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Gravitational acceleration is the rate at which objects accelerate towards the center of a celestial body, such as Earth or another planet, due to gravity. On Earth, this acceleration is typically denoted as "g" and has a value of approximately 9.8 meters per second squared (m/s²). This means that if you drop an object, its speed increases by 9.8 m/s every second
In projectile motion, gravitational acceleration affects how long an object stays in the air and plays a crucial role in determining the vertical motion. Although horizontal motion is constant, vertical motion is subject to gravity, causing the projectile to follow a curved trajectory.
Gravitational acceleration can vary significantly on other planets due to their different masses and radii. Therefore, understanding how gravity affects motion helps astronauts and scientists anticipate how objects will behave on different planetary bodies.

The horizontal range of a projectile is the total horizontal distance an object travels while in motion. It is influenced by two primary factors: initial velocity and time of flight. In our exercise, the initial horizontal speed of the ball remains constant both on Earth and Planet X.
The range on Earth can be represented by the formula:\[ R = v_0 \times t, \] where \( v_0 \) is the initial horizontal velocity, and \( t \) is the time of flight. Since the horizontal speed remains the same, any change in range must be due to changes in time of flight, which is affected by gravitational acceleration.
On Planet X, the range was observed to be 2.76 times greater than on Earth, indicating that the projectile’s time in the air was also substantially increased due to the planet's weaker gravity.

The time of flight refers to how long a projectile remains in the air. It depends on the initial velocity and the gravitational acceleration of the environment in which the projectile is launched.
For a ball rolling off a table, the time of flight is determined solely by the gravitational acceleration and the height of the table. The equation is expressed as:\[ t = \sqrt{\frac{2h}{g}}, \] where \( h \) is the table height and \( g \) is the gravitational acceleration.
On Planet X, with a longer flight time required for a greater range and weaker gravitational pull, the time of flight increases. The weaker gravitational acceleration on Planet X means that objects spend more time in the air compared to Earth's considerably stronger gravitational pull. This is why the ball was able to travel a much greater horizontal distance of 2.76 times that on Earth.

Comparing gravitational forces between planets helps us understand how gravity influences phenomena such as projectile motion and everyday experiences. Although Captain Curious performed the same experiment on Earth and Planet X, results differed due to the planets’ differing gravitational fields.
In our scenario, Planet X's gravitational acceleration was found to be significantly weaker than Earth's — approximately 1.287 m/s² compared to Earth’s 9.8 m/s². This weaker acceleration means that objects fall more slowly on Planet X, allowing them to travel farther horizontally during the same fall time.
Comparative gravitational studies are essential for space exploration, ensuring equipment and vehicles are designed to operate under various planetary conditions. Understanding these differences also aids in planning missions and conducting experiments on celestial bodies throughout our solar system.