Question

1. A spacecraft made 58376 orbits of the Earth and travelled a distance
of 2.656 x 10^8 kilometres.

(a) Calculate the distance travelled in I orbit correct to the nearest kilometre.

(b) The orbit of the spacecraft is a circle. Calculate the radius of the orbit.

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Answer 1

Given info : A spacecraft made 58376 orbits of the Earth and travelled a distance of 2.656 x 10^8 kilometres.

To find :

(a) calculate the distance travelled in 1 orbit to the nearest kilometre.

(b) The orbit of the spacecraft is a circle. calculate the radius of the orbit.

solution : distance travelled in 1 orbit = total distance travelled by the spacecraft/no of revolution of orbit.

= (2.656 × 10^8)/(58376)

= 4.55 × 10³ km

Therefore the distance travelled in one orbit is 4.55 × 10³ Km.

now the radius of orbit is r.

then, distance travelled in 1 orbit = 4.55 × 10³ km

⇒2πr = 4.55 × 10³ km

⇒r = (4.55)/(2 × 3.14) × 10³ = 0.7245 × 10³ = 724.5 km

Therefore the radius of the orbit is 724.5 km (approximately).