Question

14. It takes satellite A 7 days to complete one full orbit around a planet, at a distance of 5.0 units. Satellite B orbits it in 6 days. How far is it from the planet?

Answer 1

Answer:

it from the planet is 4.51 unit

Explanation:

given data

time t1 = 7 days

distance a1= 5.0 units

time t2 = 6 days

to find out

How far is it from the planet

solution

we know that from Kepler second law of planetary motion

T² is directly proportional to a³

so T² = K a³   ...........1

here for for both time we can say

$\frac{T1^2}{T2^2}= \frac{K a1^3}{K a2^3}$

a2³ = a1³ × $\frac{T2^2}{T1^2}$

a2³ = 5³ × $\frac{6^2}{7^2}$

a2³ = 4.51 unit

so it from the planet is 4.51 unit