Problem B.1: Altitude of the ISS – Part 2 (6 Points)

As mentioned in Problem A.2, the ISS loses altitude due to the collision with atmospheric particles. This causes the ISS to experience a drag force Fd according to the drag equation

Fd =

1

2

· ρ · Cd · A · v

2

with the atmospheric density ρ, the dimensionless drag coeicient Cd, the ISS’s cross-sectional

area A, and the ISS’s speed relative to the particles v.

Use the rate of descent from Problem A.2 to estimate

(a) the vacuum density ρ at the current position of the ISS and

(b) the total amount of matter (in kg) which collides with the ISS every day.

Note: The following constants may be helpful: the gravitational constant: 6.67 x 10-11 m3kg-1s

-2

,

the mass of Earth: 5.97 x 1024 kg, the drag coeicient of the ISS: 1.3, the cross-sectional area of

the ISS: 4800 m2

, the total mass of the ISS: 450 tons.
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