Trajectories on Mars!

Classical Mechanics Level 1

A stone is thrown from the surface of Earth, where the acceleration due to gravity is $9.8 \text{ m/s}^2.$ The stone travels along a parabolic trajectory.

If the same stone is thrown exactly the same way from the surface of Mars, where the acceleration due to gravity is $3.7 \text{ m/s}^2,$ then the Martian trajectory is $\text{\_\_\_\_\_\_\_\_\_\_}$ the trajectory on Earth,

smaller than bigger than the same as

2 solutions

Pranshu Gaba
Dec 13, 2017

Relevant wiki: Projectile Motion

The gravity is weaker on Mars compared to Earth, so when the ball is thrown on Mars with the same velocity as on Earth, it will take more time to slow down, turn back and start falling back towards the surface. It will go higher up and further ahead on Mars compared to Earth.

explanation is commendable! @Pranshu Gaba , but there are some flaws in it. cheers!

nibedan mukherjee - 2 years, 7 months ago

Thanks! What flaws did you find in my explanation?

Pranshu Gaba - 2 years, 7 months ago

First of all nyc to knw u mate! ur exp. is gr8 no offence! Virtually all major members of the solar system are approximately spherical in shape; and a spherical body will produce a force of attraction precisely like that of a single mass point located at the center of the body. Therefore, the fundamental problem is that of motion under the gravitational influence of a mass concentrated at a point. Time frame is irrelevant here. If the presence is in synodic skolem (as of mars), the particle will experience a anti-gravity retrograde motion.

nibedan mukherjee - 2 years, 7 months ago

I don't even know how that's at all confusing.

Erin Smith - 1 year, 2 months ago

Rohan Joshi
Oct 7, 2020

The time taken for a projectile to return to the ground is 2u sinθ/g, where u is the initial velocity and θ is the angle of launch. Since g on Mars is less than g on Earth ,the projectile takes longer to fall back. Also, the maximum height reached and horizontal distance covered are u^2 sin^(2)θ/2g and u^2*sin(2θ)/g respectively, both of which are inversely proportional to g.

Trajectories on Mars!

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