Find the magnitude of the gravitational attraction force that the earth exerts on a 62-kilogram astronaut who is 8.00 X 10^7 meters away from the center of the earth.
Useful numbers: M^earth=5.98 X 10^24kg; G=6.67 X 10^-11 N*m^2kg^-2
Please walk me through your steps, don't just suggest a formula-thank you.
This is only one step - The Universal Law of Gravitation
F=G• m•M/(R)²
R= 8.00 X 10^7 m,
m=62 kg
Question though, the answer in the book says that the answer is 3.9 Newtons...do I need to convert this answer or something?
F=G• m•M/(R)² =
=6.67•10^-11•62•5.98•10^24/(8• 10^7)²=3.87 N ≈3.9 N
Fabulous! Thank you!!!
To find the magnitude of the gravitational attraction force that the earth exerts on the astronaut, we can use Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where F is the force of gravitational attraction, G is the gravitational constant, m1 is the mass of the first object (in our case, the astronaut), m2 is the mass of the second object (in our case, the earth), and r is the distance between the centers of the two objects.
Let's break down the steps:
Step 1: Identify the given values:
- Mass of the astronaut (m1) = 62 kg
- Mass of the Earth (m2) = 5.98 × 10^24 kg
- Distance between the astronaut and the center of the Earth (r) = 8.00 × 10^7 meters
- Gravitational constant (G) = 6.67 × 10^-11 N*m^2kg^-2
Step 2: Square the distance of separation:
- Square the distance (r^2) = (8.00 × 10^7 meters)^2 = 6.40 × 10^15 meters^2
Step 3: Plug in the values into the formula:
- F = (6.67 × 10^-11 N*m^2kg^-2) * (62 kg * 5.98 × 10^24 kg) / (6.40 × 10^15 meters^2)
Step 4: Simplify the expression:
- Multiply the masses of the astronaut and the Earth: (62 kg * 5.98 × 10^24 kg) = 3.71 × 10^26 kg
- Divide the multiplied mass by the square of the distance: (3.71 × 10^26 kg) / (6.40 × 10^15 meters^2)
= 5.80 × 10^10 kg*m/s^2
Step 5: Multiply the value by the gravitational constant:
- F = (6.67 × 10^-11 N*m^2kg^-2) * (5.80 × 10^10 kg*m/s^2)
= 3.88 N
Therefore, the magnitude of the gravitational attraction force that the Earth exerts on the 62-kilogram astronaut, who is 8.00 × 10^7 meters away from the center of the Earth, is approximately 3.88 Newtons.