Answer:
Based on the information provided, it can be deduced that:
- <u>The mass of Jupiter is about four times higher than the mass of saturn</u>.
Explanation:
The orbital period (name given to the time it takes for a celestial body to perform the full orbit with respect to another celestial body) is usually calculated by <u>Kepler's third law</u> (whose formula is in the attached file), where:
- a = the semi-axis of the largest orbit (that is, the longest radius in the ellipse made by the celestial body).
- μ = G * M
- G = Gravitational constant (which is always the same)
- M = the mass of the most massive body (in this case the planet).
So that the example is quite simple we will invent values without units, so that we can see the difference in mass, first, since it is inferred that jupiter is four times more massive than saturn, then a mass will be chosen for <u>Jupiter of 8</u> and a mass of <u>2 for Saturn</u> (which maintains this relationship), the <u>gravitational constant 6.674 * 10 ^ (- 11)</u> and the <u>semi-major axis</u>, since it is the same as mentioned in the statement, a value will be given of <u>2.5</u>, replacing these values you have:
1. T= 2*(3,1416) square root (2.5^(3))/(6.674 * 10 ^ (- 11))* 2 (in the case of <u>Saturn-Mimas</u>).
2. T= 2*(3,1416) square root (2.5^(3))/(6.674 * 10 ^ (- 11))* 8 (in the case of <u>Jupiter-Amalthea</u>).
And the relationship between the two values obtained is:
- 2149719.433 / 1074859.716 = <u>2</u>
Since the time ratio is double, it is found that <u>the ratio between the mass of Jupiter and that of Saturn is 4:1 approximately</u>.