The diameters of Earth and the Sun are approximately 1.3 107 m and 1.4 109 m respectively, and the average Sun-Earth distance is 1.5 1011 m. Consider a scale model of the solar system, where Earth is represented by a peppercorn 2.3 mm in diameter. Calculate the diameter of the Sun in this model.
Use the ratio of the peppercorn to earth's diameter to find a conversion factor.
2.3 *1.4*10^9 /(1.3*10^7)
= 2.3 *(1.4/1.3) * 100 mm
To calculate the diameter of the Sun in the given scale model, we can use the ratio of the peppercorn to Earth's diameter as a conversion factor.
First, let's calculate the conversion factor by dividing the diameter of the peppercorn by the diameter of Earth:
Conversion Factor = Diameter of Peppercorn / Diameter of Earth
= 2.3 mm / 1.3 x 10^7 m
Now we need to convert the diameter of the Sun from the actual size to the scale model using the conversion factor.
Diameter of the Sun in the scale model = Conversion factor x Diameter of the Sun
To find the diameter of the Sun in the scale model, we need to multiply the conversion factor by the diameter of the Sun:
Diameter of the Sun in the scale model = Conversion Factor x Diameter of the Sun
= 2.3 mm / 1.3 x 10^7 m x 1.4 x 10^9 m
Now we can simplify this equation and calculate the diameter of the Sun in the scale model of the solar system.