Question

Use Bode's law to determine the approximate distance between Uranus and Saturn. Show all your work which should include the entire Bode law.

Answer 1

To approximate the distance between Uranus and Saturn using Bode's law, we can use a simple formula given by a = 0.4 + 0.3n, where a represents the distance from the Sun in astronomical units (AU) and n is the position of the planetary orbit.

Step-by-step explanation:

To approximate the distance between Uranus and Saturn using Bode's law, we can use the following formula:

a = 0.4 + 0.3n

where a represents the distance from the Sun in astronomical units (AU) and n is the position of the planetary orbit counting outward from Mercury as 0. For Uranus, n = 5 and for Saturn, n = 6. Plugging in these values, we get:

Distance to Uranus (aUranus) = 0.4 + 0.3(5) = 0.4 + 1.5 = 1.9 AU

Distance to Saturn (aSaturn) = 0.4 + 0.3(6) = 0.4 + 1.8 = 2.2 AU

Therefore, the approximate distance between Uranus and Saturn is 2.2 - 1.9 = 0.3 AU.