# Is the gravity on Kepler 39b higher than on the Sun?

According to the formula for gravitational acceleration $$a = GM/r^2$$ where $$G=6.674 \times 10^{-11}$$, Jupiter with mass 1.89813 × 10^27 kg and radius 69,911,000 m gives a gravity around 25m/s^2. The Sun with mass 1.989 × 10^30 kg and radius 695,510,000m will have a gravity around 270m/s^2.

But using the data for Kepler 39B, mass 18 times that of Jupiter 3.416634 × 10^28, and radius about 5/4 of Jupiter's 87,220,000m, I get almost 300m/s^2, higher than the Sun's.

Is this right?

I did and redid it, and still concerned that I am doing something wrong.

• What makes you think it is wrong? – user24157 Apr 25 '19 at 18:25
• Well, I kinda found this the hard way. Coding a realisticalish space game, I assumed that any planet would always have less gravity than the sun(!), and set a hard limit of 200m/s2 on heavy G planets, which caused a serious bug-hunt, because once set radius and planet density parameters loose, but within realistic values, I started to get "ridiculous" G forces for gas giants and metallic planets... Turns out the simulation WAS working after all :D – Jorge Al Najjar Apr 26 '19 at 7:02

Eyeballing the calculation, you can see that the sun is 10 times the radius of Jupiter and 1000 times the mass, so it's surface gravity should be about $$1000/10^2=10$$ times greater than Jupiter's, which is what you find. But Kepler 39b is 18 times more massive than Jupiter and only marginally larger. That's a big uptick in density. So that it's surface gravity would be about $$18/(1.25)^2=11.52$$ times stronger than Jupiter's (also what you find). And $$11.52>10$$, so Kepler 39b has higher surface gravity.