Calculate the true weight of a 60 kg astronaut on: a) the surface of Mars, and b)the surface of Saturn.
Mass of Mars= 6.42x10^23
Mass of Saturn= 5.69x10^26
Using W=mg
W = (60 kg)(9.81m/s^2) = 558.6 N
Weight = mass x surface gravity
W (Mars) = (60 kg)(6.42x10^23)= 3.85 x 10^25
W (Saturn) = (60 kg)(5.69x10^26)= 3.41 x 10^28
To calculate the true weight of the astronaut on different celestial bodies, we need to use the formula for gravitational force:
Weight = Mass x Gravitational Acceleration
Let's calculate the weight on each of the surfaces:
a) Surface of Mars:
Gravitational Acceleration on Mars (gMars) = (6.67430 x 10^-11 N m^2/kg^2) * (6.42 x 10^23 kg) / (3.38 x 10^6 m)^2
gMars ≈ 3.71 m/s^2
Weight on Mars = 60 kg x 3.71 m/s^2
Weight on Mars ≈ 222.6 N
Therefore, the true weight of the astronaut on the surface of Mars is approximately 222.6 Newtons.
b) Surface of Saturn:
Gravitational Acceleration on Saturn (gSaturn) = (6.67430 x 10^-11 N m^2/kg^2) * (5.69 x 10^26 kg) / (6.0 x 10^7 m)^2
gSaturn ≈ 11.2 m/s^2
Weight on Saturn = 60 kg x 11.2 m/s^2
Weight on Saturn ≈ 672 N
Therefore, the true weight of the astronaut on the surface of Saturn is approximately 672 Newtons.
To calculate the true weight of the astronaut on the surface of Mars and Saturn, we need to use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where:
- F is the force of gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 N(m/kg)^2)
- m1 is the mass of the astronaut
- m2 is the mass of the celestial body (Mars or Saturn)
- r is the radius of the celestial body
a) For the surface of Mars:
To calculate the true weight on Mars, we need to find the mass of Mars, which is given as 6.42x10^23 kg. Then, we need to determine the radius of Mars, which is approximately 3,397 km (or 3,397,000 meters).
1. Calculate the force of gravity on Mars:
F_mars = G * (m1 * m2) / r^2
= (6.67430 × 10^-11 N(m/kg)^2) * (60 kg) * (6.42x10^23 kg) / (3,397,000 meters)^2
2. Calculate the weight on Mars:
Weight_mars = F_mars
b) For the surface of Saturn:
To calculate the true weight on Saturn, we need to find the mass of Saturn, which is given as 5.69x10^26 kg. Also, we need to determine the radius of Saturn, which is approximately 58,232 km (or 58,232,000 meters).
1. Calculate the force of gravity on Saturn:
F_saturn = G * (m1 * m2) / r^2
= (6.67430 × 10^-11 N(m/kg)^2) * (60 kg) * (5.69x10^26 kg) / (58,232,000 meters)^2
2. Calculate the weight on Saturn:
Weight_saturn = F_saturn
By following these steps, you can calculate the true weight of a 60 kg astronaut on the surface of both Mars and Saturn.