How much would a 80kg astronaut weigh on Earth? How much would they weigh 500 km above the surface of the Earth?
Thank you!
on Earth, weight= mg
at the higher altitude,
weight= mg* (re/(re+800))^2 where re is the radius of earth in km.
80 * 9.81 = weight on surface where R = Rearth
weight * R^2 = constant = G m M
weight at Rearth +500,000 meters
weight*(Rearth+5*10^5)^2 = 80*9.81 * Rearth^2
so
weight up there = 80*9.81 (Rearth)^2/(Reart+5*10^5)^2
To calculate the weight of an object, you can use the formula:
Weight = mass × acceleration due to gravity
On Earth, the acceleration due to gravity is approximately 9.8 m/s².
1. Weight on Earth:
Weight = 80 kg × 9.8 m/s²
Weight on Earth = 784 N
So, an 80 kg astronaut would weigh approximately 784 Newtons on Earth.
2. Weight 500 km above the surface of the Earth:
To calculate the weight at this height, we need to consider that the strength of gravity decreases as you move farther from the Earth's surface. The formula for the acceleration due to gravity at a certain height (h) above the surface of the Earth is:
g' = g / (1 + h / R)²
Where:
g' is the adjusted acceleration due to gravity,
g is the acceleration due to gravity on the surface of the Earth, and
R is the radius of the Earth.
Using this formula, we can calculate the weight of the astronaut 500 km above the surface of the Earth:
Weight 500 km above Earth
= mass × acceleration due to gravity at 500 km above Earth's surface
Roughly, the radius of the Earth (R) is 6,371 km.
Weight 500 km above Earth
= 80 kg × (9.8 m/s²) / (1 + 500,000 m / 6,371,000 m)²
Now, let's perform the calculation:
Weight 500 km above Earth
= 80 kg × 9.8 m/s² / (1 + 0.0785)²
≈ 624 N
So, an 80 kg astronaut would weigh approximately 624 Newtons 500 km above the surface of the Earth.
To determine the weight of an object, we need to consider the force of gravity acting on it. On Earth's surface, the acceleration due to gravity is approximately 9.8 m/s^2.
To calculate the weight of the 80kg astronaut on Earth, we can use the formula:
Weight = mass × acceleration due to gravity
Weight = 80 kg × 9.8 m/s^2
Weight ≈ 784 Newtons
Therefore, the astronaut would weigh approximately 784 Newtons on the surface of the Earth.
Now, let's calculate the weight of the astronaut 500 km above the surface of the Earth. Since the distance is significant, we need to consider the variation in the acceleration due to gravity with distance from the Earth's surface.
The acceleration due to gravity decreases as you move away from the Earth's surface. According to the inverse square law, the acceleration due to gravity decreases by a factor of (1/R^2), where R is the distance from the center of the Earth.
Using this information, we can calculate the effective acceleration due to gravity at a height of 500 km:
Acceleration due to gravity at the Earth's surface = 9.8 m/s^2
Distance from Earth's surface = 500 km = 500,000 meters
Effective acceleration due to gravity at 500 km:
(9.8 m/s^2) × (1 / (1 + (500,000 / 6,371,000) )^2 )
≈ 8.693 m/s^2
Now, we can use the formula to calculate the weight of the astronaut 500 km above the Earth's surface:
Weight = mass × acceleration due to gravity
Weight = 80 kg × 8.693 m/s^2
Weight ≈ 695.44 Newtons
Therefore, the astronaut would weigh approximately 695.44 Newtons 500 km above the surface of the Earth.