I am learning about Space exploration. Is the critical inclination the same on every planet (in the solar system) or does it depend on the planet?
Answer: Critical inclination varies between planets.
According to this paper, https://arxiv.org/ftp/arxiv/papers/1108/1108.4639.pdf,
Most previous researches about the critical inclination were made under the assumption that the oblateness term J2 is dominant among the harmonic coefficients. This assumption is effective for most large celestial bodies, including Earth, Mars, and Moon. However, there exist some celestial bodies where the other first few harmonic coefficients are of the same order of magnitude as the oblateness term J2, or even greater than J2. For example, the J3 and J4 terms of Venus are of the same order of magnitude as J2. For these central bodies, the concept of the critical inclination is different from that of the traditional sense.
… for some cases, the value of the critical inclination is far away from that of the traditional sense or even has multiple solutions.
In addition, the critical inclination is sometimes dependent on orbital altitude, as is the case with Jupiter. https://www.mdpi.com/2226-4310/8/7/183
… if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase.