On a scale where the Sun is about the size of a grapefruit (7 centimeters) and...

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Physics

On a scale where the Sun is about the size of a grapefruit (7centimeters) and the Earth is about 15 meters away, how far awayfrom Earth is the nearest star? A) about 7Ã—10âˆ’2 meters. B) about2Ã—101 meters. C) about 5Ã—103 meters. D) about 5Ã—106 meters. E)There is not enough information to tell.

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3.7 Ratings (586 Votes)

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)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 4.2441 * (9460730472580800 meters)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 4.015 * 10^16 meters

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 4.015 * 10^13 kms

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

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

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

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