The nearest star to the Sun is Proxima Centauri. This star has a mass of

Question 5

(a) Define gravitational field strength. [1]

(b) The nearest star to the Sun is Proxima Centauri.

This star has a mass of 2.5 × 10²⁹ kg and is a distance of 4.0 × 10¹³ km from the Sun.

The Sun has a mass of 2.0 × 10³⁰ kg.

(i) State why Proxima Centauri may be assumed to be a point mass when viewed from the Sun. [1]

(ii) Calculate

1. the gravitational field strength due to Proxima Centauri at a distance of 4.0 × 10¹³ km, [2]

2. the gravitational force of attraction between the Sun and Proxima Centauri. [2]

(c) Suggest quantitatively why it may be assumed that the Sun is isolated in space from other stars. [2]

 [Total: 8]

Reference: Past Exam Paper – November 2016 Paper 42 Q1

Solution:

(a) Gravitational field strength is defined as the (gravitational) force acting per unit mass. 

(b)

(i)

The radius/diameter/size of Proxima Centauri is much less than the separation (of the Sun and the star (Proxima Centauri)). (Separation = 4.0 × 10¹³ km)

OR

(because) it is a uniform sphere

(ii)

1.

field strength = GM / x²

{distance should be in metre.}

field strength = (6.67×10^-11 × 2.5×10²⁹) / (4.0×10¹³ × 10³)²

field strength = 1.0 × 10^-14 N kg^-1                         

2.

{Force = mg}

force = field strength × mass

force = 1.0×10^-14 × 2.0×10³⁰  

or

force = GMm / x²

force = (6.67×10^-11 × 2.5×10²⁹ × 2.0×10³⁰) / (4.0×10¹³ × 10³)²

force = 2.0 × 10¹⁶ N

(c)

The force (of 2 × 10¹⁶ N) would have little effect on the (large) mass of the Sun and would cause a negligible acceleration (of 1.0 × 10^–14 m s^–2).

OR

Many stars are all around the Sun. The net effect of the forces/fields is zero.