Two satellites are in orbit around Mars with the same orbital radius and same velocity. Satellite 2 has twice the mass of satellite 1. The radial acceleration of satellite 2 has

Question

BlackTom AI · Accepted Answer

Question restatement: Two satellites share the same orbital radius and velocity around Mars, but Satellite 2 has twice the mass of Satellite 1. The question asks about the radial (centripetal) acceleration of Satellite 2.

Option 1: 'the same magnitude as the radial acceleration of satellite 1.' This is correct because centrifugal/centripetal acceleration in orbital motion depends on velocity and radius via a_r = v^2 / r. Mass does not appear in this expression, so changing the mass while keeping v and r constant leaves a_r unchanged.

Option 2: 'half the magnitude of the radial acceleration of satellite 1.' This would imply a dependence on mass or some other factor, but the standard centripetal relation shows a_r is independent of mass. Therefore this is incorrect.

Option 3: 'twice the magnitude of the radial acceleration of satellite 1.' Again, mass is not a factor in the centripetal formula, so doubling the mass would not double the acceleration. This option is incorrect.

Option 4: 'four times the magnitude of the radial acceleration of satellite 1.' Like the previous two, this ignores the mass dependence and misapplies the relationship. This option is incorrect.

Additional clarification: In orbital mechanics, if two bodies share the same orbit (same r) and move with the same speed, they experience the same centripetal acceleration, regardless of their masses. The gravitational force providing this acceleration scales with mass, but the resulting acceleration itself is mass-independent due to F = m a and F = GMm/r^2 yielding a = GM/r^2 for a circular orbit, where M is the central mass (Mars) and m cancels out in the acceleration expression. Therefore, the correct understanding is that mass does not affect the radial acceleration in this scenario.

Two satellites are in orbit around Mars with the same orbital radius and same velocity. Satellite 2 has twice the mass of satellite 1. The radial acceleration of satellite 2 has 单项选择题

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