To compare the gravitational force on Gallifrey with the gravitational force on Earth, we can use Newton's law of universal gravitation. The formula for gravitational force (\(F\)) between two masses is given by:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where:
- \(F\) is the gravitational force,
- \(G\) is the gravitational constant,
- \(m_1\) is the mass of the first object (the planet),
- \(m_2\) is the mass of the second object (the star),
- \(r\) is the distance between the centers of the two objects.
In your scenario:
- The mass of the star (our Sun and Gallifrey's star) is the same (\(m_2\)).
- The distance (\(r\)) between the planet and the star is also the same (the distance between Earth and the Sun).
Given that Gallifrey has a substantially larger mass (\(m_1\)) than Earth, the gravitational force on Gallifrey would be significantly greater due to the larger mass of the planet.
If we denote:
- \(m_{earth}\) as the mass of Earth,
- \(m_{gallifrey}\) as the mass of Gallifrey (where \(m_{gallifrey} > m_{earth}\)),
- The gravitational forces can be expressed as follows:
Gravitational Force on Earth:
\[ F_{earth} = G \frac{m_{earth} \cdot m_{sun}}{r^2} \]
Gravitational Force on Gallifrey:
\[ F_{gallifrey} = G \frac{m_{gallifrey} \cdot m_{sun}}{r^2} \]
Since \(m_{gallifrey} > m_{earth}\), it follows that:
\[ F_{gallifrey} > F_{earth} \]
Conclusion: The force of gravity on Gallifrey would be larger than that on Earth because the mass of Gallifrey is substantially larger than the mass of Earth, while the distance to the star remains the same for both systems. This results in a greater gravitational attraction on Gallifrey due to its larger mass.