\(1\) Compute the differential tidal force \(\Delta F\) exerted on the Earth by Mars when it is at opposition. Express your result as a numerical fraction of the differential tidal force exerted by the Moon:
$\Delta F_{Moon} = \frac{2GM_{moon} mR_E}{r_0^3}$
Where $r_0 = 384,000 \text{ km} = 0.00257 \text{ AU}$ is the Earth-Moon distance and $M_{Moon} = 7.2 \times 10^{22} \text{ kg}$ is the mass of the Moon.
\(2\) Repeat to find the differential tidal force exerted by Jupiter at opposition, also expressed as a fraction of $\Delta F_{Moon}$
Note \(1\) \text{``m''} in the equation is a small mass particle on the surface of the Earth, which can be assumed to be 1 kg. \text{``m''} is canceled out when the fraction or ratio is applied.
\(2\) Assume that the Moon, Earth, Mars, and Jupiter are on circular coplanar orbits
\(3\) The distance between Earth and Mars is when the two objects are at the opposition configuration. The orbital size of Earth and Mars can be found online. The same for Jupiter.
Note: the mass of Mars, Mars-Earth distance, mass of Jupiter, and Jupiter-Earth distance can be found from the Internet. Only need the ratio of tidal forces.
