Q12. How big is a Moon? How big is a Mars? What is therefore the weight of the person from Q11 on the Moon? What is the person's weight on Mars?
weight = Fgravity = G * Mobject * Mplanet / Rplanet^2
where G = 6.67 * 10^-11 Newtons m^2/kg^2
For moon:
Mmoon = 7.35 * 10^22 kg
Rmoon = 1.74 * 10^6 meters
For Mars:
Mmarss = 6.42 * 10^23 kg
Rmars = 3.43 * 10^6 meters
By the way for earth
Mearth = 5.98 * 10^24 kg
Rearth= 6.38 * 10^6 meters
weight of whatever on the moon should come out around 1/6 of the weight on earth
Step 1: How big is the Moon?
The Moon has a diameter of about 3,474 kilometers (2,159 miles). It is approximately 1/4th the size of Earth.
Step 2: How big is Mars?
Mars has a diameter of about 6,792 kilometers (4,212 miles). It is roughly half the size of Earth.
Step 3: Determining weight on the Moon.
To calculate the weight of a person on the Moon, we need to know their weight on Earth. Let's assume the person from question 11 weighs 70 kilograms on Earth.
The surface gravity on the Moon is approximately 1/6th of Earth's gravity. Using this information, we can calculate their weight on the Moon as follows:
Weight on the Moon = (Weight on Earth) * (Moon's gravitational acceleration / Earth's gravitational acceleration)
= 70 kilograms * (1/6)
= 11.67 kilograms (rounded to two decimal places)
Therefore, the person's weight on the Moon would be approximately 11.67 kilograms.
Step 4: Determining weight on Mars.
Using the same principle, we can calculate the person's weight on Mars. The surface gravity on Mars is approximately 3/8th of Earth's gravity.
Weight on Mars = (Weight on Earth) * (Mars' gravitational acceleration / Earth's gravitational acceleration)
= 70 kilograms * (3/8)
= 26.25 kilograms (rounded to two decimal places)
Therefore, the person's weight on Mars would be approximately 26.25 kilograms.
To determine the sizes of the Moon and Mars, as well as the weight of a person on these celestial bodies, we can use the following steps:
1. Moon Size: The Moon has a diameter of approximately 3,474 kilometers (2,159 miles).
2. Mars Size: Mars has a diameter of about 6,779 kilometers (4,212 miles).
3. Calculate the person's weight on the Moon: To determine the weight of a person on the Moon, we need to apply the concept of gravitational force. The gravitational force on the Moon is about 1/6th of that on Earth.
If the person's weight on Earth is given, we can calculate their weight on the Moon using the following formula:
Weight on the Moon = (Weight on Earth) * (Moon's gravitational force)
4. Calculate the person's weight on Mars: Similarly, to determine the person's weight on Mars, we need to consider the gravitational force on Mars. It is around 3/8th of Earth's gravitational force.
The formula to calculate the person's weight on Mars is:
Weight on Mars = (Weight on Earth) * (Mars' gravitational force)
By plugging in the weight from Q11 into the respective formulas, you can find the person's weight on the Moon and Mars.