The force of gravity at Earth's surface on an astronaut is 634N. What is the force of gravity on the same person at each of the following distances, in multiples of Earth's radius, from the centre of Earth?
A)2 B)5 C)10 D)17.2
If
mg = GmM/R^2 = 634 N,
then I believe that
(mg)1 = GmM/(2R)^2 = 634/4 =158.2 N
(mg)2 =634/25 =25.36 N
(mg)3 =634/100= 6.34 N
(mg)4 =634/(17.2)^2 = 2.14 N
All changes are due to the changes in "g".
Hmmmm. I am not certain how the force of gravity can ever be greater on an astronaut at multiples of earth radii. It gets smaller as one goes out.
To find the force of gravity at different distances from the center of the Earth, we can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
where:
F is the force of gravity
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 / kg^2)
m1 and m2 are the masses of the two objects (in this case, the person's mass and the mass of the Earth)
r is the distance between the center of the Earth and the person
Given that the force of gravity on the astronaut at Earth's surface is 634 N, we can use this as a reference to find the force at other distances.
Let's calculate the force of gravity at each distance:
A) At a distance of 2 times Earth's radius from the center of the Earth:
The distance (r) is equal to 2 times the Earth's radius.
F = (G * m1 * m2) / r^2
F2 = (G * m1 * m2) / (2R)^2
B) At a distance of 5 times Earth's radius from the center of the Earth:
The distance (r) is equal to 5 times the Earth's radius.
F5 = (G * m1 * m2) / (5R)^2
C) At a distance of 10 times Earth's radius from the center of the Earth:
The distance (r) is equal to 10 times the Earth's radius.
F10 = (G * m1 * m2) / (10R)^2
D) At a distance of 17.2 times Earth's radius from the center of the Earth:
The distance (r) is equal to 17.2 times the Earth's radius.
F17.2 = (G * m1 * m2) / (17.2R)^2
Remember, the mass of the astronaut (m1) remains the same, and the mass of the Earth (m2) also remains the same.
Now, let's calculate the force at each distance using the formula and the given values.
To find the force of gravity at different distances from the center of the Earth, we need to use the formula for the force of gravity:
F = G * (m1 * m2) / r^2
Where:
F is the force of gravity,
G is the gravitational constant (approximately 6.67430 x 10^-11 Nm^2/kg^2),
m1 and m2 are the masses of the two objects (in this case, the mass of the astronaut and the mass of the Earth),
r is the distance between the centers of the two objects.
Let's assume the mass of the astronaut remains constant.
First, we need to determine the radius of the Earth. The average radius of the Earth is approximately 6,371 kilometers.
A) For a distance of 2 times the Earth's radius (2 * 6,371 km):
r = 2 * 6,371 km = 12,742 km
Now we can calculate the force of gravity at this distance:
F = G * (m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2) * (m1 * m2) / (12,742 km)^2
B) For a distance of 5 times the Earth's radius (5 * 6,371 km):
r = 5 * 6,371 km = 31,855 km
F = G * (m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2) * (m1 * m2) / (31,855 km)^2
C) For a distance of 10 times the Earth's radius (10 * 6,371 km):
r = 10 * 6,371 km = 63,710 km
F = G * (m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2) * (m1 * m2) / (63,710 km)^2
D) For a distance of 17.2 times the Earth's radius (17.2 * 6,371 km):
r = 17.2 * 6,371 km = 109,507.2 km
F = G * (m1 * m2) / r^2
F = (6.67430 x 10^-11 Nm^2/kg^2) * (m1 * m2) / (109,507.2 km)^2
By plugging the numbers into these equations, you can calculate the force of gravity at each distance.