In a drawing that represents a scale model of the solar system, the sun is placed at the center and the planets are shown orbiting in circles around it. While in reality Mars is 1.5 AU away from the sun, in the model Mars appears at 30 cm from it. This means that the scale of the model is 1 AU = 20 cm.
Neptune is 30 AU away from the sun. Taking into consideration where the planets may be shown in their orbits, what is the maximum possible distance that can be drawn between Mars and Neptune in the scale model?
KEY: Approximate Distance= AD
Scale Model:
Planet AD(km) AD (AU) AD Scale 1AU= 2cm
Mercury 58,000,000 0.4 0.8
Venus 108,000,000 0.7 1.4
Earth 150,000,000 1 2
Mars 228,000,000 1.5 3.0
Jupiter 778,000,000 5.2 10.4
Saturn 1,427,000,000 9.5 19.0
Uranus 2,871,000,000 19.2 38.4
Neptune 4,498,000,000 30 60.0
A: 570cm
B: 630cm
C: 28.5cm
D: 1.5 cm
My guess is A
max is when they are on opposite sides of the Sun
... not the same side
I need answers
Oh, you're a brave one, going for the highest option! But I'm sorry to say that your guess is incorrect. The correct answer is C: 28.5cm. In the scale model, Mars is positioned at 30cm and Neptune is 30 AU away from the sun, which gives us a maximum distance of 30cm - 3cm (representing Mars) = 27cm. So the maximum possible distance that can be drawn between Mars and Neptune in the scale model is 27cm. Keep those brain gears turning!
To determine the maximum possible distance that can be drawn between Mars and Neptune in the scale model, we need to find the difference in their distances from the sun and convert it to the scale of the model (1 AU = 20 cm).
Given that Mars is 1.5 AU away from the sun in reality and appears at 30 cm in the model, we can calculate its distance in the model as follows:
Distance of Mars in the model = 1.5 AU × 20 cm/AU = 30 cm
Similarly, we can calculate the distance of Neptune in the model using its distance from the sun in reality:
Distance of Neptune in the model = 30 AU × 20 cm/AU = 600 cm
Now, to find the maximum possible distance between Mars and Neptune in the scale model, we subtract the distance of Mars from the distance of Neptune:
Maximum distance between Mars and Neptune in the model = Distance of Neptune - Distance of Mars
= 600 cm - 30 cm
= 570 cm
Therefore, the correct answer is A: 570 cm.