Question

On a scale where the Sun is about the size of a grapefruit (7 centimeters) and the Earth is about 15 meters away, how far away from Earth is the nearest star? A) about 7×10−2 meters. B) about 2×101 meters. C) about 5×103 meters. D) about 5×106 meters. E) There is not enough information to tell.

Answer 1

By using ratios:-

actual distance between the sun and the earth = 1.496 * 10^8 kms

given distance between the sun and the earth = 0.015 kms

actual distance between the earth and nearest star (Proxima Centauri) = 4.2441 light years (approximately)

                                                                                                                    = 4.2441 * (9460730472580800 meters)

                                                                                                                    = 4.015 * 10^16 meters

                                                                                                                    = 4.015 * 10^13 kms

therefore, 0.015/x = (1.496 * 10^8)/(4.015 * 10^13)

                  x = 4026 kms = 4026 * 10^3 meters = 5 * 10^6 meters (approximately)

the answer is option D) about 5×10^6 meters