The International Space Station (ISS) orbits Earth in a nearly circular orbit that is 345 km above Earth's surface.

1) How many hours does it take for the ISS to make each orbit? (Express your answer to three significant figures.)

2) Some of the experiments performed by astronauts in the ISS involve the effects of "weightlessness" on objects. What gravitational force does Earth exert on a 13.0-kg object in the ISS? Express your answer in newtons. (Express your answer to three significant figures.)

3) What gravitational force does Earth exert on a 13.0-kg object in the ISS? Express your answer as a fraction of the force that Earth would exert on the object at Earth's surface. (Express your answer to three significant figures.) (in %)

1) v = 7.70 10³ m/s, 2) F = 115 N and 3) (F/W) % = 90.2%

Explanation:

1) To solve the problem let's use Newton's second law where force is gravitational force and acceleration is centripetal

F = ma.

F = G m M / r²

a = v² / r

G m M / r² = m v² / r

G M / r = v²

Let's look for the distance is the distance from the surface of the has to the station 345 103 m plus the radius of the Earth

r = Re + 345 103

r = 6.37 10⁶ + 3.45 10⁵

r = 6.715 10⁶ m

Let's calculate the speed

v = √ (6.67 10⁻¹¹ 5.98 10²⁴ / 6,715 10⁶) = √ (59,399 10⁶)

v = 7.70 10³ m/s

The speed module is constant, so we can use the uniform motion relationships

v = d / t

The distance is the length of the circle

d = 2π r

d = 2π 6.715 106

d = 42.2 10⁶ m

Let's calculate the time

t = d / v

t = 42.2 10⁶ / 7.70 10³

t = 5.48 10³ s

2) Let's use the universal gravitation equation

F = G m M / r²

F = 6.67 10⁻¹¹ 13.0 5.98 10²⁴ / (6.715 10⁶) ²

F = 11.5 10¹ N

F = 115 N

3) in this for we are asked the relationship is out with the weight of the body on earth

F / W = F / mg

F / W = 115 / (13.0 9.8)

F / W = 0.902

F / W% = 90.2%