \frac{1}{3×10^6} \approx 1.16×10^{-3}\ \text{m}$

Step7: Calculate scaled Moon-Earth distance

$\text{Scaled distance} = 384000 \times \frac{1}{3×10^6} = 0.128\ \text{m}$

Answer:

a) ~4.24 meters
b) ~2.68×10⁸ meters

1. Scaled Moon diameter: ~1.16×10⁻³ meters; Scaled Moon-Earth distance: ~0.128 meters