Question

A space probe is fired from the earth towards the sun, how far from the earth will the sun's gravitational pull on the probe balance the earth's pull?(mass of the sun ms=2×10^30 kg,mass of the earth me=6×10^24 kg, distance between the earth and sun r=1.5×10^11 m )​

Answer 1

Dear Student,

● Answer -

x = 2.6×10^8 m

◆ Explanation -

# Given -

r = 1.5×10^11 m

Ms = 2×10^30 kg

Me = 6×10^24 kg

# Solution -

Let x be distance from earth at which gravitational pull from earth and sun balances.

G.F.(sun) = G.F.(earth)

GMsm/(r-x)^2 = GMem/x^2

Ms/(r-x)^2 = Me/x^2

Ms × x^2 = Me × (r-x)^2

2×10^30 × x^2 = 6×10^24 × (r-x)^2

10^6 × x^2 = 3 × (r-x)^2

As r >> x, (r-x)^2 ~ r^2.

10^6 × x^2 = 3 × r^2

x^2 = 3 × (1.5×10^11)^2 / 10^6

x^2 = 6.75×10^16

x = 2.6×10^8 m

Hence, gravitational pull balanced at 2.6×10^8 m from earth.

Thanks dear...

Answer 2

tq for answer my friend. your answer is is 2.6 × 10^8 metre