A meteoroid is moving towards a planet. It has mass m = 0.86x10 kg and speed v1

(a) PE = – G×M×m/R

(b) PE1 = –1.89×10¹⁷J

(c) E = 1/2mv² + (– G×M×m/R)

(d) E1 = 9.50×10²³J

(e) E = 1/2mv² + (– G×M×m/R)

Explanation:

Given

m = mass of meteoroid = 0.86×10⁹kg

v1 = speed of meteoroid at R1 = 4.7×10⁷m/s

R1 = distance of meteoroid from the center of the planet = 2.3×10⁷m

M = mass of the planet = 7.6×10²⁵kg

R = radius of planet = 0.74×10⁷m

(a) PE = – G×M×m/R

The above equation has a negative sign because the force of gravity between the planet and the meteoroid is directed inward towards the planet and the potential energy decreases in the direction of the increasing force. So the closer the meteoroid gets to the planet the lesser becomes it's potential energy.

(b) We are required to calculate the Potential energy at R1, PE1

PE1 = – G×M×m/R1 =

– (6.67×10-¹¹ × 7.6×10²⁵ × 0.86×10⁹)/(2.3×10⁷)

= –1.89×10¹⁷J

(c) E = total mechanical energy which is a sum of the potential and kinetic energy at any given position

E = KE + PE

E = 1/2mv² + – G×M×m/R

(d) E1 is the total mechanical energy at R1

E1 = 1/2mv1² + (– G×M×m/R1)

E1 = 1/2×0.86×10⁹×(4.7×10⁷)² +

(–6.67×10-¹¹ × 7.6×10²⁵ × 0.86×10⁹)/(2.3×10⁷)

E1 = 9.50×10²³J

(e) E = 1/2mv² + (– G×M×m/R)

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