What is the true weight of a 60-kg astronaut on:
a) the surface of Mars?
b) the surface of Saturn?
given:
mass of Mars= 6.42x10^23
mass of Saturn= 5.69x10^26
To find the weight of an object, we need to use the formula:
Weight = mass × acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s². However, this value changes depending on the celestial body we are considering. We can calculate the weight of the astronaut on Mars and Saturn using their respective masses.
a) The surface of Mars:
To find the weight on Mars, we need to know the mass of the astronaut (60 kg) and the mass of Mars (6.42 × 10^23 kg).
Weight on Mars = mass of the astronaut × acceleration due to gravity on Mars
The acceleration due to gravity on Mars is approximately 3.71 m/s².
Weight on Mars = 60 kg × 3.71 m/s²
b) The surface of Saturn:
To find the weight on Saturn, we need to know the mass of the astronaut (60 kg) and the mass of Saturn (5.69 × 10^26 kg).
Weight on Saturn = mass of the astronaut × acceleration due to gravity on Saturn
Unfortunately, the acceleration due to gravity on Saturn is not readily available as we don't have precise measurements of its gravity. Saturn is a gas giant with a relatively low-density atmosphere, which makes the calculation of its surface gravity complex. Thus, we currently do not have enough data to accurately estimate the acceleration due to gravity on Saturn's surface.
So, for part b), we cannot determine the true weight of a 60-kg astronaut on the surface of Saturn without more information on its surface gravity.
To calculate the weight of the astronaut on the surface of Mars and Saturn, we need to use the equation for gravitational force:
Weight = mass x gravitational acceleration
a) Surface of Mars:
The mass of the astronaut is given as 60 kg, and the mass of Mars is given as 6.42 x 10^23 kg. The gravitational acceleration on Mars is approximately 3.71 m/s^2.
Weight on Mars = mass x gravitational acceleration
= 60 kg x 3.71 m/s^2
≈ 222.6 N
Therefore, the weight of the 60 kg astronaut on the surface of Mars would be approximately 222.6 Newtons.
b) Surface of Saturn:
The mass of the astronaut is still 60 kg, but this time we need to use the mass of Saturn, which is given as 5.69 x 10^26 kg. The gravitational acceleration on Saturn is approximately 10.4 m/s^2.
Weight on Saturn = mass x gravitational acceleration
= 60 kg x 10.4 m/s^2
≈ 624 N
Hence, the weight of the 60 kg astronaut on the surface of Saturn would be approximately 624 Newtons.